Genetic improvement of functional traits in dairy cattle

GENETIC IMPROVEMENT OF FUNCTIONAL 

TRAITS IN DAIRY CATTLE BREEDING SCHEMES 

WITH GENOMIC SELECTION 

LINE HJORTØ BUCH 

PhD THESIS • DECEMBER 2010

Genetic improvement of functional 

traits in dairy cattle breedinG schemes 

with Genomic selection 

line hjortø buch 

PhD thesis • AArhus FAculty oF science AnD technology • 2011 

Department of Genetics and Biotechnology 

Faculty of Science and Technology 

Aarhus University 

P.O. Box 50 

DK-8830 Tjele 

Videncentret for Landbrug 

Agro Food Park 15 

DK-8200 Aarhus N 

Cover illustration 

„Aalborg Bos“ by Lise Færch (1918-1999) 

Tryk: www.digisource.dk 

ISBN: 978-87-91949-73-9

Preface 

This thesis is submitted to the Faculty of Agricultural Sciences, Aarhus University, in 

fulfillment of the requirements for a PhD degree. The work presented here is the result of an 

Industrial PhD project financed by the Ministry of Science, Technology and Innovation and 

Knowledge Centre for Agriculture, Cattle. 

Many people have helped and supported me through this project and because of that I have 

found the last three years to be interesting, challenging and only occasionally frustrating. 

Therefore, I would like to thank: 

Anders Christian Sørensen 

Morten Kargo Sørensen 

Peer Berg 

Jan Lassen 

Louise Dybdahl Pedersen 

Hanne Jørgensen 

My other colleagues here in Foulum 

My colleagues in Skejby 

Helen Hansen-Axelsson 

Jette Jakobsen 

Jan-Åke Eriksson 

Kjell Johansson 

Hans Stålhammar 

My family and especially my father 

and all the others who have contributed to this thesis. 

____________________ 

Line Hjortø Buch 

Foulum, December 2010

Table of Contents 

SUMMARY.................................................................................................................7 

SAMMENDRAG.......................................................................................................11 

GENERAL INTRODUCTION ...................................................................................15 

PAPER I...................................................................................................................27 

PAPER II..................................................................................................................39 

PAPER III.................................................................................................................53 

PAPER IV.................................................................................................................79 

GENERAL DISCUSSION.........................................................................................97 

CONCLUSIONS AND PERSPECTIVES................................................................111

Summary 

Use of genomic information in dairy cattle breeding has been assigned a high priority in 

recent years. So far, the main focus has been on the development of methods for predicting 

genetic merit. The next step is to study the effect of genomic selection on future breeding 

schemes. Hopefully, this thesis will contribute to the understanding of the potential 

advantages of genomic selection on genetic gain in the functional traits. The overall objective 

of this thesis is to investigate the hypothesis that precise phenotypic measurements that are 

closer to the traits in the proper breeding goal provide the opportunity for higher genetic gain 

in the functional traits, also in breeding schemes with genomic selection. 

The results of this project are presented in four papers of which two are accepted for 

publication, and two are submitted to scientific journals. The first two papers are based on real 

data from first-parity Swedish Red cows and the last two papers are based on simulated data. 

A general introduction to the investigations is given in the beginning of the thesis. 

Paper I presents estimates of the genetic parameters for protein yield, clinical mastitis, 

somatic cell score, number of inseminations and days from calving to first insemination. The 

data set contained information on approximately 624 000 cows and the statistical analyses 

were conducted on the basis of tri-variate linear animal models. The results show that the 

genetic correlation between clinical mastitis and days from calving to first insemination (0.38 

± 0.05) is higher than the genetic correlation between clinical mastitis and number of 

inseminations (0.05 ± 0.06). The reason may be that clinical mastitis and days from calving to 

first insemination usually are observed in the early part of the lactation when the cow is likely 

to be in negative energy balance, whereas number of inseminations generally is recorded 

when the cow starts to regain body resources. All genetic correlations between protein yield 

and the functional traits are moderate and unfavorable, ranging from 0.22 ± 0.02 to 0.47 ± 

0.03. The effect of including genetic and phenotypic correlations between the trait groups 

milk production, udder health and female fertility on the accuracy of the selection index was 

also investigated for a heifer, a cow and a proven bull. The difference between the accuracy 

obtained by multi-trait and single-trait evaluations is largest for the cow (0.012) and smallest 

for the bull (0.004) because the phenotype of the cow for one trait can assist in predicting the 

Mendelian sampling term for a correlated trait. 

7

Summary 

In Paper II, genetic parameters for four hoof diseases were estimated using tri-variate linear 

animal models. The hoof diseases were reported by hoof trimmers instead of veterinarians 

which has been the standard procedure until now. The data set contained information on 314 

300 cows; among these, approximately 64 000 cows had records on presence or absence of 

hoof diseases. The hoof diseases fall into two groups of which the first is related to hygiene 

(dermatitis and heel horn erosion) and the second is related to feeding (sole hemorrhage and 

sole ulcer). The results indicate that the hygiene-related hoof diseases and the feed-related 

hoof diseases are only partly influenced by the same genes because the genetic correlations 

among traits within the two groups are high (0.87 ± 0.05 and 0.73 ± 0.07), whereas the 

genetic correlations between traits in different groups are low (≤ 0.23 ± 0.11). In addition, 

genetic correlations between the four hoof diseases and protein yield, clinical mastitis, 

somatic cell score, number of inseminations and days from calving to first insemination were 

estimated. The two groups of hoof diseases show different patterns of genetic correlations to 

the other functional traits, but both groups are unfavorably correlated to protein yield. The 

effect of including hoof diseases in the selection index was also investigated. The results of 

this investigation showed that the inclusion of hoof diseases will not only reduce the genetic 

decline in resistance to hoof diseases but also be favorable for other functional traits and 

improve overall genetic merit. 

In Paper III, four breeding schemes with or without genomic selection and with or without 

intensive use of young bulls were compared with respect to annual genetic gain, annual 

genetic gain of the functional trait in the breeding goal and rate of inbreeding per generation 

using stochastic simulation. The simulated population was meant to mirror a dispersed 

breeding nucleus of 20 000 cows. The breeding goal and the selection index consist of a milk 

production trait and a functional trait. On the assumptions that the reliability of the direct 

genomic values (DGV) is the same for all animals and all traits and that the economic values 

of the two breeding goal traits are of the same size, we find that the two breeding schemes 

with genomic selection result in higher annual genetic gains, greater contributions of the 

functional trait to the annual genetic gains and lower rates of inbreeding than the two breeding 

schemes without genomic selection. Thus, the use of genomic information may lead to more 

sustainable breeding schemes. A short generation interval increases the effect of using 

genomic information on the annual genetic gain. Hence, a breeding scheme with genomic 

selection and with intensive use of young bulls seems to offer the greatest potential. The 

8

Summary 

inclusion of genomically enhanced breeding values for an indicator trait in the selection index 

increases the annual genetic gain in the two breeding schemes with genomic selection. 

Furthermore, it increases the contribution of the functional trait to the annual genetic gain and 

it decreases the rate of inbreeding. Thus, indicator traits may still be profitable to use even 

though genomically enhanced breeding values for the breeding goal traits are available. 

In Paper IV, different strategies of building a reference population for a new functional trait 

were compared using a deterministic prediction model. The trait was either recorded on all 

cows in the population (30 000 cows) or on a small scale (2 000 cows). We took a breeding 

scheme with genomic selection and with intensive use of young bulls as our starting point. 

For large-scale recording, four scenarios were compared. In these scenarios, the reference 

population contained sires; sires and test bulls; sires and cows; or sires, cows and test bulls. In 

addition to varying the composition of the reference population, the heritability of the trait 

was also varied (h 2 = 0.05 vs. 0.15). The results show that a reference population of sires, 

cows, and test bulls results in the highest accuracy of the DGV for a new functional trait 

regardless of its heritability. For small-scale recording, two scenarios were compared. In the 

first scenario, the reference population contained the 2 000 cows with phenotypic records and 

in the second scenario the reference population contained the sires of these cows. The results 

show that a reference population of cows results in the highest accuracy of the DGV whether 

the heritability is 0.05 or 0.15. The reason is that variation is lost when phenotypic data are 

summarized in the estimated breeding values for sires. Four main conclusions are: (1) the 

fewer phenotypic records, the larger effect of including cows in the reference population, (2) 

it is possible to achieve reasonably high accuracies of the DGV for new traits within a few 

years from commencement of recording, (3) for small-scale recording, the accuracies of the 

DGV will continue to increase for several years, whereas the increases in the accuracy of the 

DGV quickly decrease with large-scale recording, and (4) a higher heritability benefits a 

reference population of cows more than a reference population of bulls. 

A general discussion in which the results are related to existing knowledge and put into 

perspective is given immediately after the papers. In addition, a number of future challenges 

are described where further knowledge of breeding schemes with genomic selection is 

necessary. The overall hypothesis of this thesis is confirmed as genomic selection in 

combination with precise phenotypic measurements that are closer to the traits in the proper 

breeding goal will lead to higher genetic gain in the functional traits. 

9

Sammendrag 

Anvendelsen af genomisk information inden for malkekvægavl har haft høj prioritet i de 

seneste år. Det primære fokusområde har hidtil været udviklingen af metoder til at prædiktere 

direkte genomiske avlsværdital. Det næste trin er at undersøge effekten af genomisk selektion 

på fremtidige avlsplaner. Forhåbentlig vil denne afhandling bidrage til forståelsen af de 

mulige fordele ved genomisk selektion for den genetiske fremgang for de funktionelle 

egenskaber. Det overordnede formål med denne afhandling er at undersøge hypotesen om at 

præcise fænotypiske målinger, der er tættere på egenskaberne i det sande avlsmål, giver 

mulighed for større genetisk fremgang for de funktionelle egenskaber, også i avlsplaner med 

genomisk selektion. 

Resultaterne af dette projekt er præsenteret i fire artikler, hvoraf to er antaget til 

offentliggørelse, og to er sendt til videnskabelige tidsskrifter. De to første artikler er baseret 

på data fra køer i første laktation af racen Svensk rødt kvæg, og de to sidste artikler er baseret 

på simulerede data. En overordnet introduktion til undersøgelserne er givet i begyndelsen af 

afhandlingen. 

I artikel I præsenteres estimater for de genetiske parametre for proteinydelse, klinisk mastitis, 

celletal, antal insemineringer og dage fra kælvning til første inseminering. Datasættet 

indeholdt information om omkring 624.000 køer, og de statistiske analyser blev udført på 

grundlag af tri-variate lineære enkeltdyrsmodeller. Resultaterne viser, at den genetiske 

korrelation mellem klinisk mastitis og dage fra kælvning til første inseminering (0,38 ± 0,05) 

er højere end den genetiske korrelation mellem klinisk mastitis og antal insemineringer (0,05 

± 0,06). Årsagen er muligvis, at klinisk mastitis og dage fra kælvning til første inseminering 

som oftest observeres i den første del af laktationen, når koen sandsynligvis er i negativ 

energibalance, hvorimod antal insemineringer ofte registreres, når koen begynder at genvinde 

kropsreserver. Alle genetiske korrelationer mellem proteinydelse og de funktionelle 

egenskaber er moderate og ugunstige, rangerende fra 0,22 ± 0,02 til 0,47 ± 0,03. Effekten af 

at inkludere genetiske og fænotypiske korrelationer mellem egenskabsgrupperne 

mælkeproduktion, yversundhed og hunlig frugtbarhed på sikkerheden for selektionsindekset 

blev undersøgt for en kvie, en ko og en afkomsafprøvet tyr. Forskellen mellem den sikkerhed, 

der opnås ved fleregenskabsvurdering og enkeltegenskabsvurdering, er størst for koen (0,012) 

11

Sammendrag 

og mindst for tyren (0,004), fordi koens fænotype for én egenskab kan bidrage til at 

prædiktere den mendelske udspaltning for en korreleret egenskab. 

I artikel II blev genetiske parametre for fire klovsygdomme estimeret ved brug af tri-variate 

lineære enkeltdyrsmodeller. Klovsygdommene blev registreret af klovbeskærere i stedet for 

dyrlæger, hvilket har været almen praksis hidtil. Datasættet indeholdt information om 314.300 

køer, og blandt disse havde omkring 64.000 køer registreringer for tilstedeværelse eller fravær 

af klovsygdomme. Klovsygdommene falder i to grupper, hvoraf den første er relateret til 

hygiejne (dermatitis og balleforrådnelse), og den anden er relateret til fodring (såleblødning 

og sålesår). Resultaterne indikerer, at de hygiejnerelaterede klovsygdomme og de 

fodringsrelaterede klovsygdomme kun delvist påvirkes af de samme gener, fordi de genetiske 

korrelationer mellem egenskaberne inden for de to grupper er høje (0,87 ± 0,05 og 0,73 ± 

0,07), hvorimod de genetiske korrelationer mellem egenskaberne i de forskellige grupper er 

lave (≤ 0,23 ± 0,11). Derudover blev de genetiske korrelationer mellem de fire 

klovsygdomme og proteinydelse, klinisk mastitis, celletal, antal insemineringer og dage fra 

kælvning til første inseminering estimeret. De to grupper af klovsygdomme viser forskellige 

mønstre af genetiske korrelationer til de andre funktionelle egenskaber, men begge grupper er 

ugunstigt korreleret til proteinydelse. Effekten af at inkludere klovsygdomme i 

selektionsindekset blev også undersøgt. Resultaterne af denne undersøgelse viste, at 

inkluderingen af klovsygdomme ikke kun reducerer den genetiske tilbagegang for 

modstandsdygtighed overfor klovsygdomme, men også er gunstig for de andre funktionelle 

egenskaber og forbedrer det overordnede genetiske niveau. 

I artikel III blev fire avlsplaner med og uden genomisk selektion samt med og uden intensiv 

anvendelse af unge tyre sammenlignet med hensyn til årlig genetisk fremgang, årlig genetisk 

fremgang for den funktionelle egenskab i avlsmålet og indavlsstigning pr. generation ved brug 

af stokastisk simulering. Den simulerede population skulle afspejle en spredt avlskerne på 

20.000 køer. Avlsmålet og selektionsindekset består af en mælkeproduktionsegenskab og en 

funktionel egenskab. Under antagelse af at sikkerheden for de direkte genomiske avlsværdital 

er den samme for alle dyr og alle egenskaber, og at de økonomiske værdier for de to 

egenskaber i avlsmålet er af samme størrelse, finder vi, at de to avlsplaner med genomisk 

selektion resulterer i større årlige genetiske fremgange, større bidrag fra den funktionelle 

egenskab til de årlige genetiske fremgange og lavere indavlsstigninger end de to avlsplaner 

uden genomisk selektion. Som følge deraf vil anvendelsen af genomisk selektion formentlig 

12

Sammendrag 

føre til mere bæredygtige avlsplaner. Et kort generationsinterval øger effekten af at bruge 

genomisk information på den årlige genetiske fremgang. En avlsplan med genomisk selektion 

og med intensiv brug af unge tyre ser således ud til at have det største potentiale. 

Inkluderingen af genomiske avlsværdital for en indikatoregenskab i selektionsindekset øger 

den årlige genetiske fremgang i de to avlsplaner med genomisk selektion. Den øger desuden 

bidraget fra den funktionelle egenskab til den årlige genetiske fremgang, og den mindsker 

indavlsstigningen. Som følge deraf er indikatoregenskaber givetvis fortsat fordelagtige at 

bruge, selvom genomiske avlsværdital for egenskaberne i avlsmålet er tilgængelige. 

I artikel IV blev forskellige strategier til at opbygge en referencepopulation for en ny 

funktionel egenskab sammenlignet ved brug af en deterministisk prædiktionsmodel. 

Egenskaben blev enten registreret på alle køer i populationen (30.000 køer) eller i mindre 

omfang (2000 køer). Vi tog udgangspunkt i en avlsplan med genomisk selektion og intensiv 

brug af unge tyre. Fire scenarier blev sammenlignet ved fænotypisk registrering i stort 

omfang. I disse scenarier indeholdt referencepopulationen tyre; tyre og testtyre; tyre og køer 

eller tyre, køer og testtyre. Udover at variere referencepopulationens sammensætning blev 

egenskabens arvbarhed også varieret (h 2 = 0,05 vs. 0,15). Resultaterne viser, at en 

referencepopulation bestående af tyre, køer og testyre resulterer i den højeste sikkerhed for de 

direkte genomiske avlsværdital for en ny funktionel egenskab uanset arvbarhedens størrelse. 

To scenarier blev sammenlignet ved fænotypisk registrering i mindre omfang. I det første 

scenarium indeholdt referencepopulationen de 2000 køer med fænotypiske registreringer, og i 

det andet scenarium indeholdt referencepopulationen fædrene til disse køer. Resultaterne 

viser, at en referencepopulation bestående af køer resulterer i den højeste sikkerhed for de 

direkte genomiske avlsværdital, uanset om arvbarheden er 0,05 eller 0,15. Årsagen er, at 

variation går tabt, når fænotypiske data opsummeres i tyrenes estimerede avlsværdital. Fire 

hovedkonklusioner er: (1) jo færre fænotypiske registreringer, desto større effekt af at 

inkludere køer i referencepopulationen, (2) det er muligt at opnå forholdsvis høje sikkerheder 

for de direkte genomiske avlsværdital for nye egenskaber inden for få år efter at registreringen 

påbegyndes, (3) sikkerhederne for de direkte genomiske avlsværdital vil fortsætte med at stige 

i flere år ved registrering i mindre omfang, hvorimod stigningerne i sikkerhederne hurtigt 

aftager ved registrering i stort omfang, og (4) en højere arvbarhed gavner en 

referencepopulation bestående af køer mere end en referencepopulation bestående af tyre. 

13

Sammendrag 

En overordnet diskussion gives umiddelbart efter artiklerne, hvori resultaterne relateres til 

eksisterende viden og sættes i perspektiv. Derudover beskrives en række fremtidige 

udfordringer, hvor yderligere kendskab til avlsplaner med genomisk selektion er nødvendig. 

Den overordnede hypotese for denne afhandling kan bekræftes, idet genomisk selektion i 

kombination med præcise registreringer, der er tættere på egenskaberne i det sande avlsmål, 

vil føre til større genetisk fremgang for de funktionelle egenskaber. 

14

General introduction 

Animal breeding has been undeniably successful in generating genetic progress for traits 

related to output. The future of animal breeding depends on how the discipline adapts to the 

demand for better and especially more healthy products from healthy animals. Moving 

forward we need to concern ourselves with understanding the biology of the traits we want to 

improve, the defined breeding goal, the quality of the phenotypic data, procedures to utilize 

the data in the best possible way, and strategies for using the new technological tools, i.e. first 

and foremost genomics. 

Breeding goal 

Defining the breeding goal is the initial step in the development of a breeding scheme 

(Goddard, 1998). The breeding goal specifies the traits to be improved and the relative 

importance of each of these traits (Falconer and Mackay, 1996). Today, most dairy cattle 

breeding goals consist of functional traits as well as milk production traits (Miglior et al., 

2005). In this context, functional traits is a collective term for all traits that increase efficiency 

by lowering the costs of production, e.g. health, female fertility, calving ease, feed efficiency 

and milkability (Groen et al., 1997). It is important to distinguish between the traits in the 

breeding goal and in the selection index as they may differ from each other (Goddard, 1998). 

Hence, traits without economic importance, which are measurable and genetically correlated 

to the traits in the breeding goal, could be included in the selection index (Groen et al., 1997). 

However, it requires that the genetic variances of the breeding goal traits and the genetic 

correlations between the breeding goal traits and the selection index traits are estimated 

precisely for selection decisions to be optimal. If a breeding goal trait is recorded on a small 

scale or is not recorded due to high costs or other constraints, the genetic parameters cannot 

be estimated precisely. Consequently, one has to settle for the precision that it is possible to 

achieve or to rely on estimates obtained from other similar populations of dairy cattle. 

However, in many cases these two options are not used in practice. Consequently, most 

breeding goals contain traits that are measurable rather than traits that directly contribute to 

the proper breeding goal (Oldenbroek, 2007). Therefore, I find it necessary also to distinguish 

between the proper breeding goal that contains all economically important traits and the 

applied breeding goal that contains measurable traits. 

15

Genetic trends in the functional traits 


The applied breeding goals are important in setting the direction for the genetic improvement. 

However, this direction also depends on a number of other factors. There are at least three 

reasons why a functional trait is not necessarily improved even though it is included in the 

applied breeding goal. Firstly, negative genetic trends in the functional traits could be due to 

large economic values on the milk production traits and negative genetic correlations between 

the milk production traits and the functional traits even if the economic values are determined 

correctly. Secondly, it is difficult to obtain genetic gain in functional traits because several 

important functional traits have a low heritability and the accuracy of selection depends on the 

heritability. However, it is possible to obtain a relatively high accuracy of selection for a 

functional trait with a low heritability if information on progeny is available. Thirdly, negative 

genetic trends in the functional traits may occur if the sires of the selection candidates are 

bulls without estimated breeding values (EBV) for the functional traits, e.g. foreign bulls. 

This has been proven in practice in the eighties and the nineties as the majority of the young 

Black and White bulls that were progeny tested in the Nordic countries at that time originated 

from imported semen of foreign bull sires or embryos from foreign cows that did not have 

EBV for the functional traits (Christensen, 1998). Even if the foreign bull sires have EBV for 

the functional traits, negative genetic trends in the functional traits may be difficult to avoid 

because the correlation between the same milk production trait in two different countries 

generally is higher than the correlation between the same functional trait in two different 

countries (Interbull, 2010). Consequently, the composition of the genetic gain changes 

towards more gain in the milk production traits and less gain in the functional traits when 

foreign bull sires are selected (Buch et al., 2009). For these reasons, the traits in the applied 

breeding goal and in the selection index should be chosen carefully, and the traits in the 

selection index should be recorded with great accuracy. 

Recording of functional traits 

The relative emphasis on the functional traits has increased in the applied breeding goals 

(Miglior et al., 2005). However, the EBV for the functional traits may contribute less to the 

overall ranking of the animals than their economic value indicates because the EBV for the 

functional traits are regressed more towards the mean than the EBV for the milk production 

traits (Ducrocq, 2010). This is caused by the fact that the accuracy of selection and thereby 

the variability of the EBV is positively affected by the heritability of the trait. The use of 

16


progeny testing weakens this effect to some degree as the ratio between accuracies of bull 

proofs for different traits are closer to unity than the ratio of heritabilities. However, not all 

selection decisions are based on progeny testing results. Two examples of functional traits 

with low heritabilities are female fertility and resistance to mastitis. 

Female fertility is included in the applied breeding goal in most countries but it has proven 

difficult to improve. One reason may be that female fertility is a complex trait that can be 

divided into more underlying traits, e.g. the ability to recycle after calving and the ability to 

become pregnant (Jorjani, 2005). The interval from calving to first insemination is an indirect 

measure of the interval from calving to first ovulation. However, the measure is influenced by 

management to some degree, which partly explains the low heritability of the trait (Petersson 

et al., 2007). Progesterone-based measures obtained from milk samples are less affected by 

management, have moderate heritabilities and could be used to increase the accuracy of 

selection for an earlier start of cyclical ovarian activity after calving (Petersson et al., 2007). 

This is an example of a recording that is more useful than the traditional recording because it 

is closer to the biology of the trait of interest. In general, we should aim to record the traits 

that make favorable genetic trends possible for all traits in the proper breeding goal whenever 

cost-effective (Woolliams et al., 2005). 

Resistance to mastitis is an example of a trait in the proper breeding goal, which is difficult 

and costly to measure on a large scale. Consequently, the traits in the applied breeding goal 

are approximations to the traits in the proper breeding goal as mentioned above. Today, 

correlated traits such as somatic cell score are included in the total merit index in several 

countries (Miglior et al., 2005) although they only partly explain resistance to mastitis. In 

order to approach the trait in the proper breeding goal, veterinary treatments of mastitis is 

included in the Nordic total merit index. However, this measure still only indicates the cow’s 

resistance to mastitis. The problem is especially that untreated cows are considered healthy, 

which is not always the case. The technological development enables the recording of 

functional traits resembling the traits in the proper breeding goal to a greater extent than 

previously. Consequently, a third option could be to select on pathogen-specific mastitis 

obtained by culturing bacteria from milk samples or by a real-time polymerase chain reaction 

based method (Sørensen et al., 2010). By doing so it is possible to take different causes and 

consequences of the pathogens into account (Sørensen et al., 2010). Thus, by recording traits 

17


that are closer to the traits in the proper breeding goal it is possible to clarify the applied 

breeding goal to a greater extent than before. 

The quality of the data 

The veterinarians report veterinary treatments of the individual cow to a central database in 

the Nordic countries. However, traits that are recorded on the individual cow may suffer from 

missing observations because the farmer treats the diseased cow himself and does not report 

it. Another example could be that the farmer decides to cull a diseased cow rather than 

initiating a course of treatment. In other words, the recorded occurrence of a disease may 

differ from the true occurrence because some animals are misclassified, usually as being 

healthy even though they are affected. It may well be that the recorded occurrence of a disease 

approximates the true occurrence if the trait is recorded continuously on all cows to whom it 

is relevant, e.g. every time a cow is milked or every time a veterinarian or a hoof trimmer 

visits the herd. Misclassification of truly affected animals results in inaccuracies in the data 

and possibly in a lower estimate of the heritability of the trait. This is especially true if the 

recorded occurrence of the disease is low and the data are analyzed by means of linear models 

(Mäntysaari et al., 1991). The genetic evaluation of disease traits is based on linear models in 

the Nordic countries (NAV, 2010) so the problem is relevant in practice here. For these 

reasons, we expect that it is possible to improve the animals’ disease resistance at a higher 

rate if the occurrence of the disease is measured more precisely (Paper II). 

As the dairy herds become larger and larger one concern is that the quality of the recordings 

will decrease. The concern may be unfounded because more and more traits are recorded 

automatically, e.g. it is possible to detect if a cow is in heat or not by comparing her present 

level of activity with her normal level of activity. Thus, several management tools have been 

developed in order to cope with the decreasing number of working hours per cow and if it is 

possible to transmit the automatic recordings to a central database then they may turn out to 

be new phenotypic records that are less affected by management. However, due to the vast 

amount of data it may be necessary to develop functions to condense the data before they are 

used in the genetic evaluation (Woolliams et al., 2005). The utility of these new phenotypic 

records will depend on the extent to which it is possible to maintain the genetic variation after 

the condensation of the data (Woolliams et al., 2005). 

18


Some functional traits, e.g. milking speed, are judged by the Danish dairy farmers. Naturally, 

these traits are affected by management. However, both milking speed and milk flow can be 

recorded in automatic milking systems today. Analyses of both types of data have shown that 

the farmers record a combination of milking speed and milk flow probably because they 

subconsciously partly correct for the milk yield when they judge the milking speed (Kevin 

Byskov, Knowledge Centre for Agriculture, Århus N, Denmark, personal communication). 

The analyses also showed that the heritability estimates for milking speed and milk flow 

measured in automatic milking systems were considerably higher than for milking speed 

judged by dairy farmers. Thus, some traits in the genetic evaluation are likely to become more 

objective than previously and it may affect response to selection favorably. 

Genetic evaluation 

Farm animals like dairy cattle are often selected on the basis of an index containing more 

traits that are genetically and phenotypically correlated. As a consequence of this, a multi-trait 

evaluation is the best methodology to genetically evaluate them (Mrode, 2005). Two essential 

benefits of using multi-trait evaluation are a higher accuracy of the evaluation and the ability 

to take selection bias into account. It is possible to improve the accuracy of evaluation for a 

trait with a low heritability by including information on a correlated trait in the genetic 

evaluation (Thompson and Meyer, 1986). However, if the two traits have equal heritabilities 

then the largest effect of multi-trait evaluation is obtained if the genetic and residual 

correlations between the traits are large and have opposite signs (Thompson and Meyer, 

1986). In addition, multi-trait evaluation provides insight into the effect of selection for higher 

milk yield on the functional traits that are unfavorably correlated to the milk production traits 

(Woolliams et al., 2005). Thus, we expect that the milk production traits support the 

functional traits and that the functional traits support each other in multi-trait evaluations 

(Paper I). 

Reliable estimates of genetic and phenotypic correlations among traits are needed in order to 

obtain accurate EBV from multi-trait evaluations (Mrode, 2005). Estimates of the genetic 

parameters are also required in order to predict how the genetic improvement of one trait will 

cause simultaneous changes in other traits (Falconer and Mackay, 1996) and ideally this 

should be done before a breeding goal is brought into use (Woolliams et al., 2005). A good 

understanding of the often unfavorable genetic correlations between milk production traits 

19


and functional traits is especially needed so that harmful correlated responses to selection do 

not come as a surprise. If the predicted annual genetic gain in some traits is not acceptable, 

one remedy may be to add or replace some traits in the genetic evaluation with other more 

precise traits. Finally, knowledge about the genetic correlations among traits that are ethically 

and/or economically important may contribute to the understanding of the biology of the traits 

(Paper I and Paper II). 

Many offspring are needed to achieve accurate breeding values if the heritability of the trait is 

low. This is a problem for the genetic evaluation of young animals. In a situation like that 

indirect selection may be beneficial to use. Somatic cell score, udder depth and fore udder 

attachment are used as additional sources of information for veterinary treatment of mastitis in 

the Nordic selection index because they have moderate heritabilities and they are moderately 

correlated to veterinary treatment of mastitis (NAV, 2010). The use of genomic information in 

the genetic evaluation provides the opportunities for prediction of accurate breeding values 

for young animals (Hayes et al., 2009). Therefore, we expect that the inclusion of an indicator 

trait in the selection index will only improve the annual genetic gain marginally if genomic 

information about the breeding goal trait is known (Paper III). 

Genomic selection 

Genomic selection is a new tool for selection of animals based on marker information in 

addition to whatever traditional information that is available (Meuwissen et al., 2001). The 

implementation of genomic selection takes place in two steps. Firstly, the effects of dense 

genetic markers are estimated in a reference population that consists of animals with both 

marker information and phenotypic information. The phenotypic information can be recorded 

on the animals in the reference population or their relatives. That is, daughter yield deviations, 

deregressed proofs or EBV can be used as phenotypic information for proven bulls. Secondly, 

the effects of the dense genetic markers are used to predict direct genomic values (DGV) for 

animals without phenotypic records. In genomic selection, the accuracy of the DGV is 

affected by the reliability of the EBV for the progeny tested bulls that are included in the 

reference population, among other things (Hayes et al., 2009). The reliability of the EBV for 

well-proven progeny tested bulls differ less between the milk production traits and the 

functional traits than the heritabilities of these two trait groups. Thus, we expect that breeding 

20


schemes with genomic selection will result in larger genetic gains in the functional traits 

compared to breeding schemes without genomic selection (Paper III). 

Correlated response in breeding schemes with genomic selection 

The expected effects of selection should also be predicted for potentially important traits that 

are not included in the applied breeding goal (Woolliams et al., 2005). In this context, 

potentially important traits is a collective term for all traits that have an acceptable genetic 

level for the time being but the genetic level for these traits could be unacceptable over time, 

e.g. because of non-linearity. The necessity of doing this may be even more important in 

breeding schemes with genomic selection. According to Mark and Sandøe (2010) the genetic 

level for a potentially important functional trait may change unfavorably when the selection 

response for the selection index traits increases as a consequence of genomic selection. This is 

due to the fact that the correlated response for a potentially important trait is proportional to 

the genetic standard deviation of the potentially important trait, the genetic correlation 

between the potentially important trait and the selection index, the accuracy of the selection 

index and the selection intensity (Falconer and Mackay, 1996). Hence, it is important to 

monitor potentially important traits not only to predict the effects of genomic selection but 

also to learn more about the effects of genomic selection on the biology of dairy cattle. 

New traits 

The technological development enables the recording of new functional traits, e.g. feed 

efficiency, that have not been included in the applied breeding goal before even though they 

are of economical importance. Examples of indicator traits for feed efficiency could be feed 

intake and the weight of the cow. So far, these traits have only been recorded in experimental 

herds and consequently the number of phenotypes has been too small to predict accurate 

breeding values. A phenotypic record influences the breeding value of more animals if it is 

included in the genetic evaluation in combination with genomic information than if it is 

included in the genetic evaluation without genomic information because it affects all animals 

that carry the same marker allele. For this reason, it is possible to achieve a higher accuracy of 

selection for a trait by utilizing genomic information. Thus, we expect that genomic selection 

enables genetic improvement of new traits within a reasonably short period of time (Paper 

IV). 

21


Moving towards the recording of traits in the proper breeding goal it is likely that some of the 

new functional traits are recorded on a part of the population rather than the entire population. 

If this is the case, it is even more important to maximize the amount of information extracted 

from the phenotypic records. As stated above, a phenotypic record in a breeding scheme with 

genomic selection is worth more than a phenotypic record in a conventional breeding scheme 

without genomic selection. In addition, a relationship matrix based on marker information is 

more accurate than a matrix based on pedigree information (Sonesson et al., 2010). As a 

result, DGV generally have higher accuracy than EBV, unless the EBV are based on 

information on offspring or own performance. Today, it is common practice to include 

progeny tested bulls in the reference population (Hayes et al., 2009). However, variation is 

lost when bulls are genotyped instead of cows because the phenotypic records are summarized 

in the EBV of the bulls. Thus, we expect a higher accuracy of the DGV for a functional trait 

that is recorded on a small scale if the reference population contains cows instead of or in 

addition to proven bulls (Paper IV). 

Inbreeding 

Functional traits are often more affected by inbreeding depression than non-functional traits 

(Falconer and Mackay, 1996). Therefore, dairy cattle breeders and other stakeholders should 

make a serious effort to control the rate of inbreeding in order for progress in the functional 

traits to be expressed. Until now, higher genetic gains generally led to higher rates of 

inbreeding even though attempts to control inbreeding were made, e.g. by restricting the 

number of selected sons per sire. However, it is likely that the rate of inbreeding per 

generation can be lower if the young animals are selected on the basis of genomically 

enhanced breeding values rather than parent average breeding values and if the same intensity 

of selection is maintained. One reason is that genomically enhanced breeding values to a 

greater extent than parent average breeding values give information about the animal’s 

Mendelian sampling term. This enables a better differentiation within families, which reduces 

the rate of inbreeding per generation (Daetwyler et al., 2007). Moreover, the rate of 

inbreeding per generation may be reduced because DGV have a higher accuracy whether the 

heritability is high or low. This causes a strong Bulmer effect that reduces the between family 

genetic variance (Daetwyler et al., 2007). Thus, we expect lower rates of inbreeding in 

22


breeding schemes with genomic selection than in breeding schemes without genomic 

selection (Paper III). 

Overall hypothesis 

On the basis of the issues described above, the overall objective of this thesis is to investigate 

the hypothesis that precise phenotypic measurements that are closer to the traits in the proper 

breeding goal provide the opportunity for higher genetic gain in the functional traits, also in 

breeding schemes with genomic selection. 

More specifically we expect that: 

It is possible to improve the animals’ disease resistance at a higher rate if the 

occurrence of the disease is measured more precisely (Paper II) 

The milk production traits support the functional traits and the functional traits support 

each other in multi-trait evaluations (Paper I) 

Knowledge about the genetic correlations among traits that are ethically and/or 

economically important may contribute to the understanding of the biology of the 

traits (Paper I and Paper II) 

The inclusion of an indicator trait in the selection index will only improve the annual 

genetic gain marginally if genomic information about the breeding goal trait is known 

(Paper III) 

Breeding schemes with genomic selection will result in larger genetic gains in the 

functional traits compared to breeding schemes without genomic selection (Paper III) 

Genomic selection enables genetic improvement of new traits within a reasonably 

short period of time (Paper IV) 

The accuracy of the DGV for a functional trait that is recorded on a small scale is 

higher if the reference population contains cows instead of or in addition to proven 

bulls (Paper IV) 

The rate of inbreeding per generation is lower in breeding schemes with genomic 

selection than in breeding schemes without genomic selection (Paper III) 

The following four papers deal with these issues. 

23

References 


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Factors affecting the exchange of genetic material between Nordic and US Holstein 

populations. J. Dairy Sci. 92:4023-4034. 

Christensen, L. G. 1998. Possibilities for genetic improvement of disease resistance, 

functional traits and animal welfare. Acta Agric. Scand. A Animal Sci. Suppl. 29:77-89. 

Daetwyler, H. D., B. Villanueva, P. Bijma, and J. A. Woolliams. 2007. Inbreeding in genomewide 

selection. J. Anim. Breed. Genet. 124 369:376. 

Ducrocq, V. 2010. Sustainable dairy cattle breeding: illusion or reality? No 66 in Proc. 9 th 

World Congr. Genet. Appl. Livest. Prod., Leipzig, Germany, August 1-6, 2010. 

Falconer, D. S., and T. F. C. Mackay. 1996. Introduction to quantitative genetics. Fourth 

edition. Pearson Education Limited, Essex, UK. 

Goddard, M. E. 1998. Consensus and debate in the definition of breeding objectives. J. Dairy 

Sci. 81:6-18. 

Groen, A. F., T. Steine, J.-J. Colleau, J. Pedersen, J. Pribyl, and N. Reinsch. 1997. Economic 

values in dairy cattle breeding, with special reference to functional traits. Report of an EAAPworking 

group. Livest. Prod. Sci. 49:1-21. 

Hayes, B. J., P. J. Bowman, A. J. Chamberlain, and M. E. Goddard. 2009. Invited review: 

Genomic selection in dairy cattle: Progress and challenges. J. Dairy Sci. 92:433-443. 

Interbull. 2010. Evaluation summaries for production traits and functional traits. 

http://www.interbull.org/index.php?option=com_wrapper&view=wrapper&Itemid=61 

Accessed December 6, 2010. 

Jorjani, H. 2005. Preliminary report of Interbull pilot study for female fertiliy traits in 

Holstein populations. Proceedings of the Interbull Open Meeting, Uppsala, Sweden, June 3-4, 

2005. Interbull Bull. 33:34-44. 

Mark, T., and P. Sandøe. 2010. Genomic dairy cattle breeding: risks and opportunities for 

cow welfare. Anim. Welf. 19:113-121. 

Mäntysaari, E. A., R. L. Quaas, and Y. T. Gröhn. 1991. Simulation study on covariance 

component estimation for two binary traits in an underlying continuous scale. J. Dairy Sci. 

74:580-591. 

Meuwissen, T. H. E., B. J. Hayes, and M. E. Goddard. 2001. Prediction of total genetic value 

using genome-wide dense marker maps. Genetics 157:1819-1829. 

Miglior, F., B. L. Muir, and B. J. Van Doormaal. 2005. Selection indices in Holstein cattle of 

various countries. J. Dairy Sci. 88:1255-1263. 

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Mrode, R. A. 2005. Linear models for the prediction of animal breeding values. Second 

edition. CABI Publishing, Wallingford, UK. 

NAV. 2010. NAV routine evaluation – general description. 

http://www.nordicebv.info/NR/rdonlyres/92DAA130-5330-401D-A898- 

56FA003B0300/0/CDEBV2010.pdf Accessed November 11, 2010. 

Oldenbroek, K. 2007. Glossary. Pages 215-228 in Utilisation and conservation of farm animal 

genetic resources. Wageningen Academic Publishers, Wageningen, The Netherlands. 

Petersson, K.-J., B. Berglund, E. Strandberg, H. Gustavsson, A. P. F. Flint, J. A. Woolliams, 

and M. D. Royal. 2007. Genetic analysis of postpartum measures of luteal activity in dairy 

cows. J. Dairy Sci. 90:427-434. 

Sonesson, A. K., J. A. Woolliams, and T. H. E. Meuwissen. 2010. Maximising genetic gain 

whilst controlling rates of genomic inbreeding using genomic optimum contribution selection. 

No 892 in Proc. 9 th World Congr. Genet. Appl. Livest. Prod., Leipzig, Germany, August 1-6, 

2010. 

Sørensen, L. P., T. Mark, M. K. Sørensen, and S. Østergaard. 2010. Economic values and 

expected effect of selection index for pathogen-specific mastitis under Danish conditions. J. 

Dairy Sci. 93:358-369. 

Thompson, R., and K. Meyer. 1986. A review of theoretical aspects in the estimation of 

breeding values for multi-trait selection. Livest. Prod. Sci. 15:299-313. 

Woolliams, J., P. Berg, A. Mäki-Tanila, T. Meuwissen, and E. Fimland. 2005. Sustainable 

management of animal genetic resources. Prinfo Unique, Larvik, Norway. 

25

Paper I 

Udder health and female fertility traits are favourably correlated and support 

each other in multi-trait evaluations 

Line Hjortø Buch, Morten Kargo Sørensen, Jan Lassen, Peer Berg, Jette Halkjær Jakobsen, 

Kjell Johansson & Anders Christian Sørensen 

Journal of Animal Breeding and Genetics (2010), doi:10.1111/j.1439-0388.2010.00904.x

ORIGINAL ARTICLE 

Udder health and female fertility traits are favourably 

correlated and support each other in multi-trait evaluations 

L.H. Buch 1,2 , M.K. Sørensen 1,2 , J. Lassen 2 , P. Berg 2 , J.H. Jakobsen 3 , K. Johansson 4 & A.C. Sørensen 2 

1 Danish Agricultural Advisory Service, Aarhus N, Denmark 

2 Department of Genetics and Biotechnology, Aarhus University, Tjele, Denmark 

3 Department of Animal Breeding and Genetics, Swedish University of Agricultural Sciences, Uppsala, Sweden 

4 Swedish Dairy Association, Stockholm, Sweden 

Keywords 

Dairy cattle; functional trait; genetic 

evaluation; genetic parameter; mastitis. 

Correspondence 

L.H. Buch, Department of Genetics and 

Biotechnology, Aarhus University, P.O. Box 

50, DK-8830 Tjele, Denmark. 

Tel: +45 89 99 12 24; Fax: +45 89 99 19 00; 

E-mail: Line.HjortoBuch@agrsci.dk 

Received: 11 December 2009; 

accepted: 14 September 2010 

Introduction 

Summary 

In recent decades, dairy cattle breeding goals have 

become more complex, as the relative emphasis on 

the milk production traits has decreased compared 

to the functional traits such as disease resistance and 

reproduction traits. Thorough knowledge of all traits 

in the breeding goal is of great significance as accurate 

estimates of the genetic parameters are necessary 

for the prediction of breeding values (BV) and 

J. Anim. Breed. Genet. ISSN 0931-2668 

Genetic parameters were estimated for protein yield (PY), clinical mastitis 

(CM), somatic cell score, number of inseminations (NI) and days 

from calving to first insemination (CFI) in first-parity Swedish Red cows 

by series of tri-variate linear animal models. The heritability of PY was 

moderate (0.34 0.004), and the heritabilities of the functional traits 

were all low (0.014 0.001–0.14 0.004). The genetic correlation 

between CM and CFI (0.38 0.05) was stronger than the correlation 

between CM and NI (0.05 0.06), perhaps because CM and CFI usually 

are observed in early lactation when the cow is likely to be in negative 

energy balance, whereas NI generally is recorded when the cow is not 

in negative energy balance any more. The genetic correlation between 

NI and CFI was very close to zero ()0.002 0.05), indicating that these 

two fertility traits have different genetic backgrounds. All genetic correlations 

between PY and the functional traits were moderate and unfavourable, 

ranging from 0.22 0.02 to 0.47 0.03. In addition, the 

effect of including genetic and phenotypic correlations between the trait 

groups milk production, udder health and female fertility on the accuracy 

of the selection index was quantified for a heifer, a cow and a proven 

bull. The difference between the accuracy obtained by multi-trait 

and single-trait evaluations was largest for the cow (0.012) and small for 

the heifer and the bull (0.006 and 0.004) because the phenotype of the 

cow for one trait could assist in predicting the Mendelian sampling term 

for a correlated trait. 

may enhance understanding of the biological background 

and the consequences of genetic changes 

caused by artificial selection. Many studies have 

focused on the genetic relationships between milk 

production traits and functional traits, and most of 

them have found unfavourable genetic correlations 

(for review see Rauw et al. 1998). The unfavourable 

relationships are hypothesized to occur from the 

allocation of limited resources to different body 

functions in the animal. Fewer studies have focused 

ª 2010 Blackwell Verlag GmbH • J. Anim. Breed. Genet. (2010) 1–9 doi:10.1111/j.1439-0388.2010.00904.x

Multi-trait evaluation of udder health and fertility L. H. Buch et al. 

on the genetic relationships among the functional 

traits even though some of them are very cost-intensive. 

The reason may be that large-scale registration 

of functional traits is relatively new in many countries. 

The Nordic countries have recorded and 

included functional traits in the genetic evaluation 

of dairy cattle for many years. This provides the 

opportunity to select for these traits. In the breeding 

scheme for SRB (Swedish Red) dairy cattle, the 

opportunity have been utilized and as a result, the 

genetic trends in mastitis resistance and female fertility 

have been relatively flat for the SRB cows 

(Pedersen et al. 2008). That has not been the case 

for all dairy cattle populations (e.g. Liu et al. 2008; 

AIPL 2010), and therefore the genetic parameters for 

the SRB cows may differ from other dairy cattle 

populations. 

The technological development has enabled the 

recording of a large number of breeding goal traits 

and correlated characters in recent years. However, 

it is still expensive to collect the large amount of 

data that is used in national BV evaluations and to 

maintain databases, so the records should be utilized 

to their full potential. When a multi-trait evaluation 

is performed, two or more traits are analysed simultaneously, 

and the genetic and phenotypic correlations 

between the traits are taken into account. 

Thus, a multi-trait evaluation ensures a more accurate 

evaluation of animals than single-trait evaluations 

(Mrode 2005). Among the potential advantages 

of multi-trait evaluations over single-trait evaluations 

are an increased accuracy of the evaluations 

and a reduced selection bias (Thompson & Meyer 

1986). However, the advantages of applying a multitrait 

evaluation depend on the parameters of the 

traits and the quality of these estimates (Schaeffer 

1984; Thompson & Meyer 1986). Especially, genetic 

correlations are often estimated with large uncertainty. 

To our knowledge, little is known about the 

genetic correlations between udder health and 

female fertility traits in the Nordic Red dairy breeds. 

The major objective of this study was, therefore, to 

estimate genetic parameters for protein yield (PY), 

clinical mastitis (CM), somatic cell score (SCS), number 

of inseminations (NI) and days from calving to 

first insemination (CFI). A second objective was to 

test the hypothesis that udder health and female fertility 

traits support each other in multi-trait evaluations 

by quantifying the effect of including genetic 

and phenotypic correlations between the three trait 

groups milk production, udder health and female 

fertility on the accuracy of the selection index. 

Materials and methods 

Data 

Records on PY, CM, SCS, NI and CFI in first-parity 

SRB cows were extracted from the Swedish Cattle 

Database. For all cows, date of first calving was 

between January 1996 and December 2006. Thus, 

all cows had the opportunity to achieve a complete 

lactation. 

PY was recorded as 305 days PY, and both completed 

and projected lactation yields were included. 

A record was included in the analyses if the cow had 

at least 45 days in milk, the projected lactation yield 

was between 25 and 800 kg and age at first calving 

was in the interval from 20 to 38 months. 

Records on CM originated from the Swedish 

national health recording system, where clinical 

treatments are reported by veterinarians or as a reason 

for culling. The trait was defined as a binary 

trait, where 0 indicates that the cow was not treated 

or culled for CM and 1 indicates that the cow was 

either treated or culled for mastitis. Mastitis incidences 

were registered from 10 days before calving 

to 150 days after calving. 

Somatic cell counts were registered in 10 000 cells 

per ml and transformed to SCS using the common 

logarithm with base 10. The samples were collected 

in the interval from 5 days after calving to 150 days 

after calving, and subsequently, the geometric mean 

was calculated. 

The interval from calving to first insemination and 

the NI were used as the measures of the cows’ abilities 

to recycle after calving and to become pregnant. 

Records on these traits were based on AI information 

reported by technicians or farmers. A record 

was included in the analyses if the interval from 

calving to first insemination was between 20 and 

230 days. Series of six or seven inseminations were 

set to five inseminations, and series containing more 

than seven inseminations were not available. 

The data set contained approximately 624 000 animals 

with a record on at least one of the five traits. 

The number of observations and overall means are 

given in Table 1 for each of the traits in the final 

data set. 

Because of computational limitations, six subsets 

were randomly made based on herd identification. 

Two subsets contained approximately 150 000 observations, 

and four subsets contained approximately 

80 000 observations. For each subset, a pedigree file 

was traced in the Swedish Cattle Database and pruned 

for non-informative animals. The pedigree files contained 

between 200 000 and 355 000 animals. 

2 ª 2010 Blackwell Verlag GmbH • J. Anim. Breed. Genet. (2010) 1–9

L. H. Buch et al. Multi-trait evaluation of udder health and fertility 

Table 1 Number of observations, means, standard deviations (SD), 

minima and maxima of protein yield (PY, kg), clinical mastitis (CM, 

case), somatic cell score (SCS), number of inseminations (NI) and days 

from calving to first insemination (CFI) 

Trait Observations Mean SD Minimum Maximum 

PY 543 181 257 47 25 514 

CM 607 293 0.075 0.26 0 1 

SCS 549 394 0.70 0.43 0.008 3.0 

NI 473 620 1.8 1.1 1 5 

CFI 473 620 87 33 20 230 

Statistical analyses 

Series of tri-variate animal models were used, where 

y1 was a vector of PY records, and y2 and y3 were two 

of four vectors of records on udder health (CM, SCS) 

or female fertility traits (NI, CFI). PY was included in 

all analyses to account for the effect of ongoing selection. 

The model can be arranged in the following way: 

2 3 2 

32 

3 

y1 X1 0 0 b1 

6 7 6 

76 

7 

4 y2 5 ¼ 4 0 X2 0 54 

b2 5 

y3 0 0 X3 b3 

2 

32 

3 2 3 

Z1 0 0 a1 e1 

6 

76 

7 6 7 

þ 4 0 Z2 0 54 

a2 5 þ 4 e2 5; 

0 0 Z3 a3 e2 

where, X1, X2 and X3 were design matrices relating 

fixed effects in b1, b2 and b3 to y1, y2 and y3. 

The fixed effects for PY were: 

2 3 

hy 

6 ymc 7 

6 7 

6 alt 7 

b1 ¼ 6 7 

6 bdo 7; 

6 7 

4 5 

bbp 

bhet 

and the fixed effects for udder health and female fertility 

traits were: 

2 3 

hy 

6 mc 7 

6 7 

budder health ¼ 6 age 7 

4 5 and bfertility 

2 3 

hy 

6 ymc 7 

¼ 6 7 

4 bbp 5 ; 

bbp 

bhet 

bhet 

where hy was the effect of herd and year of calving. 

Year of calving started July 1st one year and ended 

June 30th the following year. The effect of year and 

month of calving was included in ymc, the effect of 

age at calving in months and 5-year period was 

included in alt, the effect of month of calving was 

included in mc, and the effect of age at calving in 

months was included in age. bdo was a regression on 

days open, and bbp and bhet were vectors of regressions 

on breed proportion and degree of heterozygosity. 

The random effects of animal were included in a1, a2 and a3, where the design matrices Z1, Z2 and Z3 relate records to the animal effects. The random 

residuals were e1, e2 and e3. The covariance structures 

for the random effects were: 

2 3 

a1 

6 7 

var4 

5 ¼ G ¼ G0 A; 

a2 

a3 

2 

6 

where; G0 ¼ 4 

r 2 a1 ra1;a 2 ra1;a 3 

ra1;a 2 r 2 a2 ra2;a 3 

ra1;a 3 ra2;a 3 r 2 a3 

and A is the additive relationship matrix, 

2 3 

e1 

6 7 

var4 

5 ¼ R ¼ R0 I; 

e2 

e3 

2 

6 

where; R0 ¼ 4 

r 2 e1 re1;e 2 re1;e 3 

re1;e 2 r 2 e2 re2;e 3 

re1;e 3 re2;e 3 r 2 e3 

3 

7 

5; 

3 

7 

5; 

and I is the identity matrix. 

Fixed linear regressions on breed proportion and 

degree of heterozygosity were included in the models 

to take imported genetic material into account. 

Breed proportions were extracted from the Swedish 

Cattle Database for each of the animals, and degree 

of heterozygosity was calculated for each cow with 

data. bbp included regressions on the proportions of 

Canadian Ayrshire, Danish Red, Finnish Ayrshire, 

Norwegian Red, SRB and other genes. Finally, b het 

included regressions on the degrees of heterozygosity 

for all pairwise combinations of the breeds mentioned 

above. 

Data were analysed using the dmu package (Madsen 

& Jensen 2008). The average of the heritability 

estimates or of the correlation estimates (l*) was calculated 

by means of the following formula because 

the sizes of the subsets differed: 

l ¼ 1 X 

SW 

6 

i¼1 

ª 2010 Blackwell Verlag GmbH • J. Anim. Breed. Genet. (2010) 1–9 3 

l i 

SE 2 i


where l i was the parameter estimate from subset i 

or the average of the estimates if the parameter was 

computed more than once within each subset. The 

latter concerned the heritability estimates and the 

correlations between PY and the functional traits. 

The sum of weights (SW) was calculated using the 

following formula: 

SW ¼ X6 

1 

SE i¼1 

2 i 

where SE i was the standard error of the estimate 

from subset i or the average of the standard errors if 

the parameter was computed more than once within 

each subset. 

Effect of true multi-trait prediction of BV 

The Selection Index Programme (SIP, Wagenaar et al. 

1995) was used to calculate correlations between the 

selection index and the aggregate genotype under a 

simplified, Nordic-like dairy cattle situation. The 

genetic and phenotypic parameters found in the first 

part of this study were used as input to the programme. 

The breeding goal contained the traits PY, 

CM, NI and CFI. SCS is an important indicator trait 

in the selection index but was not included in the 

breeding goal as an improvement of the trait on one 

unit does not affect profit at the current average 

herd level in the Nordic countries. The breeding goal 

traits represent three trait groups: milk production, 

udder health and female fertility. The current Nordic 

economic values of the trait groups in € per index 

unit (Pedersen et al. 2008) were attached to the 

individual, breeding goal traits by converting the 

Nordic economic values of the trait groups into € per 

unit of the individual, breeding goal traits (Table 2). 

The conversion was made by means of the genetic 

and phenotypic parameters found in this study. The 

economic value of female fertility was divided 

Table 2 The economic values for the breeding goal traits in € per 

unit. The values are based on the economic values per index unit in 

the Nordic total merit index (Pedersen et al. 2008) and then converted 

into € per unit by means of the genetic and phenotypic parameters 

found in this study 

Trait group Trait € per unit 

Milk production Protein yield, kg 4.29 

Udder health Clinical mastitis, case )1088 

Female fertility Number of inseminations )107 

Female fertility Days from calving to first insemination )2.19 

between NI and CFI to maintain the same ratio of 

economic values of the two traits as in the Nordic 

total merit index. 

The simulated selection index contained the traits 

PY, CM, SCS, NI and CFI. Three scenarios were 

developed to study the effect of including some or 

all genetic and phenotypic correlations between the 

three trait groups milk production (PY), udder health 

(CM, SCS) and female fertility (NI, CFI) in multitrait 

evaluations. In scenario I, the genetic and phenotypic 

correlations between selection index traits in 

different trait groups were set to zero; i.e. only the 

genetic and phenotypic correlations between CM 

and SCS and between NI and CFI were used, 

thereby reflecting a trait group by trait group evaluation 

(Table 3). In scenario II, the genetic and phenotypic 

correlations between the selection index traits 

in the trait groups udder health and female fertility 

were set to zero; i.e. the genetic and phenotypic correlations 

between CM and the two female fertility 

traits and between SCS and the two female fertility 

traits were not used. However, the correlations 

between PY and the functional traits were used. In 

scenario III, all genetic and phenotypic correlations 

between selection index traits were used reflecting a 

multi-trait evaluation across the three traits groups. 

The scenarios resembling single-trait evaluations (I) 

and multi-trait evaluations (III) are more realistic 

than the scenario using the genetic and phenotypic 

correlations between the selection index traits in 

some trait groups (II). Still, it was necessary to compare 

scenario II and scenario III to test the hypothesis 

that udder health and female fertility traits 

support each other in multi-trait evaluations. To 

sum up, the breeding goal contained the same traits 

in all scenarios, and all genetic and phenotypic correlations 

between the traits were used. Furthermore, 

the selection index contained the same traits in all 

Table 3 Correlations (both genetic and phenotypic) between the 

selection index traits taken into account in scenarios I, II and III 

Trait group Milk production Udder health Female fertility 

Trait 1 

PY CM SCS NI CFI 

PY – II, III II, III II, III II, III 

CM – I, II, III III III 

SCS – III III 

NI – I, II, III 

CFI – 

1 Traits: PY, protein yield; CM, clinical mastitis; SCS, somatic cell score; 

NI, number of inseminations; CFI, days from calving to first insemination. 



Table 4 Heritabilities (diagonal), genetic correlations 

(above the diagonal) and residual 

correlations (below the diagonal) for protein 

yield (PY), clinical mastitis (CM), somatic cell 

score (SCS), number of inseminations (NI) and 

days from calving to first insemination (CFI) 

with standard errors in parentheses 

scenarios but the assumed values of genetic and phenotypic 

correlations between selection index traits 

differed from one scenario to another. 

The correlation between the index and the aggregate 

genotype was calculated for a heifer, a cow and 

a proven bull. All selection candidates were assumed 

to have a dam with records on own performance, a 

sire with 1000 daughters and a maternal grand sire 

with 1000 daughters. The relationship between the 

daughter group of the sire and the daughter group 

of the maternal grand sire was assumed to be zero. 

It was also assumed that no genotype by environment 

interactions existed and that the animals did 

not share a common environment. The heifer had 

no information beside pedigree information, the cow 

had records on own performance for all traits and 

the proven bull had 150 daughters with records. 

Results 

Estimates of (co)variance components 

The genetic correlations between PY and the functional 

traits were all moderate and significantly larger 

than zero (Table 4). Mastitis and SCS were 

strongly correlated (0.73 0.06). Genetically, CFI 

was more strongly correlated to CM than NI. On the 

contrary, SCS was almost equally correlated to NI 

and CFI (0.09 0.05 and 0.15 0.04, respectively). 

The genetic correlation between NI and CFI was 

weak and not significantly different from zero 

()0.002 0.05). All residual correlations were low. 

The genetic and residual correlation matrices were 

both positive definite. 

The heritability estimate of PY was moderate 

(0.34 0.004), and the heritability estimates of the 

functional traits were all low. However, the heritability 

estimate of SCS (0.14 0.004) was considerably 

higher than for the other functional traits. 

Accuracies of the selection indices 

The correlation between the index and the aggregate 

genotype was slightly lower in scenario I than sce- 

PY CM SCS NI CFI 

PY 0.34* (0.004) 0.40* (0.032) 0.22* (0.017) 0.47* (0.031) 0.30* (0.025) 

CM )0.10* (0.003) 0.014* (0.001) 0.73* (0.056) 0.051 (0.060) 0.38* (0.049) 

SCS )0.16* (0.004) 0.12* (0.004) 0.14* (0.004) 0.094* (0.047) 0.15* (0.038) 

NI 0.12* (0.003) )0.021* (0.002) )0.028* (0.003) 0.018* (0.002) )0.0020 (0.053) 

CFI 0.051* (0.003) 0.0022 (0.002) )0.0010 (0.003) )0.077* (0.002) 0.038* (0.002) 

*The estimate is significantly different from zero, p < 0.05, using a t-test. 

Table 5 Correlations between index and aggregate genotype for a 

heifer, a cow and a proven bull in three scenarios where: (I) the correlations 

between the selection index traits in different trait groups were 

assumed to be zero, (II) the correlations between the selection index 

traits in the trait groups udder health and female fertility were 

assumed to be zero and (III) all correlations between the trait groups 

milk production, udder health and female fertility were included in the 

prediction of BV 

Selection candidate Scenario I Scenario II Scenario III 

Heifer 0.573 0.578 0.579 

Cow 0.663 0.673 0.675 

Proven bull 0.914 0.914 0.918 

BV, breeding values. 

nario III for all selection candidates (Table 5). The difference 

between the correlation obtained in scenarios 

I and III was smallest for the bull (0.004) and largest 

for the cow (0.012). Within each scenario, the weakest 

correlation between the index and the aggregate 

genotype was obtained for the heifer, and the strongest 

correlation was obtained for the proven bull. 

Discussion 

Genetic correlations 

This study was undertaken to estimate genetic 

parameters for PY, two udder health traits and two 

female fertility traits. All genetic correlations 

between PY and the four functional traits were positive 

and thus unfavourable. On the contrary, all 

genetic correlations among the functional traits were 

either favourable or not significantly different from 

zero. 

The genetic correlations between PY and the functional 

traits found in this study tend to be stronger 

(more unfavourable) than the genetic correlations 

found in previous studies of Nordic Red cows (e.g. 

Oltenacu et al. 1991; Pösö &Mäntysaari 1996; Nielsen 

et al. 1997). This may be because of the fact that 

genes affecting both traits favourably move more 

quickly towards fixation than genes affecting one 

trait favourably and the other unfavourably. Therefore, 

genes affecting two traits in opposite directions 

ª 2010 Blackwell Verlag GmbH • J. Anim. Breed. Genet. (2010) 1–9 5


tend to remain segregating and contributing to the 

unfavourable correlation (Falconer & Mackay 1996). 

According to Rauw et al. (1998), the unfavourable 

genetic correlations between PY and the functional 

traits can be interpreted such that dairy cows with 

high genetic merit for milk yield mobilize a disproportionately 

large part of their energy reserves to 

milk production. Consequently, their performance in 

other manifestations of life, such as disease resistance 

and female fertility, is constrained. This interpretation 

indicates that energy balance, often 

measured as body condition score (BCS), is an 

important connecting link. Genetic correlations 

between on the one hand BCS and on the other 

hand milk yield (Veerkamp 1998), disease occurrence 

(Lassen et al. 2003) and female fertility (De 

Haas et al. 2007; Banos & Coffey 2009) indicate relationships 

to energy balance at the genetic level. One 

of the biological mechanisms behind the relationships 

may be that dairy cows are more susceptible to 

diseases in early lactation because of suppression of 

the immune system (Goff & Horst 1997). This suppression 

is caused by hormonal changes associated 

with parturition and may be enhanced if the cow 

suffers from energy or nutrient deficiencies (Goff & 

Horst 1997). Just as the immune system, female fertility 

may be impaired if the cow suffers from energy 

or nutrient deficiencies (O’Callaghan & Boland 

1999). Thus, the unfavourable genetic relationships 

between PY and the functional traits rest probably 

on a physiological basis and may be explained by 

the energy balance in early lactation. 

The higher genetic correlation between CM and 

CFI than between CM and NI may also be explained 

by the negative energy balance in early lactation, 

because the lowest average BCS can be observed in 

the fourth month after calving (Coffey et al. 2001; De 

Haas et al. 2007). Thus, the traits CM and CFI are 

typically observed during the period when the cow is 

likely to be in negative energy balance, while the 

recording of NI usually starts when the cow starts to 

regain body resources. We found, in addition, that 

the partial genetic correlation between CM and CFI 

given PY was 0.30, which indicates that the relationship 

is not only mediated by PY (results not shown). 

In a study of first-parity Norwegian Red cows, Heringstad 

et al. (2006) found a genetic correlation 

between number of CM cases and number of services 

to the conception of 0.10 using a linear sire model. 

Furthermore, Norberg et al. (2009) found a genetic 

correlation between CM and CFI of 0.24 0.06 in a 

study of first-parity Danish Red cows. These results 

support the findings in our study. 

Contrary to the genetic correlations between CM 

and the two fertility traits, SCS was almost equally 

correlated to NI and CFI. Norberg et al. (2009) 

reported a similar low genetic correlation between 

SCS and CFI (0.04 0.04). The authors are unaware 

of any prior studies presenting estimates of the 

genetic correlation between SCS and NI in Nordic 

Red cows. However, Buch & Norberg (2008) found a 

genetic correlation between SCS and NI of 

0.17 0.06 in a study of first-parity Danish Holstein 

cows using a linear animal model. These results back 

up the results in our study, where SCS is weakly 

correlated to the two fertility traits. 

From a biological point of view, female fertility is 

a complex trait containing several aspects that are 

not possible to measure by means of a single measure. 

For that reason, two measures of fertility were 

included in this study. The low genetic correlation 

between NI and CFI found in our study emphasizes 

that the traits are genetically different. Our finding 

agreed with the estimate found by Roxström et al. 

(2001) in a study of first-parity SRB cows using a 

linear sire model (0.13 0.07). 

Heritabilities 

The heritability for CM was lower than the estimate 

recorded by Ødega˚rd et al. (2004) in a study of firstparity 

Norwegian Red cows using a linear sire model 

and in agreement with the estimates found by Pösö 

&Mäntysaari (1996) in a study of first-parity Finnish 

Ayrshire cows using a linear sire model. Mäntysaari 

et al. (1991) showed that the heritability 

estimate for a binary trait depended on the incidence 

when data were analysed by means of a linear 

model. Thus, the differences between the abovementioned 

heritability estimates are likely due to a 

higher reported incidence of mastitis in the Norwegian 

study (20.7%) compared to the Finnish study 

and this study (5.4 and 7.5%). 

Multi-trait evaluations 

We hypothesized that inclusion of correlations 

among functional traits would increase the accuracy 

of the selection index and found support for this 

hypothesis. However, the increases were small. The 

accuracy of the selection index for the heifer and 

the cow increased more from scenarios I to II than 

from scenarios II to III indicating that the correlations 

between PY and the functional traits are more 

important than the correlations among the functional 

traits. 



Because the heifer or a young bull has no records 

on own performance, there is no information about 

the Mendelian sampling term, and therefore the 

accuracy of the predicted BV is low. The total merit 

indices of the sire and the dam both contribute to 

the total merit index of the heifer. However, the 

total merit index of the sire contributes more as it is 

predicted with greater accuracy. The effect of applying 

a multi-trait evaluation on the accuracy of the 

sire’s total merit index is small, and for that reason, 

the gain in accuracy is small for the heifer as well. 

For the proven bull, the gain in accuracy is also 

small as he already has 150 daughters providing 

information about the Mendelian sampling term. 

There is more information about the Mendelian 

sampling term of the cow than the heifer as the cow 

has performance records. As a result, the accuracy of 

the genetic evaluations is higher for the cow than 

the heifer, and multi-trait evaluations utilizing information 

about correlated traits are of greater value 

for the cow than the heifer and the proven bull. 

When BV are predicted using sire models, as is the 

case today for most functional traits evaluated by 

Nordic Cattle Genetic Evaluation, information about 

the cow’s own performance is ignored. For that reason, 

cows are in the same situation as heifers in 

practice. Therefore, the full multi-trait model is more 

important when animal models are used. 

In Sweden, an approximate multi-trait selection 

index approach has been used since 1999 to calculate 

total merit indices for females. Today, Nordic Cattle 

Genetic Evaluation uses a similar approach to take 

account of the unfavourable genetic correlations 

between milk production and udder health and 

female fertility traits and the favourable genetic correlations 

between udder health and udder conformation 

traits. The approach is based on selection index 

theory, and BV predicted by means of single-trait 

models are included in the calculations. 

The accuracy of each trait and thus the total merit 

index may increase if information on correlated 

traits is included in the evaluations. To what extent 

the accuracy of each trait is improved depends on 

the heritabilities and the genetic and residual correlations 

between the traits. For instance, the gain in 

accuracy is expected to be larger for the functional 

traits than PY as most functional traits have lower 

heritabilities than PY (Thompson & Meyer 1986). It 

is often difficult to achieve genetic gain in the functional 

traits so higher accuracies in these traits are 

desirable. Moreover, it is beneficial to use multi-trait 

models if the genetic correlations between the traits 

are strong (Ducrocq 1994). In this study, the genetic 

correlations between PY and the functional traits 

were stronger than the correlations among the functional 

traits. Again the gain in accuracy is expected 

to be larger for the functional traits than PY and 

caused by additional information about the functional 

traits via PY. The gain in accuracy depends 

also on the absolute difference between the genetic 

and residual correlations, i.e. if the difference 

between the genetic and residual correlations is large 

and ⁄ or if the correlations have different signs (Schaeffer 

1984; van der Werf et al. 1992). In this particular 

case, a multi-trait evaluation was expected to be 

an improvement on single-trait evaluations as all 

residual correlations were weak and most of the 

genetic and residuals correlations had different signs. 

If BV are predicted by means of multi-trait evaluations, 

then the optimal weights depend on the 

genetic regression of breeding goal traits on selection 

index traits and the economic values. In cases where 

the index traits and the breeding goal traits are the 

same, the total merit index is a sum of estimated BV 

weighted by the economic values, as the optimal 

weights are equal to the economic values. However, 

if BV are predicted by means of single-trait evaluations, 

then the optimal weights depend on the 

covariances between the estimated BV (Ducrocq 

1994). These are often hard to obtain and difficult to 

approximate because they are affected by the genetic 

and residual correlations between the traits and the 

different family structures (van der Werf et al. 1992). 

The total merit indices obtained in the scenarios are 

based on optimal weights. Thus, the accuracies 

obtained in scenario I may be overestimated, compared 

with the accuracies obtained in national evaluation 

centres, as it is likely that most national 

evaluation centres use economic values instead of 

optimal weights. So, the difference in accuracies 

between scenarios I and III is a conservative 

estimate. 

The economic values were based on the economic 

values per index unit in the Nordic total merit index 

and subsequently converted into € per unit by 

means of the genetic and phenotypic parameters 

found in this study. Some of the heritabilities for the 

functional traits in this study are lower than the heritabilities 

used by Nordic Cattle Genetic Evaluation 

(NAV 2010). For that reason, the relative ratios 

between the economic values differ from the relative 

ratios between the economic values in the Nordic 

total merit index. Also as a consequence of the lower 

heritabilities, the selection index is less balanced and 

more based on improving milk production than the 

Nordic total merit index. Thus, the effect of using a 



multi-trait model on the accuracy of the selection 

index is likely to be an underestimate compared to 

the effect that could be obtained by Nordic Cattle 

Genetic Evaluation. 

Multi-trait analyses require precise estimates of 

genetic and phenotypic correlations between all 

traits (Mrode 2005). The consequence of incorrect 

parameters is an increase in the prediction error variance, 

and as a general rule, traits with lower heritabilities 

suffer more from an increase in prediction 

error variance than traits with higher heritabilities 

(Schaeffer 1984). We used the genetic and phenotypic 

correlations that were estimated in the first 

part of this study as prerequisites in the programme 

SIP. Both Schaeffer (1984) and van der Werf et al. 

(1992) found that the accuracies of multi-trait evaluations 

are relatively robust to errors in the parameters 

used. 

The computational burden of full multi-trait animal 

models including all trait groups is still the limiting 

factor for large-scale application in the genetic 

evaluations of dairy cattle and is owing to the 

amount of data and the use of very different types 

of models (Ducrocq et al. 2001). However, it has 

been shown in a stochastic simulation study mimicking 

a dairy population of 100 000 cows that an 

approximate multi-trait BLUP model can work and 

lead to genetic gains similar to those of a full linear 

multi-trait model (Lassen et al. 2007). 

Threshold models may be better than linear models 

for the analyses of ordered categorical traits with 

low heritability and low incidence (Mrode 2005). 

Thus, threshold models would perhaps have been 

the best method for analysing CM and NI in this 

study. However, linear models are applied in the 

joint Nordic genetic evaluation of dairy cattle, and 

we wanted to mimic this situation. Furthermore, it 

seems reasonable that linear models will be applied 

if multi-trait models are to be used for the genetic 

evaluation of dairy cattle in the future. The heritability 

estimates of CM and NI would likely have 

been higher if threshold models had been applied 

instead of linear models. However, the application 

of threshold models may overestimate the actual 

effect of a multi-trait evaluation over single-trait 

evaluations on the accuracy of the selection index, 

and therefore linear models were the method of 

choice. 

Conclusions 

Genetically, CFI was more strongly correlated to CM 

than NI. The reason may be that CM and CFI pri- 

marily are observed in the early part of the lactation 

period when the cows are likely to be in negative 

energy balance, whereas NI usually is recorded 

when the cows start to regain body resources. The 

genetic correlation between NI and CFI was low, 

which indicates that the traits are not influenced by 

the exact same genes. The accuracy of the selection 

index was higher for all selection candidates when 

multi-trait evaluations were compared to single-trait 

evaluations although differences were small, and 

multi-trait evaluations were of greater value for 

cows than for heifers and proven bulls. 

Acknowledgements 

This research was financed by a grant from the Danish 

Ministry of Science, Technology and Innovation 

and the Danish Cattle Federation. The authors thank 

the Swedish Dairy Association for providing data 

and especially Jan-A˚ ke Eriksson for helpful information 

about the Swedish genetic evaluation system. 

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Paper II 

Hygiene-related and feed-related hoof diseases show different patterns of 

genetic correlations to clinical mastitis and female fertility 

Line Hjortø Buch, Anders Christian Sørensen, Jan Lassen, Peer Berg, Jan-Åke Eriksson, Jette 

Halkjær Jakobsen & Morten Kargo Sørensen 

Journal of Dairy Science (2011), doi:10.3168/jds.2010-3137

J. Dairy Sci. 94:1–12 

doi:10.3168/jds.2010-3137 

© American Dairy Science Association ® , 2011. 

Hygiene-related and feed-related hoof diseases show different patterns 

of genetic correlations to clinical mastitis and female fertility 

L. H. Buch,*† 1 A. C. Sørensen,† J. Lassen,† P. Berg,† J-.Å. Eriksson,‡ J. H. Jakobsen,§ and M. K. Sørensen*† 

*Knowledge Centre for Agriculture, Agro Food Park 15, DK-8200 Aarhus N, Denmark 

†Department of Genetics and Biotechnology, Aarhus University, PO Box 50, DK-8830 Tjele, Denmark 

‡Swedish Dairy Association, Box 210, 101 24 Stockholm, Sweden 

§Department of Animal Breeding and Genetics, Swedish University of Agricultural Sciences, PO Box 7023, 75007 Uppsala, Sweden 

ABSTRACT 

Hoof diseases are a problem in many dairy herds. To 

study one aspect of the problem, genetic correlations 

between 4 hoof diseases, protein yield, clinical mastitis, 

number of inseminations, and days from calving to first 

insemination were estimated in first-parity Swedish Red 

cows using trivariate linear animal models. Occurrence 

of dermatitis, heel horn erosion, sole hemorrhage, and 

sole ulcer were reported by hoof trimmers. The data set 

contained about 314,000 animals with records on at least 

one of the traits; among these, about 64,000 animals 

had records on hoof diseases. Heritabilities were low for 

all hoof diseases (0.03 to 0.05). The hoof diseases fell 

into 2 groups: (1) dermatitis and heel horn erosion (i.e., 

diseases related to hygiene) and (2) sole hemorrhage and 

sole ulcer (i.e., diseases related to feeding). The genetic 

correlations between traits within the 2 groups were 

high (0.87 and 0.73, respectively), whereas the genetic 

correlations between traits in different groups were low 

(≤0.23). These results indicate that the 2 groups of hoof 

diseases are partly influenced by the same genes. All 

genetic correlations between hoof diseases and protein 

yield were low to moderate and unfavorable. Moderate 

and favorable genetic correlations were found between 

the feed-related hoof diseases and clinical mastitis (0.35 

and 0.32), whereas the genetic correlations between 

the hygiene-related hoof diseases and clinical mastitis 

were low and not significantly different from zero. The 

genetic correlations between the hygiene-related hoof 

diseases and number of inseminations were low to moderate 

and favorable (0.32 and 0.22), and the genetic 

correlations between the feed-related hoof diseases and 

number of inseminations were low and not significantly 

different from zero. A moderate genetic correlation was 

found between sole ulcer and days from calving to first 

insemination (0.33), whereas the genetic correlations 

between days from calving to first insemination and 

Received February 4, 2010. 

Accepted November 2, 2010. 

1 Corresponding author: Line.HjortoBuch@agrsci.dk 

1 

sole hemorrhage and the hygiene-related hoof diseases 

were low and not significantly different from zero. In 

general, the 2 groups of hoof diseases showed different 

patterns of genetic correlations to the other functional 

traits, but both were unfavorably correlated to protein 

yield. A simulation study showed that inclusion of hoof 

diseases in the selection index will not only reduce the 

genetic decline in resistance to hoof diseases but also be 

favorable for other functional traits and improve overall 

genetic merit. 

Key words: hoof disease, mastitis, female fertility, 

dairy cattle 

INTRODUCTION 

The incidence of hoof diseases is high in many dairy 

cattle populations. As an example, Sogstad et al. (2005) 

conducted a study of 2,665 cows that were trimmed 

by hoof trimmers who had been taught diagnosis and 

recording of hoof diseases. Their study showed that 

41% of the cows housed in tie-stalls and 64% of the 

cows housed in freestalls had at least one disease in 

the hind hooves. Individual hoof diseases may be more 

difficult to record than lameness but it is a more precise 

measure of hoof health. Diseases in the hooves or the 

skin directly connected to the hooves may cause up 

to 90% of cases of lameness (Peterse, 1992; Webster, 

1993). However, hoof diseases do not necessarily cause 

lameness. In the study by Sogstad et al. (2005) only 1 

and 2% of the cows housed in tie-stalls and freestalls, 

respectively, were recorded as lame in the hind limbs. 

Other studies have also found few lame cows compared 

with the number of cows suffering from hoof diseases 

(e.g., Smits et al., 1992; Manske et al., 2002). Thus, 

direct measures of hoof diseases or a combination of 

direct measures of hoof diseases and lameness are preferred 

if data are available. 

The total costs of a single case of lameness are considerably 

greater than the treatment costs alone because 

lameness may reduce milk yield (Warnick et al., 2001) 

and female fertility (Hernandez et al., 2001) and hasten 

culling (Booth et al., 2004). Kossaibati and Esslemont

2 

(1997) found, for instance, that the direct costs of lameness 

caused by a digital disease, an interdigital disease, 

and sole ulcer were £121, £76, and £152 per affected 

cow, respectively, including reduced milk yield, whereas 

the total costs were £240, £131, and £425 per affected 

cow under British conditions. The incidence can be reduced 

by improved management or by genetic selection. 

A crucial prerequisite for improving traits genetically 

is that they exhibit genetic variation. Previous studies 

have shown that this is the case for hoof diseases (e.g., 

Koenig et al., 2005; van der Waaij et al., 2005). 

Both indirect selection based on correlated feet and 

leg conformation traits and direct selection based on 

veterinary treatments of feet and leg diseases are carried 

out today in the Nordic countries, but the genetic 

correlations between the 2 types of measures are not 

taken into account (NAV, 2010). The heritabilities of 

the feet and leg conformation traits are relatively high 

compared with those of the disease traits reported by 

veterinarians. However, the majority of the genetic correlations 

between hoof diseases and feet and leg conformation 

traits are low to moderate (van der Waaij et al., 

2005; Uggla et al., 2008). It is, therefore, unlikely that 

selection on conformation traits has resulted in considerable 

improvements of hoof health. Manske et al. 

(2002) found in a Swedish study that 72% of the animals 

suffered from at least one hoof disease. In comparison, 

2.1 cases of hoof diseases and 0.3 cases of laminitis were 

treated by veterinarians per 100 cows in the years 2002 

to 2003 (C. Bergsten, Swedish University of Agricultural 

Sciences, Skara, Sweden, personal communication). 

The difference between the number of diseased animals 

and the number of treatments indicates that only the 

most severe cases are treated by veterinarians. As a 

consequence of the low frequencies, records on veterinary 

treatments of individual hoof diseases show lower 

heritabilities on the observed scale (e.g., Laursen et 

al., 2009). Hoof diseases are also treated by hoof trimmers 

and farmers but these treatments have not been 

recorded regularly in all Nordic countries. Information 

about hoof diseases have, however, been reported by 

Swedish hoof trimmers since 2003. This screening of the 

population gives a more realistic picture of the number 

of cases. 

It is important to obtain knowledge about genetic 

correlations when aiming to implement new traits in 

the breeding goal. Dairy cows with high genetic merit 

for milk production are assumed to be more predisposed 

to diseases, because they allocate body reserves to milk 

production in early lactation. This is in agreement with 

the unfavorable genetic correlations that often exist 

between functional traits (e.g., udder health and female 

fertility traits) and milk production traits (for review, 

see Rauw et al., 1998). With regard to hoof diseases, 

Journal of Dairy Science Vol. 94 No. 3, 2011 

BUCh eT Al. 

Koenig et al. (2005) found unfavorable genetic correlations 

between hoof diseases and milk production in the 

range from 0.06 to 0.34. These results are consistent 

with the idea of an inexpedient allocation of resources 

to milk production traits at the expense of health and 

reproduction traits. The group of functional traits is 

more diverse than the group of milk production traits 

and therefore it may be difficult to predict the sign 

of the genetic correlations among functional traits. 

However, many studies have found favorable genetic 

correlations among functional traits (e.g., Kadarmideen 

et al., 2000). In line with these results, Koenig et al. 

(2005) found genetic correlations between hoof diseases 

and SCS in the range from 0.15 to 0.28. To the best 

of our knowledge, genetic correlations between hoof 

diseases and mastitis have never been estimated previously 

and genetic correlations between hoof diseases 

and female fertility have only been estimated in a single 

study (Onyiro et al., 2008). Besides their use in breeding 

programs, estimates of genetic correlations between 

hoof diseases and other traits of economic importance 

may lead to better understanding of the side effects of 

artificial selection; for example, whether the incidences 

of hoof diseases have changed because of artificial selection. 

The objective of this study was to estimate genetic 

parameters for 4 hoof diseases and their genetic correlations 

to protein yield, 2 udder health traits, and 2 

female fertility traits in Swedish Red (SRB) cows. A 

second objective was to quantify the effect of including 

hoof diseases in a selection index on the selection differential 

for the breeding goal traits. 

Data 

MATERIALS AND METHODS 

Records on traits related to hoof health, milk production, 

udder health, and female fertility in first-parity 

SRB cows were extracted from the Swedish Cattle 

Database. 

Hoof trimming records from January 2003 to March 

2008 were included in the analyses. Records on dermatitis 

(digital or interdigital, DE), heel horn erosion 

(HH), sole hemorrhage (sole or white line hemorrhage, 

SH), and sole ulcer (ulceration of sole or white line 

area, SU) were reported by professional hoof trimmers. 

The diseases were assessed as no case, light case, 

or severe case. The recording scheme was established 

with focus on these traits because they are the most 

common hoof diseases in Sweden. The guidelines for 

the classification of the individual hoof diseases were 

developed by the Swedish Dairy Association, and all 

hoof trimmers who volunteered to report to the cen-

tral database were informed about these guidelines to 

obtain a uniform identification of the hoof diseases. 

Dermatitis, HH, and SH were reported per cow, and for 

each of the 3 diseases the final assessment was based 

on the hoof with the most severe case. Sole ulcer was 

reported for each hoof because the farmers utilize this 

information for individual follow-ups. We used only the 

assessment of the hoof with the most severe case by 

which SU was defined like the other traits. The hoof 

traits were defined as binary traits in this study, where 

0 indicates no case and 1 indicates a light or severe 

case. This was due to few recordings of severe cases. 

The hoof trimmers reported healthy cows (zeros for all 

4 hoof diseases) as well as diseased cows, and they could 

report more than one hoof disease per cow. Information 

about hoof trimming strategies within herds, such as 

frequency of trimming and selection of cows for trimming 

(e.g., all cows or those previously diagnosed with 

a hoof disease), was not available. As a consequence, 

only records on the first hoof trimming after first calving 

were included in the analyses. For inclusion of the 

records in the analyses, hoof trimming should be done 

within 1 yr after calving, and age at first calving should 

be in the interval from 20 to 38 mo. Records without 

hoof trimmer identification were deleted. After editing, 

hoof trimming records from 63,962 cows gathered by 

217 hoof trimmers in 4,188 herds remained (Table 1). 

The mean number of days in milk at trimming was 146 

d with a standard deviation of 91 d. The distribution 

of records was slightly skewed because 53 and 85% of 

the hoof-trimmed cows were trimmed during the first 

4 and 8 mo after calving. Age at first calving was, on 

average, 28.2 mo, with a standard deviation of 3.3 mo. 

The mean number of cows per herd and year of calving 

was 8 cows, and the mean number of daughters per sire 

was 35 cows. The prevalence of DE, HH, SH, and SU 

were 6.9, 17, 25, and 4.0% at the first hoof trimming 

after first calving. 

For the remaining traits, only records from firstparity 

cows with hoof trimming records or first-parity 

hOOF DISeASeS CORRelATe TO OTheR FUNCTIONAl TRAITS 

Table 1. Number of observations, prevalence, means, and SD for traits associated with hoof health, milk 

production, udder health, and female fertility 

Trait 

Observations, 

n 

Prevalence, 

% Mean SD 

Dermatitis, case 63,962 6.9 — — 

Heel horn erosion, case 63,962 17 — — 

Sole hemorrhage, case 63,962 25 — — 

Sole ulcer, case 63,962 4.0 — — 

Protein yield, kg 273,994 — 262 47 

Clinical mastitis, case 297,747 7.6 — — 

SCS 277,664 — 0.70 0.43 

Number of inseminations 238,033 — 1.8 1.07 

Days from calving to first insemination 238,033 — 85 32 

cows with the same herd identification as those with 

hoof trimming records were merged to the hoof health 

data set. Because we wanted to include protein yield 

in all the analyses to account for the effect of selection, 

we had to include records on protein yield over 

an extended period. Thus, date of first calving should 

be between January 1996 and December 2006, which 

meant that all cows had the opportunity to achieve a 

complete lactation. We decided also to include records 

on the other functional traits from 1996 to 2006 because 

the additional records would reduce the standard errors 

of the genetic correlations. In this study, hoof trimming 

records from herd mates that were not hoof trimmed 

were set missing. This editing procedure applied both 

to the cows that for some unknown reasons were not 

trimmed although other cows in the herd were trimmed 

and to the cows that were second-parity cows or older 

when the hoof trimmers started to record hoof diseases. 

However, the majority of the hoof trimming records 

that were set missing belonged to the second category. 

This practice differs from the routine genetic evaluation 

of feet and leg diseases reported by veterinarians 

in which untreated cows are assumed to be healthy. 

However, if all cows without hoof trimming records had 

been regarded as healthy in this study, the prevalence 

of the hoof diseases would have been incorrect. 

Protein yield was recorded as 305-d lactation protein 

yield (PY), and both completed and extended lactations 

were included. Only cows with at least 45 DIM 

were kept in the data set. In addition, the extended 

lactations should be between 25 and 800 kg of protein, 

and age at first calving should be in the interval from 

20 to 38 mo. 

Records on clinical mastitis (CM) originated from 

the Swedish national health recording system, where 

clinical treatments are reported by veterinarians, or 

from the record of reasons for culling reported by farmers. 

The trait was defined as a binary trait, where 0 

indicates that the cow was not treated or culled for 

CM, and 1 indicates that the cow was either treated or 


3

4 

culled for CM. Treatments and cullings for CM were 

registered in the interval from 10 d before calving to 

150 d after calving, and the prevalence during that 

interval was 7.6%. 

Somatic cell counts were registered in 10,000 cells/ 

mL and transformed to SCS using the common logarithm 

with base 10. The milk samples were collected in 

the interval from 5 to 150 d after calving and finally the 

geometric mean of the samples was calculated. 

The cow’s abilities to resume its normal cycle and to 

become pregnant were measured as days from calving 

to first insemination (CFI) and number of inseminations 

(NI), respectively, although these measures are 

affected by management to some degree. Unfortunately, 

measures completely independent of management 

strategies (e.g., progesterone measurements) were not 

available. Records on CFI and NI were based on AI 

information reported by technicians or farmers. Only 

records where the interval from calving to first insemination 

was between 20 and 230 d were included in the 

analyses. Series of 6 or 7 inseminations were set to 5 

inseminations, and series containing more than 7 inseminations 

were not available. 

The final data set contained 314,300 animals with 

a record on at least one of the traits. About 48,000 

hoof-trimmed cows had records on PY and CM, about 

46,000 hoof-trimmed cows had records on SCS, and 

about 40,000 hoof-trimmed cows had records on the 

female fertility traits. 

Two subsets were formed due to computational limitations. 

The partition was based on even and odd herd 

identification numbers and the subsets contained about 

152,000 and 162,000 animals with observations. A pedigree 

file was traced in the Swedish Cattle Database for 

each of the 2 subsets and pruned for noninformative 

animals; that is, animals with unknown parents and 

without records that only relate to the cows in the subsets 

through one offspring. 

Statistical Analyses 

The editing procedures and the models were based 

on those used in the Swedish routine genetic evaluation 

before Finland, Sweden, and Denmark started to 

publish joint Nordic breeding values and the current 

model for hoof health (Eriksson, 2006). In this study all 

Swedish models were extended with fixed linear regressions 

on breed proportion and degree of heterozygosity, 

and animal models were used instead of sire models. 

Series of trivariate linear animal models were used, 

where y 1 was a vector of PY records, and y 2 and y 3 

were vectors of records on hoof health (DE, HH, SH, 

SU), udder health (CM, SCS), or female fertility traits 


BUCh eT Al. 

(NI, CFI). Protein yield was included in all analyses to 

account for the effect of selection. The model was as 

follows: 

éy 

ù éX 

0 0 ù éb 

ù é 

ê 1 ú ê 1 ú ê 1 ú êZ 

0 0 ù é 

ú êa 

ù 

1 

1 ú 

ê 

êy 

ú 

0 X 0 b 

2 ú = 

ê 

ú ê ú 

ê 2 ú ê 2 ú + 

ê 0 Z 0 

ú ê 

ú êa 

ú 

2 2 ú 

ê ú ê 

ú ê ú ê ú ê ú 

y 0 0 X b 

ë 

ê 3 û 

ú 

ë 

ê 

3 û 

ú 

ë 

ê 3 û 

ú 

ë 

ê 0 0 Z 

û 

ú 

ë 

êa 

3 3 û 

ú 

é0 

0 0 ù é 0 ù ée 

ù 

ê ú ê ú ê 1 ú 

+ 

ê 

0 H 0 

ú ê 

h 

ú 

ê 

e 

2 ú ê 2 ú + 

ê ú 

ê 2 ú, 

ê ú ê ú ê ú 

0 0 H h e 

ë 

ê 

3 û 

ú 

ë 

ê 3 û 

ú 

ë 

ê 2 û 

ú 

where X 1, X 2, and X 3 were design matrices relating 

fixed effects in b 1, b 2, and b 3 to y 1, y 2, and y 3. 

The fixed effects for PY were 

b 

1 

é hy ù 

ê ú 

êymcú 

ê ú 

ê 

alt 

ú 

ê ú 

= ê ú , 

ê bdo 

ú 

ê ú 

ê bbp 

ú 

ê ú 

ê b ú 

ë het û 

and the fixed effects for hoof health, udder health, and 

female fertility traits were: 

b 

b 

hoof health = 

udder health = 

and b 

fertility = 

é hy ù 

ê ú 

ê mc ú 

ê ú 

ê age 

ú 

ê ú, 

ê ls ú 

ê ú 

ê bbp 

ú 

ê ú 

êb 

ú 

ë hetû 

é hy ù 

ê ú 

ê mc ú 

ê ú 

ê age 

ú 

ú, 

ê ú 

ê bbp 

ú 

ê ú 

êb 

ú 

ë hetû 

é hy ù 

ê ú 

êymcú 

ê ú 

ê b 

ú, 

bp ú 

ê ú 

b 

ë 

ê het û 

ú

where hy was the effect of herd and year of calving, and 

ymc was the effect of year and month of calving (year 

of calving started July 1 one year and ended June 30 

the following year). Furthermore, alt was the effect of 

age at calving in months within 5-year periods, mc was 

the effect of month of calving, age was the effect of age 

at calving in months, and ls was the effect of lactation 

stage in months; b do was a regression on days open, 

and b bp and b het were vectors of regressions on breed 

proportion and degree of heterozygosity. 

The random effects of animal were included in a 1, 

a 2, and a 3, where the design matrices Z 1, Z 2, and Z 3 

relate records to the animal effects. To take account of 

potential differences between hoof trimmers, random 

effects of hoof trimmer were included in h 2 and h 3, 

where the design matrices H 2 and H 3 relate records to 

the hoof trimmer effects. Matrices H 2 and H 3 are zeros 

except for the hoof health traits. The random residuals 

were e 1, e 2, and e 3. The covariance structures for the 

random effects were 

éa 

ù 

ê 1 ú 

var 

ê 

a 

ú 

ê G G A 

2 ú = = Ä , 0 

ê ú 

a 

ë 

ê 3 û 

ú 

é 2 

ê s s s 

ê 

where G = ê 

2 

s s s 

0 ê 

ês 

s s 

ë , , 

a1 a1, a2 a1, a3 

a1, a2 a2 a2, a3 

2 

a1a3 a2 a3 a3 

2 

with each element defined as s = additive genetic 

ai 

variance of direct effects for trait i, and s = addi- 

ai, aj 

tive genetic covariance between direct effects for trait i 

and trait j. A is the additive relationship matrix, 

é 0 ù 

ê ú 

var 

ê 

h 

ú 

ê T T I, 

2 ú = = Ä 0 

ê ú 

h 

ë 

ê 3 û 

ú 

é 

ê0 

0 0 

ê 

where T = ê 2 

0 s s 

0 ê 

, 

ê 

2 

ê0 

s s 

ë h , h h 

h2 h2 h3 

2 3 3 

2 

with each element defined as s = variance due to 

hi 

hoof trimmer effects for trait i, and s = covariance 

hi, hj 


ù 

ú 

ú, 

ú 

û 

ù 

ú 

ú, 

ú 

û 

between hoof trimmer effects for trait i and trait j. I is 

the identity matrix of proper order, 

ée 

ù 

ê 1 ú 

var 

ê 

e 

ú 

ê R R I, 

2 ú = = Ä 0 

ê ú 

e 

ë 

ê 3 û 

ú 

é 2 

ê s s s 

ê 

where R = ê 

2 

s s s 

0 ê 

ês 

s s 

ë , , 

e1 e1, e2 e1, e3 

e1, e2 e2 e2, e3 

2 

e1e3 e2 e3 e3 

2 

with each element defined as s = residual variance 

ei 

for trait i, and s = residual covariance between 

ei, ej 

trait i and trait j. I is the identity matrix of proper 

order. 

Fixed linear regressions on breed proportion and degree 

of heterozygosity were included in the models to take 

imported genetic material into account. Breed proportions 

were extracted from the Swedish Cattle Database 

for each of the animals, and degree of heterozygosity 

was calculated for each cow with data; bbp included the 

proportions of Canadian Ayrshire, Danish Red, Finnish 

Ayrshire, Norwegian Red, SRB, and other genes, 

and bhet included the degrees of heterozygosity for all 

pairwise combinations of the breeds mentioned above. 

Twenty-two analyses were performed on each of the 2 

subsets, and data were analyzed by means of the DMU 

package (Madsen and Jensen, 2008). The average of the 

estimates obtained from the 2 subsets was calculated 

and asymptotic standard errors of the parameters were 

computed under the assumption that estimates from 

different subsets are independent. 

The heritability estimates on the observed scale 

2 

(h ) were transformed to the underlying continuous 

obs 

2 

scale (hund ) using the following formula (Dempster and 

Lerner, 1950): 

h 

p( 1 - p) 

= ´ h 

2 

j 

2 

2 

und obs 

where p was the incidence of disease and j was the 

value of a standard normal density function at the 

threshold that divides the probability mass to proportions 

p and 1 − p. 

Estimation of Partial Genetic Correlations 

Estimating the partial genetic correlation between 2 

hoof diseases when the other 7 traits were held constant 

, 

ù 

ú 

ú, 

ú 

û 


5

6 

provided the opportunity to examine if the genetic correlation 

was direct or mediated through the correlations 

to the other traits. The partial genetic correlation 

matrix G * can be calculated as follows (Whittaker, 

1990): 

* 

1 - 

G =- 1 ´ ( DC D), 

where D was a diagonal matrix in which each diagonal 

element was 1 divided by the square root of the 

corresponding diagonal element in the inverse genetic 

correlation matrix, C −1 . 

The number of effective animals, n, that contributed 

to the estimation of the genetic correlation between 2 

hoof diseases was calculated using the following formula 

(Sokal and Rohlf, 1995): 

2 

rg 

n = 

SE 

- 1 

+ 2, 

2 

where r g was the genetic correlation between 2 hoof 

diseases found in the first part of this study, and SE 

was the asymptotic standard error of the genetic correlation. 

For the 6 genetic correlations n ranged from 

64 to 107. 

We tested if the partial genetic correlations were significantly 

different from zero by means of the t-statistic 

shown below (Sokal and Rohlf, 1995): 

* 

g 

t = r 

n -2-m , 

* 

1 - r 

* 

where r was the partial genetic correlation between 2 

g 

hoof diseases and m was the number of traits kept constant 

(7 in this particular case). The number of effective 

animals, n, used was the smallest value calculated on 

the basis of the 6 genetic correlations between hoof 

diseases; that is, 64. 

Estimation of Accuracies of Selection 

and Selection Differentials 

Selection Index Program (SIP, Wagenaar et al., 1995) 

was used to calculate selection differentials and accuracies 

of selection (i.e., correlations between a selection 

index and the aggregate genotype) under a simplified, 

Nordic-like dairy cattle situation. The heritabilities of 

the 4 hoof diseases found in the first part of this study 

were used as input to the program along with the genetic 

and phenotypic correlations between hoof diseases 


g 

BUCh eT Al. 

and traits related to milk production, udder health, and 

female fertility. The data set in this study contained 

only information from a part of the Swedish population 

of genetically evaluated first-parity SRB cows. For that 

reason, we decided to use the genetic and phenotypic 

parameters for PY, CM, SCS, NI, and CFI, which were 

based on information from all first-parity SRB cows 

genetically evaluated during the period from 1996 to 

2006 (Buch et al., 2010). None of the heritabilities were 

transformed to the underlying continuous scale. The 

symmetric genetic and phenotypic correlation matrices 

were both positive definite. 

The simulated breeding goal contained the traits DE, 

HH, SH, SU, PY, CM, NI, and CFI. These traits represent 

the 4 sub-indices hoof health, milk production, 

udder health, and female fertility and were chosen because 

they have relatively high economic values among 

the traits in the joint Nordic breeding goal. Somatic cell 

score was not included in the simulated breeding goal 

because the trait is an indicator trait without economic 

value in the Nordic breeding goal. The economic value 

of the simulated trait group hoof health was based on 

the economic value of feet and legs in the current subindex 

resistance against diseases other than mastitis 

in the Nordic breeding goal (Pedersen et al., 2008). 

The economic value of the sub-index in Euros (€) per 

index unit was attached to the individual breeding goal 

traits in this study by converting the economic value 

into Euros per case of the individual, simulated hoof 

diseases (Table 2). The conversion was made by means 

of the genetic and phenotypic parameters found in this 

study. The relative ratio of economic values for DE, 

HH, SH, and SU within the simulated trait group hoof 

health was 0.1, 0.2, 0.2, and 0.5. This relative ratio is 

used in the current Swedish sub-index hoof health. The 

economic values of the simulated trait groups milk production, 

udder health, and female fertility were based 

on the current economic values in the Nordic breeding 

goal as described in the study by Buch et al. (2010). 

Three scenarios were developed to study the effect 

of different selection indices. In scenario I, PY was the 

only trait in the selection index. The purpose of this 

scenario was to study whether the selection differential 

for resistance to the 4 hoof diseases would be unfavorable 

if a narrow selection index was used. In scenario 

II, the selection index contained the traits PY, CM, 

SCS, NI, and CFI, and all genetic and phenotypic correlations 

between the 5 index traits were used. The 

purpose of scenario II was to study the effect of a broad 

selection index without hoof diseases on the selection 

differential for resistance to hoof diseases. In scenario 

III, the selection index contained the same traits as 

the breeding goal and also SCS. In addition, all genetic 

and phenotypic correlations between the 9 index traits

were used. The purpose of this scenario was to study 

the effect of a broad selection index containing hoof 

diseases on the selection differential for resistance to 

the 4 hoof diseases. In other words, the breeding goal 

contained the same traits in all scenarios, and all genetic 

and phenotypic correlations between the breeding 

goal traits were used. The selection index differed from 

one scenario to another with regard to number of traits 

and the number of genetic and phenotypic correlations 

between the index traits. 

The selection differentials and the accuracies of selection 

were calculated for a proven bull. The bull was 

assumed to have 150 daughters with records, a dam 

with records on PY and SCS, and a sire with 1,000 

daughters. It was assumed that no genotype by environment 

interactions existed and that the animals did 

not share a common environment. 

RESULTS 

Heritabilities and Correlations Among Hoof Diseases 

The heritabilities for the 4 hoof diseases were low 

and ranged from 0.03 to 0.05 on the observed scale 

(Table 3). The heritabilities increased when they were 

corrected for incidence of disease and the ranking order 

among them changed. The genetic correlations between 

DE and HH and between SH and SU were high, whereas 

the remaining genetic correlations among the hoof dis- 


Table 2. Economic values for the simulated breeding goal traits in Euros per unit 

Trait group 1 

Trait € per unit 

Hoof health Dermatitis, case −8.58 

Hoof health Heel horn erosion, case −12.48 

Hoof health Sole hemorrhage, case −10.56 

Hoof health Sole ulcer, case −54.18 

Milk production Protein yield, kg 4.29 

Udder health Clinical mastitis, case −1,088 

Female fertility Number of inseminations −107 

Female fertility Days from calving to first insemination −2.19 

1 The values are based on the economic values per index unit in the Nordic breeding goal (Pedersen et al., 2008) 

and converted into €/unit by means of the genetic and phenotypic parameters found in this study (hoof health 

group) and the study of Buch et al. (2010) (all other trait groups). 

eases were low and most were not significantly different 

from zero. The residual correlations among the hoof 

diseases were low and ranged from 0.01 to 0.14. 

Correlations Between Hoof Diseases and Protein 

Yield, Udder Health, and Female Fertility Traits 

The genetic correlations between the 4 hoof diseases 

and PY were positive and ranged from 0.07 to 0.24 

(Table 4). The genetic correlations between CM and DE 

and HH were low and not significantly different from 

zero, whereas the genetic correlations between CM and 

SH and SU were moderate and positive. The genetic 

correlations between NI and DE and HH were low to 

moderate whereas the genetic correlations between CFI 

and DE and HH were low and not significantly different 

from zero. The associations between SU and the 

female fertility traits showed a different pattern as the 

genetic correlation between NI and SU was low and not 

significantly different from zero and the genetic correlation 

between CFI and SU was moderate. Most residual 

correlations were very low, especially the correlations 

between the functional traits (results not shown). 

Partial Genetic Correlations Among Hoof Diseases 

The partial genetic correlation between 2 traits was 

obtained by conditioning on the other 7 traits in this 

study. Except for the partial genetic correlation between 

2 2 

Table 3. Heritabilities on the observed scale ( h ) and the underlying scale ( hund ) and genetic (above the 

obs 

diagonal) and residual (below the diagonal) correlations for dermatitis (DE), heel horn erosion (HH), sole 

hemorrhage (SH), and sole ulcer (SU) with standard errors in parentheses 

2 

Trait hobs 2 

hund DE HH SH SU 

DE 0.03* (0.006) 0.13 0.87* (0.053) −0.04 (0.115) −0.19 (0.125) 

HH 0.03* (0.005) 0.07 0.14* (0.005) 0.23* (0.109) 0.13 (0.124) 

SH 0.05* (0.007) 0.09 0.03* (0.006) 0.08* (0.006) 0.73* (0.066) 

SU 0.03* (0.006) 0.17 0.01 (0.005) 0.07* (0.005) 0.04* (0.006) 

*The estimate was significantly different from zero, P < 0.05, using a t-test. 


7

8 

SH and SU, all partial genetic correlations were significantly 

different from zero and most were favorable 

(Table 5). The former indicates that the correlations 

among the 4 hoof diseases were not exclusively mediated 

through the correlations to the other traits. 

Accuracies of Selection and Selection Differentials 

The accuracy of selection ranged from 0.83 in scenario 

I to 0.92 in scenario III (Table 6). The genetic superiority 

of PY was largest in scenario I and smallest in scenario 

III. On the contrary, the selection differential for 

all functional traits, with the exception of DE and HH, 

was least favorable in scenario I and most favorable in 

scenario III. The selection differentials in scenario II 

were more like the selection differentials in scenario III 

than the selection differentials in scenario I. 

Genetic Correlations 

DISCUSSION 

Our results indicate that the hoof diseases under 

study fall into 2 groups, which we call hygiene-related 

and feed-related hoof diseases. The first group contains 

DE and HH and the second group contains SH and SU 

because the genetic correlations among traits within 

the 2 groups were high and the genetic correlations 

between traits in different groups were low. This division 

is in line with other characteristics of the diseases 

because DE and HH are infectious diseases, and bacterial 

and chemical actions of the environment are considered 

to be predisposing factors. The diseases are to 

a great extent related to hygiene because wet slurry on 

the floor surface of passageways softens and probably 

erodes the hoofs. This predisposes to wear on the horn 

and decreased resistance against bacteria (Webster, 

1993). Peterse (1992) suggests, moreover, that dermatitis 

can predispose to or cause heel horn erosion. Sole 

hemorrhage and SU have a multifactorial etiology but 

improper nutrition causing low ruminal pH, hard and 

rough floor surfaces, or insufficient hoof trimming are 


BUCh eT Al. 

Table 4. Genetic correlations among traits related to hoof health, milk production, udder health, and female 

fertility with standard errors in parentheses 1 

Trait PY CM SCS NI CFI 

DE 0.07 (0.068) 0.00 (0.112) 0.02 (0.082) 0.32* (0.106) 0.01 (0.102) 

HH 0.24* (0.066) −0.05 (0.110) −0.01 (0.081) 0.22* (0.112) −0.04 (0.102) 

SH 0.11* (0.056) 0.35* (0.097) 0.11 (0.069) −0.10 (0.103) 0.10 (0.091) 

SU 0.20* (0.068) 0.32* (0.109) 0.14 (0.082) −0.04 (0.114) 0.33* (0.096) 

1 DE = dermatitis, HH = heel horn erosion, SH = sole hemorrhage, SU = sole ulcer, PY = protein yield, CM 

= clinical mastitis, SCS = somatic cell score, NI = number of inseminations, CFI = days from calving to first 

insemination. 

*The estimate was significantly different from zero, P < 0.05. 

considered to be predisposing factors (Webster, 1993). 

Peterse (1992) notes, in addition, that hemorrhages and 

ulcers caused by improper nutrition can be regarded 

as clinical signs of mild and severe cases of laminitis, 

respectively. Thus, SU is a progression of SH. 

The high genetic correlations among the hygienerelated 

and the feed-related hoof diseases and the low 

genetic correlations between traits in different groups 

were in agreement with the findings by van der Waaij 

et al. (2005). On the contrary, Koenig et al. (2005) 

found a moderate positive genetic correlation between 

digital dermatitis and sole ulcer (0.56). Even so, the 

results indicate only partial overlap between the genetic 

components behind the hygiene-related and the feedrelated 

hoof diseases. 

The division of the hoof diseases into groups is also 

supported by the patterns of prevalence over the lactation 

period because the cows tended to be diagnosed 

with DE and HH through the entire lactation period, 

whereas the proportion of hoof-trimmed cows diagnosed 

with SH and SU was larger in the first part of the 

lactation. The former seems reasonable as the diseasecausing 

bacteria can exist all year round, and the latter 

may be caused by the rapid change from a prepartum 

diet low in energy to a postpartum diet high in energy 

that most dairy cows experience. Thus, improper 

nutrition containing high levels of rapidly fermented 

carbohydrates could be an important predisposing factor 

in this case. 

Table 5. Partial genetic correlations between pairs of hoof diseases 

conditioned on all possible pairs of the other 7 traits included in this 

study 

Trait 

Heel horn 

erosion 

Sole 

hemorrhage 

Sole 

ulcer 

Dermatitis 0.98* −0.42* −0.70* 

Heel horn erosion 0.46* 0.67* 

Sole hemorrhage 0.18 

*The estimate was significantly different from zero, P < 0.05, using 

a t-test.

The unfavorable genetic correlations between the 4 

hoof diseases and PY suggest that cows with high genetic 

merit for milk production are more predisposed to 

hoof diseases than cows with low genetic merit for milk 

production. Koenig et al. (2005) also found unfavorable 

genetic correlations between milk yield and digital dermatitis 

and sole ulcer (0.24 and 0.06). However, standard 

errors of these estimates were substantial (0.15 

and 0.12). Onyiro et al. (2008) estimated approximate 

genetic correlations between digital dermatitis and milk 

yield and fat yield on the basis of correlations between 

sire EBV adjusted for their reliabilities. Contrary to 

our study, Onyiro et al. (2008) found negative relationships 

(−0.31 and −0.43) indicating that daughters of 

sires with high genetic merit for milk yield and fat yield 

are less predisposed to digital dermatitis. 

Our results showed that the feed-related hoof diseases 

are genetically correlated to CM. The reason may be 

that improper feeding containing high levels of concentrates 

causes a decrease in the pH value of the rumen 

and possibly ruminal acidosis. The latter can provoke 

an abrupt release of toxic agents, such as lactic acid, 

endotoxins, and histamines, into the peripheral blood. 

These toxic agents cause the changes in the hooves that 

are collectively referred to as laminitis. The aftermath 

becomes visible in the sole after approximately 8 wk as 

hemorrhages or ulcers (Peterse, 1992; Webster, 1993). 

Laminitis can also be caused by a generalized toxemia 

deriving from severe inflammations such as mastitis or 

metritis, although it is a much rarer cause of laminitis 

compared with improper feeding (Webster, 1993). 

Thus, the genetic correlations between CM and SH and 

SU may be explained by the genetic capacity of the 

cows to degrade endotoxins. 

One possible explanation for the genetic correlation 

between SU and CFI is that exposure to bacterial 


Table 6. Correlations between selection index and aggregate genotype (r I,A) and selection differentials for the breeding goal traits in Euros at 

a selection intensity of 1 for scenarios I, II, and III 

Item 

Scenario 1 

I II III 

r I,A 0.83 0.91 0.92 

Selection differential for: 

dermatitis −0.0268 −0.0175 −0.0182 

heel horn erosion −0.167 −0.179 −0.169 

sole hemorrhage −0.0993 −0.0403 0.0264 

sole ulcer −0.352 −0.167 −0.0606 

protein yield 84.0 75.9 75.4 

clinical mastitis −13.1 −3.04 −2.32 

number of inseminations −6.67 −5.71 −5.69 

days from calving to first insemination −3.52 −0.966 −0.890 

1 I: the selection index contained only protein yield; II: the selection index contained protein yield, clinical mastitis, SCS, number of inseminations, 

and days from calving to first insemination; III: the selection index contained dermatitis, heel horn erosion, sole hemorrhage, sole ulcer, 

protein yield, clinical mastitis, SCS, number of inseminations, and days from calving to first insemination. 

endotoxins during the proestrous phase affects reproductive 

function in cattle negatively as it can delay 

the LH surge and the subsequent ovulation (Suzuki et 

al., 2001). Thus, the cows’ genetic capacity to degrade 

endotoxins may explain the genetic correlation between 

SU and CFI if the progressions of SH and SU are linked 

to the release of endotoxins from cows suffering low 

ruminal pH values and acidosis. 

The genetic correlations between NI and DE and 

HH were moderate and favorable in this study. On the 

contrary, Onyiro et al. (2008) found low and moderate 

approximate genetic correlations between digital dermatitis 

and calving interval and nonreturn rate after 

56 d (−0.07 and 0.48). The latter indicates an association 

(but not necessarily a causal connection) between 

digital dermatitis and greater conception rates (Onyiro 

et al., 2008). 

Partial Genetic Correlations 

The partial genetic correlation between DE and HH 

was higher than the genetic correlation between these 

traits (0.98 vs. 0.87). This implies that the other 7 

traits are so-called suppressor variables, meaning that 

the contributions from the other traits to the correlation 

are blurring a strong, unmediated relationship. 

According to this finding, DE and HH are influenced 

by all but the same genes when the other traits were 

held constant. The partial genetic correlations between 

DE and SH and SU were lower than the genetic correlations 

between these traits. When the other 7 traits were 

held constant, DE and SH were influenced by relatively 

more genes that affected DE in one direction and SH in 

the opposite direction. The same holds true of DE and 

SU. The partial genetic correlations between HH and 

SH and SU were higher than the genetic correlations 


9

10 

between these traits. That is to say, the animals seemed 

to have genetic predispositions for both HH and SH 

that are independent of the other 7 traits. The same 

is true for HH and SU. The partial genetic correlation 

between SH and SU was lower than the genetic correlation 

between these traits (0.18 vs. 0.73). This result 

implies that the number of genes influencing both SH 

and SU is relatively smaller when the other traits were 

held constant. 

Theoretically, threshold models are more appropriate 

to use for the analyses of ordered categorical traits with 

low heritability and low incidence (Mrode, 2005). That 

is to say, threshold models may have outperformed the 

linear models we decided to use for the analyses of the 4 

hoof diseases, CM, and NI in this study. Mäntysaari et 

al. (1991) compared the efficiency of a threshold model 

with the efficiency of a linear model in a multi-trait 

situation with 2 binary traits. They found that the 2 

models performed equally well with regard to the estimates 

of the genetic correlation. The estimates of the 

heritabilities and the residual correlation were underestimated 

and depended on the incidence when a linear 

model was used (Mäntysaari et al., 1991). However, it 

was possible to correct for the downward bias in the 

heritability estimates by transforming the estimates to 

the underlying continuous scale using a formula from 

Dempster and Lerner (1950). When a threshold model 

was used and the incidence was low (5%), the estimates 

of the residual correlation were also biased although 

not as much as the linear model estimates (Mäntysaari 

et al., 1991). As the genetic correlations were considered 

to be more important than the heritabilities and 

the residual correlations, and the prevalence of most 

of the diseases was low, we decided to analyze the categorical 

traits by means of linear models. Furthermore, 

linear models are applied in the joint Nordic genetic 

evaluation of dairy cattle, and we wanted to mimic this 

situation. 

Heritabilities 

The low heritability estimates in this study may 

be explained by the relatively few cases of hoof diseases 

and the application of linear models as mentioned 

above. Another reason may be the large influence of 

environmental factors such as hygiene level, number 

of disease-causing bacteria, and feed composition. The 

heritabilities from other recent studies were transformed 

to the underlying continuous scale by means of the formula 

from Dempster and Lerner (1950) to compare the 

estimates directly (Table 7). The transformed heritability 

estimates for various forms of dermatitis and heel 

horn erosion ranged from 0.03 to 0.20 in other recent 

studies and the transformed heritability estimates 


BUCh eT Al. 

for DE and HH in this study were within that range. 

However, direct comparisons of the various findings are 

difficult because trait definitions differ between studies. 

In addition, differences may exist between breeds. The 

heritability estimate for SH was lower than the estimate 

found by van der Waaij et al. (2005) even if the 

estimates were corrected for incidence of disease. The 

transformed heritability estimate for SU was higher 

than the estimates on the underlying continuous scale 

from Koenig et al. (2005) and van der Waaij et al. 

(2005). 

Prevalence 

Almost 40% of the cows suffered from at least one 

hoof disease at the first hoof trimming after first calving. 

This figure is considerably lower than the prevalence 

found by Sogstad et al. (2005) and van der Waaij 

et al. (2005). As in this study, each cow was recorded 

once during the time periods of their studies. However, 

their analyses were based on hoof trimming records 

from different lactations (Sogstad et al., 2005; van der 

Waaij et al., 2005). 

Thirteen percent of the hoof-trimmed cows were 

trimmed during the first month after calving. It is 

likely that hoof lesions of metabolic origin would not 

yet be visible as hemorrhages and ulcers in the sole or 

wall at that time. This may have affected the data and 

the interpretations of the results. In spite of this, the 

cows tended to be diagnosed with SH and SU in the 

first part of the lactation. 

Effect of Hoof Trimming Records on Accuracy 

of Selection and Selection Differentials 

The inclusion of hoof trimming records in the selection 

index increased accuracy of selection over the 

scenarios without hoof trimming records. However, the 

disparities between the results of scenarios II and III 

were smaller than the disparities between the results of 

scenarios I and II. The reason may be that the heritabilities 

of the hoof diseases are low, the genetic correlations 

between the hoof diseases and the other traits are 

low to moderate, and the economic value of the trait 

group hoof health is low compared with the economic 

values of the other trait groups. 

The inclusion of hoof diseases in the selection index 

reduced not only the genetic decline in most hoof diseases 

but also the genetic decline in CM, NI, and CFI. 

The reason may be that all genetic correlations between 

the functional traits and protein yield were unfavorable 

and most genetic correlations among the functional 

traits were favorable. However, the genetic deterioration 

of DE was worsened slightly from −0.0175 € to

−0.0182 € when information about the hoof diseases 

was included in the selection index. Moreover, when 

information about CM, SCS, NI, and CFI was included 

in the selection index, the genetic deterioration of HH 

worsened slightly from −0.167 € to −0.179 €. One explanation 

may be that the genetic correlations between 

the hygiene-related hoof diseases and the traits related 

to udder health are low and 2 are slightly negative. 

In addition, the economic value of the trait group udder 

health is large compared with the trait group hoof 

health. 

Koenig et al. (2005) showed, in a simulation study 

where SU was the only trait in the aggregate genotype, 

that the accuracy of a hoof health index containing 

records on foot angle was improved from 0.239 to 0.731 

when records on SU were added to the index. We found 

in this study that the genetic deterioration of the trait 

group hoof health was reduced from −0.404 to −0.221 

when hoof trimming records on DE, HH, SH, and SU 

were added to the selection index. 

The simulation results showed a genetic decline in 

hoof health even though hoof trimming records were included 

in the selection index. This is a function of both 

the genetic parameters and the economic values of hoof 

health and the other functional traits. The economic 

value of hoof health in this study was based on the 

economic value of feet and legs in the current sub-index 

resistance against diseases other than mastitis in the 

Nordic breeding goal. The prerequisites for the economic 

value of feet and legs (e.g., the phenotypic levels 

of the diseases) were based on records of veterinary 

treatments of feet and leg diseases and may differ from 

prerequisites based on hoof trimming records. Thus, to 

succeed with selection for improved hoof health it is 

advisable to update the economic value of hoof health. 

Another explanation for the genetic decline in hoof 

health may be that the simulated breeding goal con- 


Table 7. Heritability estimates (h 2 ) for hoof diseases achieved in other recent studies of Holstein dairy cattle with standard errors of the 

2 

estimates (SE) in parentheses and heritability estimates transformed to the underlying continuous scale ( hund Reference Model 1 

Cows, 

n Trait 2 

Incidence, 

% 

Koenig et al., 2005 Linear logistic AM 5,634 DD and HH 13.2 0.073 (0.009) 

SU 16.1 0.086 (0.006) 

Onyiro et al., 2008 Linear AM 93,391 DD 12.1 0.011 (0.003) 0.03 

van der Waaij et al., 2005 Linear SM 21,611 DD 21.7 0.10 (0.02) 0.20 

ID and HH 38.7 0.05 (0.01) 0.08 

SH 39.9 0.08 (0.02) 0.13 

SU 5.4 0.01 (0.01) 0.04 

1 AM = animal model; SM = sire model. 

2 DD = digital dermatitis, HH = heel horn erosion, SU = sole ulcer, ID = interdigital dermatitis, SH = sole hemorrhage. 

3 The linear model estimates were transformed by means of the formula from Dempster and Lerner (1950). 

tained fewer functional traits than the Nordic breeding 

goal. It is likely that the favorable genetic correlations 

that often exist among functional traits will assist in 

selection for improved hoof health. 

The economic values in the simulated breeding goal 

were based on the current economic values per index 

unit in the Nordic breeding goal and subsequently 

converted into Euros per unit by means of the genetic 

and phenotypic parameters found in this study and the 

study by Buch et al. (2010). Some of the heritabilities 

for the udder health and the female fertility traits used 

in this study are lower than the heritabilities used by 

Nordic Cattle Genetic Evaluation (NAV, 2010). For 

that reason, the relative ratios between the economic 

values differ from the relative ratios between the economic 

values in the Nordic breeding goal. Also, as a 

consequence of the lower heritabilities, and therefore 

lower reliabilities, the selection index is less balanced 

and more based on improving milk production than the 

Nordic total merit index. Thus, the effect of including 

hoof trimming records on the accuracy of the selection 

index may be an underestimate compared with the effect 

that could be obtained by Nordic Cattle Genetic 

Evaluation. 

CONCLUSIONS 

The results of this study indicated that the hygienerelated 

hoof diseases on the one hand and the feedrelated 

hoof diseases on the other hand are only partly 

influenced by the same genes. The 2 groups of hoof diseases 

showed different patterns of genetic correlations 

to udder health and female fertility, but both groups 

were unfavorably correlated to milk production. The 

results of the simulation study indicated that inclusion 

of hoof diseases in the selection index will not only 

reduce the genetic decline in resistance to hoof diseases 

) 

h 2 

(SE) 

2 3 

hund 11 

Journal of Dairy Science Vol. 94 No. 3, 2011

12 

but also be favorable for other functional traits and 

improve overall genetic merit. 

ACKNOWLEDGMENTS 

This research was financed by a grant from the 

Danish Ministry of Science, Technology and Innovation 

(Copenhagen, Denmark) and the Danish Cattle 

Federation (Skejby, Denmark). The authors thank the 

Swedish Dairy Association (Stockholm, Sweden) for 

providing data and especially Kjell Johansson for helpful 

information about the Swedish genetic evaluation 

system. 

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Paper III 

Genomic selection strategies in breeding programs: Strong positive interaction 

between application of genotypic information and intensive use of young bulls 

Line Hjortø Buch, Morten Kargo Sørensen, Peer Berg, Louise Dybdahl Pedersen 

& Anders Christian Sørensen 

Submitted to Journal of Animal Breeding and Genetics

Genomic selection strategies in breeding programs: Strong 

positive interaction between application of genotypic information 

and intensive use of young bulls 

Buch, L.H. 1, 2 , Sørensen, M.K. 1, 2 , Berg, P. 2 , Pedersen, L.D. 2 & Sørensen, A.C. 2 

Summary 

1 Knowledge Centre for Agriculture, Agro Food Park 15, 8200 Aarhus N, Denmark 

2 Department of Genetics and Biotechnology, Faculty of Agricultural Sciences, 

Aarhus University, P.O. Box 50, 8830 Tjele, Denmark 

We tested the following hypotheses: 1) breeding schemes with genomic selection are superior 

to breeding schemes without genomic selection regarding annual genetic gain of the aggregate 

genotype (∆GAG), annual genetic gain of the functional traits and rate of inbreeding per 

generation (∆F), 2) a positive interaction exists between the use of genotypic information and 

a short generation interval on ∆GAG and 3) the inclusion of an indicator trait in the selection 

index will only improve ∆GAG marginally if genotypic information about the breeding goal 

trait is known. We examined four breeding schemes with or without genomic selection and 

with or without intensive use of young bulls using stochastic simulations. The breeding goal 

consisted of a milk production trait and a functional trait. The two breeding schemes with 

genomic selection resulted in higher ∆GAG, greater contributions of the functional trait to 

∆GAG and lower ∆F than the two breeding schemes without genomic selection. Thus, the use 

of genotypic information may lead to more sustainable breeding schemes. In addition, a short 

generation interval increases the effect of using genotypic information on ∆GAG. Hence, a 

breeding scheme with genomic selection and with intensive use of young bulls (a turbo 

scheme) seems to offer the greatest potential. The third hypothesis was disproved as inclusion 

of genomically enhanced breeding values (GEBV) for an indicator trait in the selection index 

increased ∆GAG in the turbo scheme. Moreover, it increased the contribution of the functional 

55

Paper III 

trait to ∆GAG and it decreased ∆F. Thus, indicator traits may still be profitable to use even 

though GEBV for the breeding goal traits are available. 

Keywords: Genomic selection, breeding program, accuracy, generation interval 

Introduction 

Utilization of genotypic information in animal breeding has become a comprehensive and 

highly prioritized research area in recent years. So far the main focus has been on the 

development of methods for estimating genomically enhanced breeding values (GEBV) based 

on genotypic, phenotypic and pedigree information. The next step is to study the effects of 

genomic selection on future breeding schemes. On this basis, we would like to contribute to 

the understanding of the potential benefits of different selection strategies in dairy cattle 

breeding schemes with genomic selection. 

In the past, optimisation of dairy cattle breeding schemes was equivalent to maximising the 

annual genetic gain of the aggregate genotype. This is still an important issue but it is now 

generally accepted that breeding schemes should also seek to avoid negative genetic trends in 

the breeding goal traits in order to be sustainable. This can be achieved by setting up a 

recording system that enables response in all breeding goal traits and detection of undesirable 

changes in animal health and welfare (Fimland and Oldenbroek, 2007). Other characteristics 

of a sustainable breeding scheme are maintenance of livestock resources and use of selection 

strategies, which secure a sufficiently large effective population size to keep the rate of 

inbreeding below 1% per generation (Fimland and Oldenbroek, 2007). 

One of the challenges when striving to maximize the genetic gain is the trade-offs between the 

parameters contributing to the annual response to selection. That concerns accuracy of 

selection and generation interval in particular. These opposing factors occur because most 

functional traits have low heritabilities and nearly all traits of economic importance are 

expressed only in females. To achieve accurate estimated breeding values (EBV) based on 

phenotypic and pedigree information, progeny testing has traditionally been employed at the 

expense of postponing selection decisions. Nicholas and Smith (1983) suggested an 

alternative to the conventional progeny-testing scheme that included multiple ovulation and 

embryo transfer (MOET) and intensive use of young animals, i.e. no progeny testing. The aim 

of this juvenile scheme was to increase the annual response to selection by reducing the 

generation interval and tolerating less accuracy at the time of selection. This suggestion has 

56

Paper III 

only been used sparingly in practice because it involves a higher risk of selecting sires of sons 

that turn out to be inferior and can result in high rates of inbreeding. However, MOET has 

been included in many conventional progeny-testing schemes. 

Genomic selection creates an opportunity to modify the above-mentioned breeding schemes 

because direct genomic values (DGV) and GEBV are characterized by moderate to high 

accuracies and can be predicted on the new-born selection candidates. For that reason, we 

expect the trade-off between accuracy of selection and generation interval to be weaker and, 

as a result, the selection response per year to increase in breeding schemes using DGV or 

GEBV. Schaeffer (2006) demonstrated that a dairy cattle breeding scheme where genomic 

selection is applied and active sires are used for breeding purposes as soon as they are 

sexually mature could result in a doubling of the genetic gain compared to a conventional 

progeny-testing scheme. Since selection response per year is proportional to the accuracy of 

selection and inversely proportional to the generation interval, we expect that the increase in 

genetic gain is the result of a positive interaction between the use of GEBV and a short 

generation interval. In other words, we expect that the increase in genetic gain is greater than 

the sum of the increases in genetic gain caused by a higher accuracy of selection and a shorter 

generation interval. 

By selecting on GEBV instead of EBV it may become relatively easier to improve the 

functional traits in the breeding goal and to obtain a more balanced composition of the genetic 

gain. This expectation is based on the fact that the accuracy of DGV is influenced by the 

reliability of the EBV rather than the heritability of the trait if the reference population 

consists of proven bulls (Hayes et al., 2009). Thus, the difference in accuracy of DGV 

between traits with a low heritability and a high heritability can be relatively small if the 

marker effects are estimated on the basis of a large number of well-proven bulls (Su et al., 

2010). Dekkers (2007) used deterministic simulations to study the impact of genotypic 

information on response to selection in a pig breeding scheme using multi-trait selection. His 

results showed that selection on GEBV instead of EBV resulted in higher genetic gain of the 

aggregate genotype, of which most of the gain resulted from higher genetic gain of the less 

heritable trait. This would be in accordance with the trend in dairy cattle breeding as several 

breeding companies worldwide have shifted to broad breeding goals in an attempt to improve 

health, reproduction and longevity in addition to milk production (Miglior et al., 2005). This 

trend will be supported by the implementation of genomic selection. 

57

Paper III 

Keeping the rate of inbreeding less than 1% per generation is a challenge since the effects of 

intensity of selection on the rate of inbreeding and the annual genetic gain are oppositely 

directed. Thus, it is often necessary to weigh these two characteristics against each other in 

order to control the rate of inbreeding. In a juvenile breeding scheme without genomic 

selection and without progeny testing it is not possible to differentiate between full sibs 

because the EBV of the selection candidates are predicted as the mean of the EBV of their 

parents. That is, if the EBV of the full sibs are high enough then all full sibs will be selected 

by truncation selection, which leads to an increase in the rate of inbreeding. Progeny testing 

decreases the rate of inbreeding because the accuracy of the Mendelian sampling term 

increases when phenotypic information on progeny is used. The rate of inbreeding per 

generation may decrease even further if GEBV are used as a pre-selection criterion in a 

progeny-testing scheme because the Mendelian sampling term of each selection candidate can 

be estimated with greater accuracy at an earlier point in time. However, if GEBV are used as a 

selection criterion per se in a breeding scheme without progeny testing then it is difficult to 

anticipate if the rate of inbreeding will be higher or lower than the rate of inbreeding in a 

conventional progeny-testing scheme. 

Indirect selection is selection applied to some trait other than the one it is desired to improve 

(Falconer and Mackay, 1996) and has been common practice in dairy cattle breeding schemes 

for many years. By way of example, somatic cell score is used as an indicator trait for mastitis 

resistance in several countries (Miglior et al., 2005). The most effective way to use an 

indicator trait is in combination with the breeding goal trait, so that the indicator trait 

contributes additional information about the true breeding value of the animal for the breeding 

goal trait (Falconer and Mackay, 1996). However, the additional effect of the indicator trait on 

response to selection may be insignificant because of a moderate to high accuracy of the 

breeding goal trait when genotypic information is known. For these reasons we expect that the 

effect of including an indicator trait in the selection index on the annual genetic gain is of no 

consequence in practice if GEBV for the breeding goal trait are available. 

The objectives of this study were to test the following hypotheses: 1) breeding schemes with 

genomic selection are superior to breeding schemes without genomic selection with regard to 

annual genetic gain of the aggregate genotype, annual genetic gain of the functional traits in 

the breeding goal and rate of inbreeding per generation, 2) there is a positive interaction 

between the use of GEBV and a short generation interval on annual genetic gain of the 

58

Paper III 

aggregate genotype and 3) the inclusion of an indicator trait in the selection index will only 

improve annual genetic gain of the aggregate genotype marginally if genotypic information 

about the breeding goal trait is known. 


In order to test the first two hypotheses we examined and compared the following four 

scenarios resembling breeding schemes with or without genomic selection and with or 

without progeny testing. 

The conventional scheme: This scenario was thought to reflect a conventional progeny- 

testing scheme without genomic selection. Thus, young bulls were selected for progeny 

testing on the basis of parent average EBV and progeny testing results formed the basis of the 

selection of active sires. The scenario was taken as a reference scenario. 

The juvenile scheme: Neither genomic selection nor progeny testing results were applied in 

the selection of active sires in this scenario. Thus, active sires were selected on the basis of 

parent average EBV and used for breeding purposes as soon as they were sexually mature. 

The scenario was used to study the effect of a short generation interval. 

The pre-selection scheme: In this scenario young males and females were selected for 

genotyping on the basis of parent average GEBV. The young genotyped bulls were selected 

for progeny testing on the basis of GEBV and progeny testing results formed the basis of the 

selection of active sires. The scenario was used to study the effect of using GEBV. 

The turbo scheme: Young males and females were selected for genotyping on the basis of 

parent average GEBV in this scenario. Active sires were selected on the basis of GEBV and 

used for breeding purposes as soon as they were sexually mature. The scenario was used to 

study if an interaction between the use of GEBV and a short generation interval occurs. 

To test the third hypothesis all scenarios were repeated but this time phenotypic information 

about an indicator trait was included in the selection index. Moreover, the pre-selection 

scheme and the turbo scheme were repeated with GEBV for the indicator trait included in the 

selection index. These six scenarios will be designated indicator schemes in the text below. 

All scenarios were tested using the stochastic simulation program ADAM (Pedersen et al., 

2009), and each scenario covered a thirty-year period and was replicated 100 times. 

59

Population 

Paper III 

The simulated population resembled the dispersed breeding nucleus of a dairy cattle 

population. A base population of unrelated animals was sampled and distributed among the 

age classes one to five years for females and one to six years for males. The nucleus consisted 

of 20 000 cows distributed equally among 200 herds. Within each herd, 100 females were 

selected for mating based on EBV, or GEBV if available. Out of these, the 400 best females 

across all herds were flushed and each flush resulted in five calves. The remaining females 

produced one viable offspring each. The sex ratio among the offspring was 1:1 in all cases. 

The selection of females took place every year, and all selected females were between one 

and five years old. 

In schemes with genomic selection, 2 000 one-year-old males and 2 000 one-year-old females 

were genotyped each year. When bull calves were selected for genotyping, bull calves born as 

a result of MOET had priority. However, un-used genotyping capacity was spent on bull 

calves born without use of MOET. 

In schemes with progeny testing, 200 one-year-old bulls were progeny tested each year. These 

were selected by truncation. 

The 30 best sexually mature bulls were selected by truncation every year and used equally for 

random mating among all females in the nucleus, thus producing 667 offspring each. In 

schemes with progeny testing, active sires were at least five years old before they were used 

for breeding purposes and in schemes without progeny testing active sires were at most four 

years old. Thus, by design, the generation interval becomes longer in the conventional and the 

pre-selection schemes than in the juvenile and the turbo schemes. 

All unselected candidates as well as animals above age six were culled but 5 000 doses of 

semen from each bull calf selected for progeny testing were stored. In addition, 15% of all 

animals between one and six years were randomly culled each year to reflect involuntary 

culling before decisions on selection were made. 

To keep inbreeding at a reasonable level we included the restrictions that each bull could at 

the maximum be the sire of 20 young bulls per year and 40 young bulls in total. Furthermore, 

each bull could at the maximum be the sire of 6 active sires per year and 9 active sires in total. 

Sampling of true breeding values and phenotypic values 

The number of traits varied according to the scenario. In other words, two (three) traits were 

simulated in (indicator) schemes without genomic selection and four (five or six) traits were 

60

Paper III 

simulated in (indicator) schemes with genomic selection. The following description 

corresponds to the pre-selection indicator scheme. True breeding values for the milk 

production trait, the functional trait and the indicator trait were simulated for all animals. For 

all traits, phenotypic values were sampled for all females completing first lactation and 

daughter yield deviations (DYD) were sampled directly for all progeny tested bulls at the age 

of five years on the basis of 150 daughters with registrations for the production trait and the 

indicator trait and 135 daughters with registrations for the functional trait. Direct genomic 

values (DGV) for the milk production trait, the functional trait and the indicator trait were 

sampled for all genotyped animals without simulating chromosomes, genes, or markers. This 

method, which we call pseudo-genomic selection, is comparable to the method developed by 

Dekkers (2007). 

In order to simulate true breeding values, phenotypic values and DGV the following genetic 

and environmental parameters were used: 

⎡ 1 − 0. 

30 − 0. 

2 0. 

71 − 0. 

213 − 0. 

142⎤ 

⎢ 

⎥ 

⎢ 

− 0. 

30 1 0. 

65 − 0. 

213 0. 

71 0. 

462 

⎥ 

⎢ − 0. 

2 0. 

65 1 − 0. 

142 0. 

462 0. 

71 ⎥ 

G = ⎢ 

⎥ , 

⎢ 0. 

71 − 0. 

213 − 0. 

142 1 − 0. 

151 − 0. 

101⎥ 

⎢− 

0. 

213 0. 

71 0. 

462 − 0. 

151 1 0. 

328 ⎥ 

⎢ 

⎥ 

⎢⎣ 

− 0. 

142 0. 

462 0. 

71 − 0. 

101 0. 

328 1 ⎥⎦ 

⎡ 2. 

33 

⎢ 

⎢ 

0. 

748 

⎢0. 

466 

R = ⎢ 

⎢ 0 

⎢ 0 

⎢ 

⎣ 0 

0. 

748 

24 

1. 

97 

0 

0 

0 

0. 

466 

1. 

97 

6. 

14 

0 

0 

0 

0 

0 

0 

0. 

01 

0 

0 

0 

0 

0 

0 

0. 

01 

0 

0 ⎤ 

0 

⎥ 

⎥ 

0 ⎥ 

⎥ 

0 ⎥ 

0 ⎥ 

⎥ 

0. 

01⎥⎦ 

The genetic and environmental (co)variance matrices, G and R, are six-by-six matrices in the 

pre-selection indicator scheme. The first three traits are the milk production trait, the 

functional trait and the indicator trait and the last three traits are the DGV for the milk 

production trait, the functional trait and the indicator trait. However, the size of G and R 

varied in accordance with the scenario under study. The genetic and environmental 

parameters were computed in accordance with Dekkers (2007) and based on the assumed 

heritabilities, genetic correlations and accuracies of DGV. 

61

Paper III 

The heritabilities of the milk production trait and the functional trait are 0.30 and 0.04 and the 

phenotypic correlation between the traits is 0.05. The heritability of the indicator trait is 0.14 

and the phenotypic correlations to the milk production trait and the functional trait are 0.07 

and 0.22. Each DGV have a heritability of 0.99 and a genetic correlation to the true breeding 

value for the observed trait of 0.71. The heritability of the DGV is the repeatability of the 

marker information, and the genetic correlation implies a reliability of 50%. A heritability of 

0.99 (instead of one) is used to ensure that R is positive definite. 

For each animal i in the base population, a vector of true breeding values (tbvi) was calculated 

for all simulated traits using the following equation: 

' 

tbv i = L × 

' 

where L is the Cholesky decomposition of the genetic (co)variance matrix G, and r1 

is a 

vector of random numbers from a standardized normal distribution. 

In later generations tbvi was simulated as: 

' 

tbv = 0. 

5× 

( tbv + tbv ) + 0. 

5× 

( 1− 

( F i sire + Fi 

dam ) / 2) 

× ( L × r ) 

i 

i(sire) 

i(dam) 

r 

1 

( ) ( ) 

1 

where and F are the inbreeding coefficients of the sire and the dam. 

F i(sire) 

i(dam) 

For each female i, a vector of observations (obsi) for all simulated traits, i.e. both observed 

traits and DGV, was calculated as: 

' 

obs i = tbv i + C × 

' 

where C is the Cholesky decomposition of the environmental (co)variance matrix R, and r2 

is a vector of random numbers from a standardized normal distribution. 

For genotyped bulls, obsi for the DGV were simulated by means of the same equation as for 

females. For progeny tested bulls, obsi for the observed traits were simulated as twice the 

DYD using the following equation: 

obs i i 

1 

2 

' 

' 

= tbv + 2 × ( D× 

L × r + C × r ) × N 

2 

where D is a diagonal matrix with diagonal elements equal to 0. 

5 + 0. 

25× 

( 1− 

h ) , where h 2 

is the heritability of the trait in question, and N is a diagonal matrix containing ones divided 

by the square root of the number of daughters with registrations for each of the traits. 

Breeding goal and estimated breeding values 

The breeding goal consisted of the milk production trait and the functional trait. The traits are 

assumed to represent all milk production traits and all functional traits, and the economic 

62 

r 

2

Paper III 

values are €83 and €82 per genetic standard deviation. In consequence of this the standard 

deviation of the breeding goal is 97.62. These economic values were determined so that the 

correlation between the simulated breeding goal and the milk production trait is equal to the 

correlation between the Nordic total merit index and the milk production index. The breeding 

goal remained unchanged in all scenarios. 

The milk production trait and the functional trait were included in the selection index in all 

scenarios. In the indicator schemes, phenotypic observations of the indicator trait or 

phenotypic observations and DGV for the indicator trait were included in the selection index 

as information traits without economic values. 

Breeding values were predicted using a conventional multivariate best linear unbiased 

prediction (BLUP) model and were comparable to GEBV with back-blending in schemes with 

genomic selection: 

y = Xb + Za + e 

where y is a vector of phenotypic observations for cows, 2 times the DYD for progeny tested 

bulls, and DGV for genotyped animals, b is a vector of fixed herd-year-season effects, a is a 

vector of random animal effects, e is a vector of random residual effects, X and Z are 

incidence matrices relating phenotypic observations to fixed effects and random animal 

effects. The herd-year-season effect was modelled by allocating animals to one of four 

seasons within herd and year. For progeny tested bulls all DYD were assigned to the same 

herd-year-season effect within year. 

The following (co)variance structure was used to predict breeding values: 

⎛a 

⎞ ⎛ ⎡G ⊗ A 

⎜ ⎟ ~ N ⎜ 

0; 

⎢ 

⎝e 

⎠ ⎝ ⎣ 0 

0 ⎤⎞ 

⎥ 

⎟ 

* 

R ⎟ 

⎦⎠ 

where the matrix A was the numerator relationship matrix among all animals, and the matrix 

G was the additive genetic (co)variance matrix for animal effects, as previously defined. The 

matrix R * was defined as: 

R 

* 

⎡ r1, 

1W1 

⎢ 

⎢ M 

= ⎢ ½ 

ri 

, 1Wi 

W1 

⎢ 

⎢ M 

⎢ ½ 

⎣rn, 

1Wn 

W1 

½ 

½ 

L 

O 

L 

r 

1, 

i 

r 

n, 

i 

W 

r 

i. 

i 

W 

½ 

1 

W 

½ 

n 

63 

W 

i 

W 

½ 

i 

½ 

i 

L 

O 

L 

r 

1, 

n 

r 

i, 

n 

r 

W 

W 

n, 

n 

½ 

1 

M 

½ 

i 

M 

W 

W 

W 

n 

½ 

n 

½ 

n 

⎤ 

⎥ 

⎥ 

⎥ 

⎥ 

⎥ 

⎥ 

⎦

Paper III 

where the matrix Wi is a diagonal matrix containing ones for cows and weights for bulls for 

trait i. The weights are a function of the variance of twice the DYD and were derived as the i th 

diagonal element in the following matrix: 4(DGD + R)NNR -1 . The matrix Wi is used instead 

of an identity matrix to include the bulls with DYD in the same model as the females with one 

single observation per trait. ri,j is element in the i th row and j th column in R that is the 

(co)variance matrix for residual effects, as previously defined. The variance components used 

to predict breeding values were the same as those used to simulate the data. The breeding 

value prediction was carried out using the DMU package (Madsen and Jensen, 2008). 

Data analysis 

Data from year ten to year thirty was used in the analyses. Total genetic merit, genetic merit 

for the milk production trait and the functional trait and the inbreeding coefficient were 

monitored annually using the average over all new born animals, and regression coefficients 

of each of the four response parameters were estimated within each replicate. Annual genetic 

gain of the aggregate genotype, annual genetic gain of the milk production trait and the 

functional trait and rate of inbreeding per year were computed by regressing true breeding 

values and inbreeding coefficients on year of birth in years 10 to 30 averaged over 100 

replicates. The variance of the annual genetic gain was calculated as the variance of the 

regression coefficients across replicates. The realized accuracy of the index was the 

correlation between the selection index and the aggregate genotype on selection candidates 

before selection. Both the realized accuracy of the index and the generation interval were 

averaged over year 10 to 30 and 100 replicates. The rate of inbreeding per generation was the 

product of the generation interval and the rate of inbreeding per year within replicate and 

averaged over 100 replicates. The genetic superiority of the selected candidates is the product 

of the intensity of selection, the realized accuracy of the index, and the genetic standard 

deviation. Standard errors of the mean were calculated for each of the response parameters 

within each scenario. Differences between scenarios were tested using t-tests and were 

defined as significantly different from each other when P < 0.05. 

Results 

Annual genetic gain 

The annual genetic gain of the aggregate genotype was €22.38 in the conventional scheme 

(Table 1). In the juvenile scheme, the pre-selection scheme, and the turbo scheme, annual 

64

Paper III 

genetic gain of the aggregate genotype increased by 9, 29 and 102% compared to the 

conventional scheme. 

Table 1. Annual genetic gain of the aggregate genotype in euros (∆GAG) and annual genetic gain of 

the milk production trait and the functional trait in genetic standard deviations (∆GMP and ∆GFU) 

averaged over year 10 to 30 and 100 replicates with standard errors in brackets. 

Scheme Progeny testing 

GEBV 1 

∆GAG 2 

Conventional + - 22.38 (0.093) 

Juvenile - - 24.44 (0.212) 

Pre-selection + + 28.89 (0.062) 

Turbo - + 45.11 (0.117) 

∆GMP 2 

∆GFU 2 

0.178 (0.001) 0.093 (0.002) 

0.192 (0.003) 0.107 (0.003) 

0.201 (0.001) 0.150 (0.001) 

0.294 (0.002) 0.254 (0.002) 

1 GEBV = genomically enhanced breeding values for the milk production trait and the functional trait. 

2 All means within the column differ (P < 0.05). 

The annual genetic gain of the milk production trait was 0.178 genetic standard deviations in 

the conventional scheme (Table 1). Using the juvenile scheme, the pre-selection scheme or 

the turbo scheme instead of the conventional scheme increased the annual genetic gain of the 

milk production trait by 7, 13 and 65%. 

The annual genetic gain of the functional trait was 0.093 genetic standard deviations in the 

conventional scheme (Table 1). In the juvenile scheme, annual genetic gain of the functional 

trait increased by 15% compared to the conventional scheme. Even higher increases in the 

annual genetic gain of the functional trait were found when the pre-selection scheme or the 

turbo scheme was used instead of the conventional scheme (62 and 173%). 

Rate of inbreeding 

The rate of inbreeding was 1.15% per generation in the conventional scheme (Table 2). The 

rate of inbreeding increased by 122% when the juvenile scheme was compared to the 

conventional scheme whereas the rate of inbreeding decreased by 58 and 36% when the pre- 

selection scheme and the turbo scheme were compared to the conventional scheme. 

65

Paper III 

Table 2. Rate of inbreeding in percentage per generation (∆F) and generation interval in years (GI) 

averaged over year 10 to 30 and 100 replicates with standard errors in brackets, and variance of the 

annual genetic gain between the replicates (V∆G). 

Scheme 

Progeny testing GEBV 1 

Conventional + - 1.15 (0.026) 4.74 (0.002) 

∆F 2 

Juvenile - - 2.55 (0.066) 

Pre-selection + + 0.48 (0.008) 

Turbo - + 0.74 (0.016) 

GI 2 

2.67 (0.004) 

4.61 (0.002) 

2.38 (0.001) 



The four breeding schemes fell into two groups with regard to the generation interval as the 

generation interval was more than four years in the schemes with progeny testing and less 

than three years in the schemes without progeny testing (Table 2). 

The variance of the annual genetic gain between the replicates (V∆G) was 0.86 in the 

conventional scheme (Table 2). In the juvenile and turbo schemes, V∆G increased by 423 and 

58% whereas it decreased by 55% in the pre-selection scheme. 

Realized accuracy 

The realized accuracy of the index increased between 76 and 110% for young bulls when 

breeding schemes with genomic selection were compared to breeding schemes without 

genomic selection (Table 3). The realized accuracy of the index decreased between 19 and 

47% for active sires when breeding schemes without progeny testing were used instead of 

breeding schemes with progeny testing. Using the breeding schemes with genomic selection 

instead of the breeding schemes without genomic selection increased the realized accuracy of 

the index between 18 and 59% for production dams. The realized accuracies for bull dams 

and production dams were not significantly different from each other within breeding 

schemes. 

66 

V∆G 

0.86 

4.50 

0.39 

1.36

Paper III 

Table 3. Correlation between selection index and aggregate genotype for the four selection paths 

averaged over year 10 to 30 and 100 replicates with standard errors in brackets. 

Scheme 

PT 1 GEBV 2 Young bulls 3 

Conventional + - 0.29 (0.004) 

Juvenile - - 0.34 (0.006) 

Pre-selection + + 0.61 (0.002) 

Turbo - + 0.60 (0.002) 

Active sires 3 

0.83 (0.002) 

0.45 (0.008) 

0.85 (0.003) 

0.67 (0.004) 

Production dams 3 

0.34 (0.003) 

0.39 (0.005) 

0.46 (0.002) 

0.54 (0.002) 

Bull dams 3 

0.35 (0.003) 

0.41 (0.005) 

0.49 (0.002) 

0.57 (0.002) 

1 PT = progeny testing. 



Genetic superiority 

The genetic superiority of the active sires was higher than the genetic superiority of the bull 

dams in the conventional scheme as expected (Table 4). This implies that the product of the 

intensity of selection and the accuracy of selection, which we call the selection emphasis, was 

on the male path of the pedigree. On the contrary, the selection emphasis was on the female 

path of the pedigree when the juvenile scheme and the turbo scheme were used because the 

genetic superiority of the bull dams was higher than the genetic superiority of the active sires. 

Finally, the genetic superiorities of the active sires and the bull dams were not significantly 

different from each other in the pre-selection scheme. However, the total genetic superiority 

of the males across both selection stages was higher than the total genetic superiority of the 

females in all scenarios due to higher selection intensity of male selection. 

Table 4. Genetic superiority of the selected candidates in euros for the four selection paths averaged 

over year 10 to 30 and 100 replicates with standard errors in brackets. 

Scheme 

PT 1 GEBV 2 Young bulls 3 

Conventional + - 61.6 (1.0) 

Juvenile - - 71.5 (1.4) 

Pre-selection + + 85.0 (0.5) 

Turbo - + 86.6 (0.5) 

Active sires 3 

162.1 (1.7) 

58.1 (2.4) 

150.5 (1.9) 

108.4 (1.6) 

Production dams 3 

12.1 (0.1) 

14.1 (0.2) 

14.8 (0.1) 

21.4 (0.2) 

Bull dams 3 

80.9 (1.3) 

90.5 (1.6) 

149.2 (0.6) 

166.6 (0.9) 

1 PT = progeny testing. 


3 All means differ (P < 0.05) except the genetic superiority of the selected candidates for active sires 

and bull dams in the pre-selection scheme. 

67

Effects of an indicator trait 

Paper III 

The annual genetic gain of the aggregate genotype increased by 1.7 and 1.3% when 

phenotypic information about the indicator trait was included in the selection index of the 

conventional indicator scheme and the pre-selection indicator scheme (Table 5). The increases 

were due to higher realized accuracies of the indices (results not shown). Inclusion of GEBV 

for the indicator trait in the selection index increased annual genetic gain of the aggregate 

genotype in the pre-selection indicator scheme and the turbo indicator scheme by 1.5 and 

2.5%. However, adding GEBV for the indicator trait did not significantly increase the annual 

genetic gain of the aggregate genotype in the pre-selection indicator scheme when phenotypic 

information was already used. 

Table 5. Annual genetic gain of the aggregate genotype (∆GAG-rel), the milk production trait (∆GMP-rel) 

and the functional trait (∆GFU-rel) for six indicator schemes relative to the respective breeding schemes 

without indicator traits in the selection index. 

Indicator scheme 1 

PT 2 

GEBV 3 

Information 4 

∆GAG-rel 5 

Conventional + - P 101.7 * 

Juvenile - - P 101.6 

Pre-selection + + P 101.3 * 

∆GMP-rel 5 

96.2 * 

∆GFU-rel 5 

112.4 * 

97.9 107.9 

99.3 103.6 * 

Turbo - + P 100.2 98.7 101.4 

Pre-selection + + P and G 101.5 * 

Turbo - + P and G 102.5 * 

98.0 * 

94.8 * 

106.2 * 

111.5 * 

1 

Indicator scheme: the selection index contained the milk production trait, the functional trait and the 

indicator trait. 

2 

PT = progeny testing. 

3 

GEBV = genomically enhanced breeding values for the milk production trait and the functional trait. 

4 

Information: P = phenotypic information about the indicator trait was included in the selection index; 

P and G = phenotypic information and GEBV for the indicator trait were included in the selection 

index. 

5 

Within each breeding scheme means with superscripts differ (P < 0.05) from the corresponding mean 

in Table 1. 

Inclusion of phenotypic information about the indicator trait in the selection index decreased 

annual genetic gain of the milk production trait by 3.8% in the conventional indicator scheme. 

On the contrary, the annual genetic gain of the functional trait increased by 12 and 3.6% when 

phenotypic information about the indicator trait was included in the selection index of the 

conventional indicator scheme and the pre-selection indicator scheme. By including GEBV 

68

Paper III 

for the indicator trait in the selection index, the annual genetic gain on the milk production 

trait decreased by 2.0 and 5.2% in the pre-selection indicator scheme and the turbo indicator 

scheme. This tendency was opposite for the annual genetic gain of the functional trait, which 

increased by 6.2 and 11.5% in the pre-selection indicator scheme and the turbo indicator 

scheme when GEBV for the indicator trait were included in the selection index. 

Aside from increasing the annual genetic gain of the aggregate genotype, the rate of 

inbreeding per generation decreased significantly (by 8.1%) when GEBV for the indicator 

trait were included in the selection index of the turbo indicator scheme (result not shown). 

Apart from this, there was no significant difference on the rate of inbreeding per generation 

when an indicator trait was included in the selection index. 

Effects of restrictions 

We repeated the juvenile and the turbo schemes without restrictions on the number of male 

progeny to study the effects of the restrictions. Rate of inbreeding per generation was 

significantly higher within both scenarios when restrictions were not included in the 

simulations. However, there was no significant difference on the annual genetic gain of the 

aggregate genotype between scenarios with and without restrictions. 

Discussion 

This simulation study tested three hypotheses. Firstly, it was confirmed that breeding schemes 

with genomic selection are superior to breeding schemes without genomic selection with 

regard to annual genetic gain of the aggregate genotype, annual genetic gain of the functional 

trait in the breeding goal and rate of inbreeding per generation. Secondly, a shorter generation 

interval increases the effect of using GEBV on annual genetic gain of the aggregate genotype. 

However, our third hypothesis was disproved as the inclusion of an indicator trait in the 

selection index may improve the annual genetic gain of the aggregate genotype even if 

genotypic information about the breeding goal trait is known. 

Genetic gain 

Our results showed that schemes where active sires are selected on the basis of GEBV as soon 

as they reach sexual maturity, i.e. a turbo scheme, will result in the highest annual gain of the 

aggregate genotype. This result was expected as this type of scheme realizes the full potentials 

of genomic selection with regard to higher accuracy of selection on young animals and shorter 

69

Paper III 

generation interval. The annual genetic gain in the turbo scheme was not only higher than the 

annual genetic gain in the three other schemes but it was also higher than the sum of the 

marginal effects of using GEBV and of having a short generation interval. Thus, a positive 

interaction between the use of GEBV and a short generation interval exists. 

Composition of genetic gain 

The increases in annual genetic gain of the functional trait were relatively higher than the 

increases in annual genetic gain of the milk production trait when the pre-selection and the 

turbo schemes were compared to the conventional scheme. According to Fimland & 

Oldenbroek (2007), balancing milk production and functional traits is very important in a 

sustainable breeding scheme. This has been a difficult task in a conventional progeny-testing 

scheme as the heritabilities of the functional traits and thus the accuracies of selection often 

are low compared to the heritabilities of the milk production traits. The difference between the 

annual genetic gains of the milk production trait and the functional trait tended to be smaller 

in the turbo scheme than in the three other breeding schemes in this study. Thus, the turbo 

scheme seems to be superior with regard to composition of genetic gain. Hayes et al. (2009) 

argued that the use of GEBV could result in a more balanced composition of genetic gain 

although the contributions of the traits with low heritabilities to the increase in total merit will 

remain small if the accuracy of selection on these traits is low. We assumed that the reliability 

of the DGV was 50% for all traits as previous studies based on Nordic field data have shown 

that this is realistic for the time being (Lund et al., 2010; Su et al., 2010). However, if the data 

recording system changes so that it is not possible to supply well-proven bulls to the reference 

population then the difference in accuracy of DGV between traits with a low heritability and a 

high heritability may increase. 

Inbreeding 

The rate of inbreeding increased significantly when the juvenile scheme was used instead of 

the conventional scheme. The reason is that the absence of information on progeny increases 

the correlations between EBV of relatives and the probability of co-selection of relatives. On 

the contrary, the rate of inbreeding decreased when the pre-selection scheme and the turbo 

scheme were compared to the conventional scheme. The decreases were due to the fact that 

with genomic selection there is information on within-family variance and thus reduced 

probability of co-selection of relatives. 

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Paper III 

The Food and Agriculture Organization of the United Nations (1998) recommends that the 

effective population size is at least 50 animals per generation, i.e. the rate of inbreeding is 1% 

per generation at the maximum. The rate of inbreeding per generation was above the 

recommendation for the conventional scheme and the juvenile scheme in particular whereas 

the rate of inbreeding was below 1% per generation for both breeding schemes with genomic 

selection. Thus, the use of genotypic information in the breeding value evaluation may delay 

the reduction of the genetic diversity within the population and thereby increase the time 

horizon for the breeding scheme. 

We ran the simulations based on the assumption that the reliability of the DGV is the same for 

all animals. This may not be true in practice as the markers can capture genetic relationships 

among genotyped animals (Habier et al., 2007). As a consequence of this the accuracy of the 

DGV for selection candidates that are closely related to animals in the reference population is 

higher than the accuracy of the DGV for selection candidates that are distantly related to 

animals in the reference population (Lund et al., 2009). This may have an unfavourable effect 

on the rate of inbreeding because the selection candidates that are closely related to animals in 

the reference population have a greater of chance of being selected and subsequently being 

included in the reference population. 

All measures of inbreeding used in this study were traditional measures of inbreeding, which 

means they are based solely on pedigree information and refer to a neutral locus; i.e. it is not 

subject to selection. This assumption was violated in all the simulated breeding schemes and 

especially in the pre-selection scheme and the turbo scheme as genotypic information 

increases selection pressure on individual quantitative trait loci that affects the traits included 

in the selection index. In consequence of the fact that the traditional pedigree estimated 

inbreeding underestimates the true inbreeding in selective breeding schemes the advantage of 

using GEBV may be slightly overestimated in this study. 

The optimal or true measure of inbreeding is the actual proportion of loci that are identical by 

descent across the genome. Pedersen et al. (2010) found that marker assisted selection 

reduced pedigree estimated inbreeding as well as true inbreeding compared to conventional 

BLUP selection. However, the difference between pedigree estimated inbreeding and true 

inbreeding was larger in the breeding scheme using marker assisted selection than in the 

breeding scheme using conventional BLUP selection. Pedigree estimated inbreeding is thus a 

poorer estimate of true inbreeding when genotypic information is used (Pedersen et al., 2010). 

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Paper III 

It is difficult to comment on which of the two breeding schemes with genomic selection that 

would result in the largest difference between pedigree estimated inbreeding and true 

inbreeding. However, we hypothesize that the difference between pedigree estimated 

inbreeding and true inbreeding is larger in the pre-selection scheme than in the turbo scheme 

as the realized accuracy of the index for the active sires and thereby also the selection 

intensity on the quantitative trait loci is higher in the pre-selection scheme than in the turbo 

scheme. Meuwissen (2007) suggested that optimal contribution selection should be used in 

combination with genomic selection to prevent the reduction in genetic variability that is 

caused by strong selection for particular chromosomal regions. The kinships may be assessed 

using pedigree, markers or a combination of both (Meuwissen, 2007; Sonesson et al., 2010). 

Accuracy of selection 

The realized accuracies of the index for young bulls, production dams, and bull dams were 

higher in the juvenile scheme than in the conventional scheme in spite of a lower realized 

accuracy of the index for their sires. This is due to a lower realized accuracy of the index for 

active sires in the juvenile scheme than in the conventional scheme. Consequently, the Bulmer 

effect is weaker in the juvenile scheme than in the conventional scheme and the genetic 

variance is higher. As a result of the latter, the variance of the index for young bulls, 

production dams, and bull dams is also comparatively higher in the juvenile scheme than in 

the conventional scheme leading to higher realized accuracies of the index for young bulls, 

production dams, and bull dams. The annual genetic gain of the aggregate genotype was 

higher when the juvenile scheme was used instead of the conventional scheme. This increase 

was due to a lower generation interval more than counteracting the lower accuracy of 

selection of active sires. 

Genotyping increases the realized accuracy of the index by using the markers to explain the 

Mendelian sampling term. This applies particularly to animals without or with few records on 

themselves or on progeny. Thus, higher realized accuracies of the index for young bulls, 

production dams, and bull dams may be the reason why the annual genetic gain of the 

aggregate genotype increased when the pre-selection and the turbo schemes were compared to 

the conventional and the juvenile schemes. Both genotyping and progeny testing generate 

information about the sire’s Mendelian sampling term. Consequently, the realized accuracy of 

72

Paper III 

the index for the active sires was higher in the breeding schemes with progeny testing than in 

the breeding schemes without progeny testing and highest in the pre-selection scheme. 

Selection emphasis 

Schaeffer (2006) showed that the selection emphasis decreased for bull sires and increased for 

bull dams when a breeding scheme that resembled the turbo scheme was used instead of a 

conventional progeny-testing scheme. Because of this, genome-wide prediction is expected to 

shift the selection emphasis from the male path of the pedigree towards the female path 

(Schaeffer, 2006; Daetwyler et al., 2007). Our results underpin this expectation but the extent 

of the shift may depend on the proportion of genotypings in the two sexes. Our results 

indicate, in addition, that the selection emphasis shifts from the male path of the pedigree 

somewhat towards the female path of the pedigree when bulls become active sires early in 

life. 

Indicator traits 

It was possible to increase annual genetic gain of the aggregate genotype in the turbo indicator 

scheme by including both genotypic and phenotypic information about the indicator trait in 

the selection index. However, inclusion of phenotypic information about the indicator trait 

alone was not sufficient to increase annual genetic gain of the aggregate genotype. Our 

hypothesis was that the effect of including an indicator trait in the selection index on the 

annual genetic gain of the aggregate genotype is of no consequence in practice when genomic 

information about the functional trait in the breeding goal was already known. The reason 

behind this hypothesis was that the functional trait and the indicator trait would have equally 

high accuracies of selection when genomic information was available. Besides increasing the 

annual genetic gain of the aggregate genotype, inclusion of GEBV for the indicator trait also 

resulted in a more balanced composition of the genetic gain and it decreased the rate of 

inbreeding per generation. Thus, the turbo indicator scheme seems to be better than the turbo 

scheme in several important respects. 

Contrary to the missing effect of phenotypic information about the indicator trait in the turbo 

indicator scheme, the annual genetic gain of the aggregate genotype increased when 

phenotypic information about the indicator trait was included in the selection index of the pre- 

selection indicator scheme. This phenotypic information affects primarily the realized 

accuracy of the index for active sires through phenotypic measurements on the first-crop 

73

Paper III 

daughters. On the contrary, it is primarily the realized accuracy of the index for bull dams that 

is affected in the turbo indicator scheme through phenotypic measurements on the bull dams 

themselves. Thus, the reason why the annual genetic gain of the aggregate genotype increased 

in the pre-selection indicator scheme may be that the realized accuracy of the index increased 

for active sires when phenotypic information about the indicator trait was included in the 

selection index. At the same time, the realized accuracy of the index did not increase for bull 

dams in the turbo indicator scheme. 

Uncertainty about the breeding schemes 

The uncertainty about a breeding scheme can be expressed by V∆G. On this basis, the pre- 

selection scheme and the juvenile scheme seem to be the least and the most risky schemes 

over a 20 year period. However, V∆G in the conventional scheme and the turbo scheme were 

closer to V∆G in the pre-selection scheme than in the juvenile scheme. The variance of the 

annual genetic gain between replicates can also be approximated by means of the following 

2 

2 

expression: σ ∆G 

= 2 × ∆FYear 

× σ a , where ∆FYear 

is the rate of inbreeding per year and σ 2 a is the 

additive genetic variance. The rate of inbreeding per year may also be used as a measure of 

the uncertainty as it varies from one scenario to another whereas the other part of the 

expression is approximately the same across all scenarios. In this study, the rate of inbreeding 

per year ranks the four schemes in the same order as V∆G. However, the abovementioned 

expression is only valid under additive gene action and in the absence of selection, mutation 

and migration. In this study, the population was under selection. Thus, the additive genetic 

variance is assumed to be reduced compared to the additive genetic variance in the base 

population. 

Pseudo-genomic selection 

We assumed that the heritability of each DGV was 0.99 and thus very little uncertainty of 

measurements exists. This assumption also implied that half the DGV was transmitted 

directly from parent to offspring. The accuracy of the DGV was less than unity (0.71) 

reflecting that the markers did not explain all additive genetic variance for instance due to 

incomplete linkage and estimation errors in individual gene effect. The accuracy of the DGV 

was the same for all genotyped animals and all traits. The former may not be true if the 

haplotype effects of some animals are well known in the reference population and others are 

74

Paper III 

not, and the latter may not be true for all dairy cattle populations as some studies have found 

lower reliabilities for the functional traits than for the milk production traits while others did 

not (Hayes et al., 2009; Su et al., 2010). We also assumed that the segregation was the same 

in all families. This is probably not the case and may depend on the level of heterozygosity 

within each family. On the one hand, pseudo-genomic selection reflects a situation where 

genomic selection is used with previously estimated haplotype effects and no updating 

because the DGV was treated as an observed trait with a heritability of one. On the other 

hand, the accuracy of the DGV was constant across years, which reflects a situation where 

genomic selection is used with continuous re-estimation of haplotype effects. 

Conclusions 

Assuming that the reliability of the DGV is the same for all traits and all animals and that the 

economic value of the milk production trait and the functional trait are of the same size we 

find the turbo scheme with genomic selection and without progeny testing superior to the 

breeding schemes with other combinations of these two factors in several important respects. 

Our conclusion is based on the facts that the turbo scheme resulted in the highest annual 

genetic gain of the aggregate genotype among the four schemes and the greatest contribution 

of the functional trait to the increase in total merit. Moreover, the rate of inbreeding was 

0.74% per generation and thus below the international recommendations. Our results 

indicated, in addition, that a strong positive interaction exists between the use of genotypic 

information and a short generation interval on annual genetic gain of the aggregate genotype. 

Inclusion of genotypic as well as phenotypic information about an indicator trait in the 

selection index of the turbo scheme increased the annual genetic gain of the aggregate 

genotype. On top of that, the annual genetic gains of the milk production trait and the 

functional trait were almost equally high and the rate of inbreeding per generation decreased. 

Thus, indicator traits may still be profitable to use even though GEBV of the breeding goal 

traits are known. 

Acknowledgements 

This research was financed by a grant from the Danish Ministry of Science, Technology and 

Innovation and Knowledge Centre for Agriculture, Cattle. 

75

References 

Paper III 


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Nicholas, F. W., and C. Smith. 1983. Increased rates of genetic change in dairy cattle by 

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77

Paper IV 

The value of cows in the reference population depends on the 

availability of phenotypic records 

Line Hjortø Buch, Morten Kargo Sørensen, Peer Berg, Jan Lassen 

& Anders Christian Sørensen 

Submitted to Animal

The value of cows in the reference population depends on the 

availability of phenotypic records 

Buch, L.H. 1, 2 , Sørensen, M.K. 1, 2 , Berg, P. 2 , Lassen, J. 2 , & Sørensen, A.C. 2 

Abstract 

1 Knowledge Centre for Agriculture, Agro Food Park 15, 8200 Aarhus N, Denmark 

2 Department of Genetics and Biotechnology, Faculty of Agricultural Sciences, 

Aarhus University, P.O. Box 50, 8830 Tjele, Denmark 

Today, almost all reference populations consist of progeny tested bulls. However, older 

progeny tested bulls do not have reliable estimated breeding values (EBV) for new traits. 

Thus, it is necessary to build up a reference population for new traits. We used a deterministic 

prediction model to test the hypothesis that the value of cows in the reference population 

depends on the availability of phenotypic records. To test the hypothesis we investigated 

different strategies of building up a reference population for a new functional trait over a 10 

year period. The functional trait was either recorded on all cows in the population (30 000 

cows per year) or on a small scale (2 000 cows per year). Selection decisions were based on 

genomic information and the sires were not progeny tested before they were used for breeding 

purposes. For large-scale recording, we compared four scenarios where the reference 

population contained sires; sires and test bulls; sires and cows; or sires, cows and test bulls. In 

addition to varying the make-up of the reference population we also varied the heritability of 

the trait (h 2 = 0.05 vs. 0.15). The results showed that a reference population of test bulls, 

cows, and sires results in the highest accuracy of the direct genomic values (DGV) for a new 

functional trait regardless of its heritability. For small-scale recording, we compared two 

scenarios where the reference population contained the 2 000 cows with phenotypic records or 

the sires of these cows. The results showed that a reference population of cows results in the 

highest accuracy of the DGV whether the heritability is 0.05 or 0.15. The reason is that 

variation is lost when phenotypic data are summarized in EBV. Four main conclusions are: 

(1) the fewer phenotypic records, the larger effect of including cows in the reference 

population, (2) it is possible to achieve reasonably high accuracies of the DGV for new traits 

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Paper IV 

within a few years from commencement of recording, (3) for small-scale recording the 

accuracy of the DGV will continue to increase for several years, whereas the increases in the 

accuracy of the DGV quickly decrease with large-scale recording, and (4) a higher heritability 

benefits a reference population of cows more than a reference population of bulls. 

Keywords: Genomic selection, accuracy of selection, reference population, phenotypic 

record, dairy cattle 

Introduction 

The accuracy of genomic selection comes from estimated associations between genotypes and 

phenotypes in the reference population. Today, almost all reference populations consist of 

progeny tested bulls, because the accuracy of the direct genomic values (DGV) depends on 

the accuracy of the phenotypic information, and progeny testing has been the only way to 

achieve high accuracies for traits with a low heritability. In addition, relatively high costs of 

genotyping have so far called for reference populations of progeny tested bulls. However, 

variation is lost when phenotypic data are summarized in estimated breeding values (EBV). 

Thus, it may be beneficial to include cows in the reference population especially if the 

phenotype is expensive to measure and/or if the costs of genotyping decrease. 

Until now, focus has been on the traits that have been recorded and included in the routine 

breeding value evaluation for a long time because all past and present progeny tested bulls 

could be included in the reference population. However, the technological development 

enables recording of new (often functional) traits that have economic importance and 

therefore should be included in the breeding goal. These new recordings may be more useful 

than the traditional recordings because they are closer to the biology of the traits of interest. 

Examples of new traits could be occurrence of hoof diseases reported by hoof trimmers and 

the weight of the cow recorded during milking in automatic milking systems. Older progeny 

tested bulls do not have reliable EBV for the new traits as the traits in question were not 

recorded on their daughters. Thus, it is necessary to use a different strategy to build up a 

reference population for the new traits. 

Breeding schemes, where sires are selected on the basis of genomically enhanced breeding 

values (GEBV) as soon as they reach sexual maturity, realize the full potentials of genomic 

selection with regard to higher accuracies of selection for young animals and shorter 

generation intervals. Thus, it is most likely that this type of scheme, which we call a turbo 

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Paper IV 

scheme, is going to be used in the long term. Schaeffer (2006) and Buch et al. (2010) found 

by means of computer simulations that a turbo scheme results in higher annual genetic gains 

of the aggregate genotype than other types of breeding schemes. However, both of these 

studies assumed high accuracies of the GEBV and DGV, respectively. Genomic selection has 

already caused changes in most dairy cattle breeding schemes. One example is that fewer 

young bulls are progeny tested than before because young bulls are pre-selected more 

accurately on the basis of GEBV than on the basis of parent average breeding values (PABV). 

Thus, both the present progeny testing scheme and the turbo scheme result in fewer bulls with 

both marker information and phenotypic information that could eventually be included in the 

reference population. 

So far, most traits are recorded on the majority of the cows in the population, e.g. milk 

production traits and somatic cell score. It is most likely that this practice is going to change 

and that new functional traits are recorded on a smaller part of the population, e.g. only on 

cows that are milked in automatic milking systems. However, the number of phenotypic 

records that are used to estimate the marker effects has a favourable effect on the accuracy of 

genomic selection (Hayes et al., 2009). The heritability of the trait also plays an important 

role for the accuracy of genomic selection as more phenotypic records are needed when the 

heritability is low (Hayes et al., 2009). Thus, the accuracies of the DGV may be lower for the 

new functional traits than for the traits that have been recorded for a long time. 

We expect that the value of cows in the reference population depends on the availability of 

phenotypic records. In other words: (1) the accuracy of the DGV will only increase 

marginally when phenotyped cows are included in the reference population in addition to 

bulls if the number of bulls with proofs is large as is the case for large-scale recording and (2) 

a reference population of cows will result in the highest accuracy of the DGV if few cows 

have phenotypic records for the new functional trait. The objective of this study is to test the 

two expectations by investigating different strategies of building up a reference population 

over a 10 year period. 


Population structure 

The population consists of 30 000 new first-parity cows per year. Based on PABV the best 2 

000 bull calves are genotyped. The 30 best sexually mature bulls are selected on the basis of 

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Paper IV 

GEBV and used directly as sires, i.e. progeny testing results are not available when the sires 

are selected. So the breeding scheme is a turbo scheme. 

Scenarios 

In order to test the first hypothesis four different strategies of building up a reference 

population were compared (Table 1). A common characteristic of the four scenarios is that all 

cows in the population have phenotypic records on the new trait. In addition, it is not possible 

to genotype more animals than the ones that are genotyped for selection purposes. However, 

in scenarios S-C and S-C-TB the 2 000 best one-year-old females are genotyped in addition to 

the males in order to select bull dams. 

S: 30 genotyped sires each with a daughter yield deviation (DYD) based on 1 000 daughters 

were added to the reference population every year. This scenario was used to study the effect 

of including sires only in the reference population. 

S-TB: 30 genotyped sires each with a DYD based on 717 daughters and 170 genotyped test 

bulls each with a DYD based on 50 daughters were added to the reference population every 

year. The scenario was used to study the effect of supplementing the reference population by 

test bulls. 

S-C: 30 genotyped sires each with a DYD based on 933 daughters and 2 000 genotyped cows 

with phenotypic records were added to the reference population each year. This scenario was 

used to study the effect of adding cows to the reference population. 

S-C-TB: 30 genotyped sires each with a DYD based on 650 daughters, 2 000 genotyped cows 

with phenotypic records and 170 genotyped test bulls each with a DYD based on 50 daughters 

were added to the reference population every year. The scenario was used to study the effect 

of supplementing the reference population by both cows and test bulls. 

Table 1. The total number of genotyped animals per year within each scenario and the total number of 

cows per year with phenotypic records for a new functional trait within the three groups of animals 

that can be included in the reference population. 

Scenario Genotyped animals 30 sires 170 test bulls 2 000 cows 

S 30 30 000 - - 

S-TB 200 21 510 8 500 - 

S-C 2 030 27 990 - 2 000 

S-C-TB 2 200 19 500 8 500 2 000 

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Paper IV 

To test the second hypothesis two strategies were compared. A common feature of the two 

scenarios is that the new functional trait is only recorded on 2 000 first-parity cows per year. 

COWS: 2 000 genotyped cows with phenotypic records on the functional trait were added to 

the reference population each year in order to study the effect of a reference population 

containing cows. 

SIRES: 30 genotyped sires each with a DYD based on 67 daughters were added to the 

reference population every year in order to study the effect of summarizing the phenotypic 

information by including the sires of the cows in the reference population. 

Accuracy of the direct genomic value 

We evaluated the scenarios by comparing the correlation between true breeding values and 

DGV also referred to as the accuracy of DGV. Goddard (2009) presented a deterministic 

model for predicting this accuracy (r(T,I)). The accuracy of the DGV is based on marker data 

and independent of pedigree relationships, i.e. only information that comes from linkage 

disequilibrium (LD) across the population is quantified. In our study a normal distribution of 

quantitative trait loci (QTL) effects was assumed. 

If the reference population contains one group of animals then the accuracy of the DGV was 

calculated using the following formula (Goddard, 2009): 

r m 

2 

2 

( T, 

I) 

r ( T, 

Tm 

) r ( T , I) 

× 

= (1) 

where the first component is the proportion of variance of the true breeding value which is 

explained by the markers and the second component is the proportion of variance of the DGV 

which is explained by the markers. 

On the assumption that all chromosome segments have the same effect r 2 (T,Tm) equals the 

expectation of r 2 that is a measure of LD. The approximate expectation of r 2 is (Sved, 1971): 

( 2 

E r 

e 

) = 1/( 

4N 

c + 1) 

where Ne is the effective population size and c is the average recombination frequency 

between neighbouring loci, i.e. the length of the genome in Morgans divided by the number of 

informative markers. 

The proportion of variance of the DGV which is explained by the markers was calculated as a 

function of the number of animals in the reference population, the prediction error variance 

(PEV), the heritability of the trait (h 2 ), the length of the genome in Morgans, and Ne (Goddard, 

2009). 

85 

(2)

Paper IV 

The prediction error variance was calculated by means of the following formula (Mrode, 

2005): 

2 

PEV = ( 1− 

r ) × V = ( 1− 

( N /( N + ( 4 / h ) −1))) 

× V 

2 

IA 

a 

where r 2 IA is the reliability of the DYD for bulls, Nd is the number of daughters with 

phenotypic records per animal in the reference population and Va is the genetic variance of the 

trait. 

If the reference population contains n groups of animals with different information contents in 

their phenotypes then the proportion of variance of the DGV which is explained by the 

markers was calculated using the following formula derived from selection index theory: 

2 

rcomb ( Tm 

, I ) = G 

d 

P 

d 

T −1 

where P is a n-by-n (co)variance matrix containing r 2 (Tm,I) on the diagonal and their products 

on the off-diagonals, and G was a n-by-1 vector of r 2 (Tm,I). 

Then the accuracy of the DGV was calculated by substituting r 2 comb(Tm,I) for r 2 (Tm,I) in 

equation (1). 

Parameter assumptions 

We assumed that the length of the genome was 30 Morgans, and that the trait was a functional 

trait with a heritability of 0.05 or 0.15. The historical effective population size was set to 900 

animals. We set this number as the value of Ne that would give results similar to the 

EuroGenomics project given the number of bulls in the reference population in that study 

(Lund et al., 2010). We also assumed that the animals in the reference population were 

genotyped for approximately 50 000 genome-wide markers of which 38 000 markers were 

informative, and that the cows in the reference population did not have daughters with 

phenotypic records. 

Results 

The accuracy of the DGV increased over time as more and more information about the marker 

effects became available regardless of the heritability of the trait and the scale of the recording 

of phenotypes (Figures 1, 2, and 3). 

86 

G 

a 

(3) 

(4)

Recording on a large scale 

Paper IV 

The accuracy of the DGV increased rapidly in all scenarios as 75% of the accuracy in year 10 

after the commencement of recording is achieved within two and three years (Figure 1). The 

increase from 0.26 to 0.44 in S-C-TB was the smallest among the four scenarios whereas the 

actual accuracy was the highest. A reference population of sires and test bulls resulted in a 

higher accuracy of the DGV than a reference population of sires and cows. The lowest 

accuracy was achieved for a reference population of sires only. For a trait with a heritability 

of 0.05 one has to genotype approximately 31 times as many cows as test bulls with 50 

daughters to achieve the same accuracy of the DGV (results not shown). 


0.50 

0.45 

0.40 

0.35 

0.30 

0.25 

0.20 

0.15 

0.10 

0.05 

0.00 

0 1 2 3 4 5 6 7 8 9 10 

Years from commencement of recording 

S-C-TB 

Figure 1. The accuracy of the direct genomic value for a trait with a heritability of 0.05 in a dairy 

cattle breeding scheme where 30 sires (S), 30 sires and 2000 cows (S-C), 30 sires and 170 test bulls 

(S-TB) or 30 sires, 2000 cows and 170 test bulls (S-C-TB) were added to the reference population 

every year. 

The accuracy of the DGV increased even faster when the heritability of the trait was 0.15 

compared to 0.05 since the accuracy of the DGV rose to 75% of the accuracy in year 10 after 

one to two years (Figure 2). The highest accuracy of the DGV was achieved for a reference 

87 

S-TB 

S-C 

S

Paper IV 

population of sires, cows, and test bulls, and the lowest accuracy was achieved for a reference 

population of sires. A reference population of sires and cows resulted in a slightly higher 

accuracy of the DGV than a reference population of sires and test bulls. Hence, the order of 

the scenarios changed as a result of a higher heritability. In general, the size of the heritability 

had a favourable effect on the accuracy of the DGV, and the difference between the four 

scenarios decreased as the heritability of the trait increased. If the heritability of the trait is 

0.15 one has to genotype approximately 17 times as many cows as test bulls with 50 

daughters to achieve the same accuracy of the DGV (results not shown). 


0.50 

0.45 

0.40 

0.35 

0.30 

0.25 

0.20 

0.15 

0.10 

0.05 

0.00 

0 1 2 3 4 5 6 7 8 9 10 


S-C-TB 


cattle breeding scheme where 30 sires (S), 30 sires and 2000 cows (S-C), 30 sires and 170 test bulls 

(S-TB) or 30 sires, 2000 cows and 170 test bulls (S-C-TB) were added to the reference population 

every year. 

Recording on a small scale 

The increases in accuracy over time are more linear when the new trait is recorded on a small 

scale as it took four to five years to achieve 75% of the accuracy that was achieved in year 10. 

This is due to the fact that the number of phenotypes is the limiting factor. The accuracy of 

88 

S-C 

S-TB 

S

Paper IV 

the DGV is higher if the reference population contains cows instead of the sires of the cows, 

and the difference increases with time (Figure 3). The difference between a reference 

population of cows and a reference population of the sires of the cows is greater if the 

heritability is 0.15 instead of 0.05 (results not shown). 


0.35 

0.30 

0.25 

0.20 

0.15 

0.10 

0.05 

0.00 

0 1 2 3 4 5 6 7 8 9 10 


COWS 

SIRES 


cattle breeding scheme where 2000 cows (COWS) or 30 sires each with 67 daughters (SIRES) were 

added to the reference population every year. 

Discussion 

We have shown that within a few years from commencement of recording it is possible to 

achieve reasonably high accuracies of the DGV for new traits even though thousands of bulls 

with reliable proofs do not exist. For small-scale recording the accuracy of the DGV will 

continue to increase for several years, whereas the increases in the accuracy of the DGV 

quickly decrease with large-scale recording. Our results also indicate that the fewer 

phenotypic records that are available, the larger effect of including cows in the reference 

population. In addition, a higher heritability will benefit a reference population of cows more 

than a reference population of bulls. 

89

Paper IV 

Lillehammer et al. (2010) showed in a stochastic simulation study that the accuracy decreases 

slightly over time in a turbo scheme where tens of bulls with daughter information are added 

to the reference population every year if a reference population containing a historical 

population of several thousand progeny tested bulls is the point of departure. This is due to 

the fact that the number of bulls added to the reference population every year in a turbo 

scheme is lower than the number of progeny tested bulls in the breeding scheme before 

genomic selection was introduced. The model from Goddard (2009) cannot model the fact 

that animals in the reference population become less informative as time goes by. Thus, 

several years after commencement of recording the accuracies of the DGV may be lower in 

reality than the ones we are able to show. However, we believe that the shape of the curves in 

Figures 1, 2, and 3 are correct as a historical reference population of progeny tested bulls does 

not exist for new traits. 

The value of the phenotypic information that is used for estimating marker effects increases 

relatively more for cows than it does for bulls as the heritability of the trait increases. This is 

the reason why the ranking order of the scenarios changed in the scenarios with large-scale 

recording and why the difference between a reference population of cows and a reference 

population of the sires of the cows increased in the scenarios with small-scale recording. 

In a turbo scheme offspring of a certain bull are selected before the daughters of that bull have 

phenotypic records. That is, the selection of young animals is based on information about 

their grand parents. On the contrary, when an offspring of a certain cow is about to be selected 

the cow already has phenotypic information and it could be included in the reference 

population. Thus, the young animals are more closely related to the animals in the reference 

population if the reference population consists of cows or a combination of bulls and cows 

instead of bulls alone. The accuracy decreases as the number of generations between the 

selection candidates and the animals in the reference population increases (Meuwissen et al., 

2001). We are not able to mimic this fact in the calculations set out above. However, we 

believe that reference populations containing bulls alone would result in lower accuracies of 

the DGV in real life than the ones we calculated. 

Large-scale recording 

We took a chip with 50 000 SNP as our starting point. However, there are other types of chips 

on the market, e.g. a low-density chip containing 3 000 SNP and a high-density chip 

90

Paper IV 

containing 800 000 SNP. It is likely that the accuracy of the DGV decreases if some of the 

animals in the reference population are genotyped with a low-density chip because the 

proportion of SNP genotypes that are imputed correctly is less than unity. In order to quantify 

this expectation Weigel et al. (2010) compared the correlation between DGV and predicted 

transmitting abilities in two scenarios reflecting that (1) the selection candidates were 

genotyped with a low density chip and the bulls in the reference population were genotyped 

with a chip containing 50 000 markers and (2) the selection candidates and a random 50% of 

the bulls in the reference population were genotyped with a low density chip and the 

remaining bulls in the reference population were genotyped with a chip containing 50 000 

markers. Their results showed that the correlation between DGV and predicted transmitting 

abilities for milk yield, protein percentage and daughter pregnancy rate decreased by 0.033, 

0.050 and 0.001 when the second scenario was used instead of the first (Weigel et al., 2010). 

We expect that the effect is the same for cows with imputed genotypes as it is for bulls. Thus, 

before marker information based on a low-density chip is collected on a large scale one has to 

decide if the saving on costs of genotyping more than compensates for the decline in 

accuracies of the DGV. 

In the long run the costs of genotyping animals will most likely be reduced even further. In 

that case it may become economically viable for the dairy farmers to genotype the production 

cows as well as the potential bull dams. By doing so it may be possible to use DGV as a 

management tool for selecting replacement heifers on dairy farms using sexed semen or for 

using genomic optimum contribution selection in the most effective way (Weigel et al., 2010). 

In addition, these cows should be included in the reference population. The accuracy of the 

DGV is 0.23 if the heritability of the trait is 0.05 and the reference population contains 30 

sires and 2 000 cows. In comparison to that the accuracy of the DGV is 0.43 or 0.46 if the 

heritability of the trait is 0.05 and the reference population contains 30 sires and 100 000 or 

200 000 cows (results not shown). Thus, it is possible to achieve a high accuracy of the DGV 

for a new trait with a low heritability in a relatively short time if the costs of genotyping cows 

become low. 

A certain amount of money has already been spent on genotyping as we assume that the 

selection candidates are genotyped prior to selection. However, if the genotyping strategy 

with the purpose of selecting is coincident with the genotyping strategy with the purpose of 

adding information to the reference population, then it is not necessary to spend more money 

91

Paper IV 

on genotyping. This is the case if males are genotyped and the reference population consists 

solely of sires, as in S, or if males and females are genotyped and the reference population 

contains a combination of sires and the highest ranking cows, as in S-C. Thus, these scenarios 

save on costs compared to S-C-TB and S-TB, which may be the most expensive scenarios 

among the ones we tested. The costs of S-C-TB and S-TB are high because it is expensive for 

an AI company to buy additional 170 bull calves and to stall them until they reach sexual 

maturity. 

If selection is based on LD information only, S and S-C-TB may be the best and the worst 

scenarios with regard to inbreeding. The reason behind this expectation is that S and S-C-TB 

result in the lowest and the highest accuracy of the DGV and thus they are nearest to and 

furthest away from random selection, respectively. However, if selection decisions are based 

on an index combining DGV and PABV then the ranking of the scenarios may be reversed so 

that S-C-TB and S are the best and the worst scenarios with regard to inbreeding. Given that 

the accuracy of the PABV is the same within the four scenarios and the accuracy of the DGV 

differs between the scenarios, the relative emphasis on the DGV is higher in S-C-TB than in 

the other scenarios because the accuracy of the DGV is higher in S-C-TB. Thus, the 

Mendelian sampling term is estimated with higher accuracy in S-C-TB, which may result in 

less across family selection. 

Concerning inbreeding, it may not be the optimal solution to include the highest ranking cows 

in the reference population as the genotyped females are selected on the basis of PABV and 

consequently they are more closely related to each other than the population as a whole. Thus, 

in addition to the 30 sires it may be a better strategy to include 2 000 cows representing the 

entire population in the reference population but it is also more costly than to include the 2 

000 highest ranking cows, which are assumed to be already genotyped. 

For large-scale recording we assumed that the highest ranking one-year-old females in the 

population were genotyped and subsequently included in the reference population when they 

have phenotypic records. However, it is most likely that the dairy farmers consciously or 

unconsciously focus their attention on these cows as they are potential bull dams. 

Consequently, preferential treatment may be a problem. Thus, there is a lot to be said in 

favour of genotyping cows for the reference population that represent the entire population 

and already have phenotypic records. 

92

Small-scale recording 

Paper IV 

The accuracy of the DGV is higher for a reference population of cows than for a reference 

population of bulls. Therefore, it is most likely that a reference population of cows also results 

in a higher response to selection. The genotyped cows that have phenotypic records on the 

new trait can also contribute to the accuracy of the DGV for the traits that have been recorded 

for a long time. Thus, the costs of genotyping cows do not have to be covered by the genetic 

gain in the new trait alone. 

The number of markers has a favourable effect on the accuracy of the DGV because a higher 

marker density increases the likelihood of finding markers in strong LD with the QTL (Hayes 

et al., 2009). Thus, it may be advisable to genotype the animals in the reference population 

with a high density chip if the trait is recorded on a small scale and has a low heritability. We 

found that the accuracy of the DGV is 0.12 if the number of effective markers is 38 000, the 

heritability of the trait is 0.05, and the reference population contains 2 000 cows. All other 

things being equal, the accuracy of the DGV is 0.21 if the number of effective markers is 600 

000 (results not shown). Thus, it is possible to achieve a much higher accuracy of the DGV by 

using a high density chip. However, the benefit of using a high density chip depends on the 

costs of genotyping and the costs of recording alike. 

The deterministic prediction model 

The deterministic prediction model we used is relatively sensitive to the historical effective 

population size. Thus, it is important to use a reasonable parameter. To investigate whether an 

effective population size of 900 animals is reasonable or not we wanted to find the effective 

population size corresponding to the recombination frequency (c). On the assumption that the 

number of previous generations (T) that corresponds to c is (2c) -1 (Hayes et al., 2003) we had 

to find the effective population size 633 generations ago. The effective population size of 

several dairy cattle populations has been estimated from LD between marker pairs (de Roos et 

al., 2008; Kim and Kirkpatrick, 2009). In the populations investigated the effective population 

size was found to be declining, e.g. from a few thousand animals about 1 000 generations ago 

to approximately 100 animals today (de Roos et al., 2008). The effective population size 

obtained from LD between marker pairs 633 generations ago was higher than 900 animals. 

This seems reasonable as T can be interpreted as the maximum age of the LD that it is 

possible to capture with the given density of markers. 

93

Paper IV 

We used a population of 30 000 first-parity cows in this study. For a larger population of 

cows the reliability of the DYD for sires (r 2 IA) came close to one. When this happens even 

small changes in r 2 IA are translated into proportionally large changes in PEV so the prediction 

formula is overly sensitive to r 2 IA when r 2 IA is close to one. 

Implications 

Today, most reference populations contain exclusively proven bulls. However, it is necessary 

to include more animals in the reference population than the sires if breeding schemes with 

genomic selection and intensive use of young bulls are to be implemented. We advocate a 

reference population of test bulls, cows and sires if all cows have phenotypic records on the 

new functional trait because it results in higher accuracies of the direct genomic values and 

likely in higher genetic gains. However, if the new trait is recorded on a small scale, a 

reference population of all phenotyped cows gives the best result. 

Acknowledgement 

This research was financed by a grant from the Danish Ministry of Science, Technology and 

Innovation and Knowledge Centre for Agriculture, Cattle. 

References 

Buch, L. H., M. K. Sørensen, J. Lassen, P. Berg, and A. C. Sørensen. 2010. Dairy cattle 

breeding schemes with or without genomic selection and progeny testing. No 418 in Proc. 9 th 


de Roos A. P. W., B. J. Hayes, R. J. Spelman, and M. E. Goddard. 2008. Linkage 

disequilibrium and persistence of phase in Holstein-Friesian, Jersey and Angus cattle. 

Genetics 179:1503-1512. 

Goddard, M. 2009. Genomic selection: prediction of accuracy and maximisation of long term 

response. Genetica 136:245-257. 

Hayes, B. J., P. M. Visscher, H. C. McPartlan, and M. E. Goddard. 2003. Novel multilocus 

measure of linkage disequilibrium to estimate past effective population size. Genome 

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Kim, E.-S., and B. W. Kirkpatrick. 2009. Linkage disequilibrium in the North American 

Holstein population. Animal Genetics 40:279-288. 

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Lillehammer, M., T. H. E. Meuwissen, and A. K. Sonesson. 2010. Effects of alternative 

genomic selection breeding schemes on genetic gain in dairy cattle. No 130 in Proc. 9 th World 

Congr. Genet. Appl. Livest. Prod., Leipzig, Germany, August 1-6, 2010. 





Meuwissen, T. H. E., B. J. Hayes, and M. E. Goddard. 2001. Prediction of total genetic value 

using genome-wide dense marker maps. Genetics 157:1819-1829. 



Schaeffer, L. R. 2006. Strategy for applying genome-wide selection in dairy cattle. J. Anim. 

Breed. Genet. 123:218-223. 

Sved, J. A. 1971. Linkage disequilibrium and homozygosity of chromosome segments in 

finite populations. Theoretical population biology 2:125-141. 

Weigel, K. A., G. de los Campos, A. I. Vazquez, C. P. Van Tassel, G. J. M. Rosa, D. Gianola, 

J. R. O’Connell, P. M. VanRaden, and G. R. Wiggans. 2010. Genomic selection and its effect 

on dairy cattle breeding programs. No 119 in Proc. 9 th World Congr. Genet. Appl. Livest. 

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95

General discussion 

In this thesis we have shown that use of phenotypes that are closer to the traits in the breeding 

goal provide the opportunity for higher genetic gain in functional traits also in breeding 

schemes with genomic selection. Paper I showed that multi-trait evaluation will only increase 

accuracy of selection marginally when the records that are available today are used. Paper II 

showed that the selection differential for the functional traits in the breeding goal increases 

when hoof diseases recorded by hoof trimmers are included in the selection index. Therefore, 

a more consistent recording of the traits is very important for genetic gain in functional traits. 

Paper III showed that the highest genetic gain for a functional trait compared to the genetic 

gain for a milk production trait, i.e. a composition of the genetic gain more proportional to the 

economic values, is obtained in a breeding scheme with genomic selection and with intensive 

use of young bulls. However, we assumed equal accuracies of the direct genomic values 

(DGV) for the milk production trait and the functional trait and for all genotyped animals, 

which of course influences our conclusion. Paper IV showed that the size of the heritability 

for the new functional trait has a favorable effect on the accuracy of the DGV. Thus, 

recordings of traits reflecting the biological traits we want to improve are important in order 

to obtain high genetic gains for functional traits compared to the genetic gains for the milk 

production traits. 

Optimisation and evaluation of breeding schemes with genomic selection 

The optimisation of a dairy cattle breeding scheme implies that a balance between accuracy of 

selection and generation interval is found. Genomic selection enables prediction of accurate 

breeding values for young animals (Hayes et al., 2009a). Thus, the advantage of waiting for 

progeny testing results was relatively larger in the past because the accuracies of the estimated 

breeding values (EBV) were low for young animals. We studied to what extent selection on 

genomic information and intensive use of young bulls affected annual genetic gain, and we 

found that a shorter generation interval increases the effect of genomic selection on annual 

genetic gain (Paper III). For that reason genomic selection seems to finally fulfil the 

expectations for early predictors that have driven research in dairy cattle genetics for several 

decades, first with physiological measures and later with identified DNA variants (Goddard 

and Hayes, 2009). 

97


Exclusive use of young breeding animals in a breeding scheme with genomic selection may 

affect the accuracy of selection because the accuracy of the DGV may decrease as the 

distance between the animals in the reference population and the selection candidates 

increases. Considering selection candidates in generation t, the animals in the reference 

population originate from generation t-2 or earlier in a breeding scheme where the active sires 

are selected directly on the basis of genomic information (a turbo scheme). In a breeding 

scheme where young bulls are selected for progeny testing on the basis of genomic 

information and active sires are selected on the basis of progeny testing results (a pre- 

selection scheme), the animals in the reference population are from generation t-1. We were 

not able to investigate the effect of distance between the animals in the reference population 

and the selection candidates in Paper III. Lillehammer et al. (2010) showed that the accuracy 

of the DGV decreases over time in a turbo scheme and that the accuracy of the DGV in a 

turbo scheme is lower than the accuracy of the DGV in a pre-selection scheme. These results 

are a combination of a greater distance between the animals in the reference population and 

the selection candidates and fewer sires with both genomic and phenotypic information 

(Lillehammer et al., 2010). It could be interesting to compare a turbo scheme and a pre- 

selection scheme where the same number of animals is added to the reference population 

every year by means of a simulation program similar to the one used in the study by 

Lillehammer et al. (2010). By doing so, it would be possible to separate the effect of a greater 

distance between the animals in the reference population and the selection candidates and 

fewer genotyped sires with proofs on the accuracy of the DGV. In order to include more bulls 

in the reference population than the active sires, it may be necessary to use test bulls in the 

turbo scheme, as we suggested in Paper IV. It is difficult to comment on the results of such a 

comparison. However, we hypothesize that the difference between the levels of the accuracies 

in a turbo scheme and in a pre-selection scheme mainly results from the distance between the 

animals in the reference population and the selection candidates. We also hypothesize that the 

difference between the tendencies in the accuracies primarily is a function of the number of 

animals that is added to the reference population every year. 

The use of genomic information has no impact on the breeding goals, at least if these are 

defined objectively and in linear terms. If economic values are determined subjectively, e.g. 

using a desired gains approach, breeding goals need to be re-evaluated when genomic 

information is included in the selection criteria. During the optimisation of a breeding scheme 

98


one should seek to find the right balance between the traits in the selection index (van der 

Werf and Banks, 2010). This is necessary because selection index methods optimize selection 

conditional on the data that are available but they do not give a prediction of what kind of data 

to be collected in order to maximise response to selection (van der Werf and Banks, 2010). 

We showed in Paper II that the estimated heritabilities of the individual hoof diseases reported 

by hoof trimmers are higher than the estimated heritabilities of the individual hoof diseases 

reported by veterinarians (Laursen et al., 2009). Thus, we would expect that the genetic gain 

increases when precise measurements of the breeding goal traits are included in the selection 


The evaluation of a breeding scheme includes assessing whether the obtained response to 

selection matches the investment in information (van der Werf and Banks, 2010). Heavy 

investments have already gone into the development and the practical application of genomic 

selection because simulation studies, among them Paper III, have shown that genomic 

selection provides the opportunity for a large increase in selection response especially if it is 

combined with intensive use of young bulls. Although genomic selection is already used in 

practice, it is still too early to estimate the consequences of genomic selection in dairy cattle 

populations. In addition, several changes in the existing progeny testing scheme are required 

before it is possible to realize the full potential of genomic selection. Consequently, most AI 

companies are still adapting their breeding scheme to the incorporation of genomic selection. 

For these reasons, genomic selection still needs to prove its worth in real life. However, when 

the breeding scheme is operational, the outcomes have to be evaluated, e.g. by comparing the 

obtained response to selection and the obtained rate of inbreeding with the expected values. 

This evaluation of the breeding scheme is crucial because we do not know the long term 

consequences of genomic selection. 

It is important to inform the dairy farmers and the dairy cattle breeders about the 

consequences of using a turbo scheme especially that the high merit sires will have less 

accurate proofs than the farmers are used to. When using genomic selection as well as young 

breeding animals, it is necessary to focus on groups of animals rather than on individuals in 

order to avoid disappointments. Some dairy cattle breeders have a tradition of knowing the 

full pedigrees of the bulls used in their herds and singling out a bull that they have particular 

confidence in. With progeny tested bulls this practice, though suboptimal, has had little effect 

on the genetic level in these herds due to the high accuracies achieved under progeny testing. 

99


Genomic selection in combination with young breeding animals is performed based on proofs 

with a lower accuracy and there is therefore a larger risk of being disappointed in a single bull 

as well as a greater chance of being positively surprised. By using teams of genomically 

selected bulls this uncertainty can be reduced. 

New traits in the genomic era 

Genomic selection does not cancel out the advantages of having a large population size 

because it enables a larger reference population and thus higher accuracies of the DGV. 

Commercial breeds with a small population size could choose to differ from breeds with a 

large population size by having a different breeding goal and/or by recording traits that are 

closer to the traits in the proper breeding goal. It is possible to obtain genetic progress for 

functional traits by including traits in the selection index that resemble the traits in the proper 

breeding goal to a great extent (Paper II) and to obtain relatively high accuracies of the DGV 

for all traits regardless of their heritability within a reasonable short period of time by using 

genomic information and thus obtain a higher genetic progress (Paper IV). So, if commercial 

breeds with a small population size specialize in recording other phenotypes that are difficult 

or expensive to measure it could make them attractive breeds for some dairy farmers and in 

crossbreeding programs. 

One such trait that should attract attention in the future is feed efficiency. Genetic 

improvement of feed efficiency can be of economic importance because feed costs represent a 

considerable part of the costs that are associated with milk production (Veerkamp, 1998). 

Despite its economic importance feed efficiency is not included in the applied breeding goal 

in most countries. This is mainly due to the fact that traits related to feed efficiency, e.g. feed 

intake and live weight, are difficult to record on a large scale in a conventional progeny 

testing scheme. In addition, feed efficiency is a complex trait like female fertility. A 

phenotypic record in a breeding scheme with genomic selection is worth more than a 

phenotypic record in a conventional progeny testing scheme without genomic selection. 

Consequently, genomic selection may create an opportunity to select for traits that are 

recorded on a small scale (Paper IV). Verbyla et al. (2010) found an accuracy of the DGV of 

0.52 for energy balance. This result is based on 527 first-parity cows that have phenotypic 

records on feed intake, live weight and milk yield. In the light of this finding, Verbyla et al. 

(2010) conclude that in the long run selection for energy balance could be performed using 

100


genomic selection. We showed in Paper IV that a reference population of cows results in a 

higher accuracy of the DGV than a reference population of the sires of these cows if the trait 

is recorded on a small scale. This would be the case if traits such as feed intake and live 

weight are measured on experimental farms. Inclusion of genomic as well as phenotypic 

information on indicator traits in the selection index may increase the annual genetic gain of 

the aggregate genotype (Paper III). So, it may be profitable to include traits that are 

genetically correlated to feed efficiency and measurable on a large scale in the selection index 

for feed efficiency as correlated traits. 

Building up a reference population 

It is necessary to build up a reference population for new traits and to maintain the reference 

population for traits that have been recorded for a long time because the accuracy of the DGV 

depends on the number of animals in the reference population, among other things. At the 

very beginning of the genomic era, genomic selection was expected to make phenotypic 

recordings redundant once estimates of allele effects were obtained. However, a decline in the 

accuracy of DGV with distance to the reference population suggests that phenotypic 

recordings are still very important (Sonesson and Meuwissen, 2009). We suggest in Paper IV 

that test bulls could be added to the reference population if the trait is recorded on a large 

scale. The AI companies may doubt whether the farmers will inseminate their cows with 

semen from test bull or not as the farmers will know that the test bulls rank below the active 

sires. In the past, nobody knew whether a given young bull under progeny testing would be 

selected as active sire or not. However, we believe that it is possible to convince farmers that 

they have to raise daughters sired by test bulls if genomic selection is going to work 

optimally. If this is not the case, AI companies should compensate farmers for the lower 

genetic level of test bull daughters. 

Earlier on, it was assumed that the markers only captured linkage disequilibrium (LD) across 

the population. However, recent research indicates that the genetic relationship between the 

animals in the reference population and the selection candidates affects the accuracy of the 

DGV positively, e.g. the accuracy of the DGV is higher if the sire of the selection candidate is 

included in the reference population (Lund et al., 2009). Both the results from Lund et al. 

(2009) and the results from Habier et al. (2007) indicate that information on the genetic 

relationship as well as LD enters into the prediction of DGV. For a training population of 255 

101


British Holstein bulls, the proportion of the reliability of the DGV that is explained by the 

genetic relationship is 91%, 75% and 81% for milk, fat and protein yield, respectively (Luan 

et al., 2010). The contribution of the genetic relationship and LD information to the accuracy 

of the DGV seems to be affected by the size of the reference population. Hence, for protein 

yield the proportion of the reliability of the DGV that is explained by the genetic relationship 

is 53% and 41% for a reference population of approximately 4 000 Nordic Holstein bulls and 

approximately 16 000 European Holstein bulls, respectively (Lund et al., 2010). The results 

from Lund et al. (2010) also indicate that the contribution of the genetic relationship and LD 

information to the accuracy of the DGV is affected by the heritability. Hence, for a reference 

population of approximately 4 000 Nordic Holstein bulls and approximately 16 000 European 

Holstein bulls the proportion of the reliability of the DGV that is explained by the genetic 

relationship is 29% and 24% for udder depth (h 2 ≈ 0.36), and it is 67% and 60% for non- 

return rate (h 2 ≈ 0.02; Lund et al., 2010). The part of the DGV that only originates from 

information on the genetic relationship is almost the same within each trait irrespective of the 

size of the reference population (Luan et al., 2010; Lund et al., 2010). In other words, the part 

of the DGV that is due to LD is estimated with greater accuracy as the size of the reference 

population and the heritability of the trait increase. 

A large reference population is even more important if the heritability of the trait is low, as is 

often the case for functional traits. In consequence, the American and Canadian reference 

populations of Holstein-Friesian bulls have been joined and the EuroGenomics collaboration 

for Holstein-Friesian dairy cattle has been established (Lund et al., 2010). Before genomic 

information was available, it was difficult for commercial breeds with a small population size 

to keep up with breeds with a large population size because they could not progeny test the 

same number of bulls. For that reason, small populations often had a lower selection intensity 

and thereby a lower selection response than breeds with a large population size. Today, it may 

be difficult for small populations to build up a large reference population and thereby obtain a 

selection response that is just as high as in breeds with a large population size. So, small 

populations need a solution in order to be more competitive. So far, it is not possible to 

produce accurate DGV in one breed by using the prediction equation for another breed (Harris 

et al., 2008; Hayes et al., 2009b). In the light of these facts, it may be a solution, especially for 

breeds with a small population size, to merge reference populations from different breeds. 

Previous studies have shown that the accuracies of the DGV may increase when a multi-breed 

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reference population is used instead of a pure breed reference population (Hayes et al., 

2009b). Markers have to be in LD with quantitative trait loci (QTL) in all breeds to have an 

effect in a multi-breed reference population and therefore the distance between the markers 

and the QTL has to be very small (Hayes et al., 2009b). Consequently, it may be necessary to 

genotype the animals in the multi-breed reference population with a chip containing more 

markers. Goddard and Hayes (2009) estimated that at least 300 000 markers are needed for 

the establishment of a multi-breed reference because of the limited extent of LD across 

breeds. However, it is an expensive solution if the animals that are already genotyped with a 

chip containing 50 000 markers have to be genotyped with a chip containing more markers. 

Thus, breeds with a large population size may not have an interest in joining a multi-breed 

reference population if the extra genetic gain is very small for their breed. On the other hand, 

if an AI company sells semen from more breeds then it may wish to retain the 

competitiveness of the breeds with a small population size to retain customers. On top of that, 

the AI company has equal breeds at its disposal that can be included in crossbreeding 

programs. So, the idea of retaining the competitiveness of the small populations may be worth 

the effort. Thus, strategies set out to maximise company revenues may have the additional 

benefit of helping to conserve biodiversity. 

Marker density 

The accuracy of the DGV increases as the density of the markers increases, because it is more 

likely to find markers that are in strong LD with the QTL when the marker density is high 

(Hayes et al., 2009a). For this reason, it may be advisable to genotype the animals in the 

reference population with a chip containing 800 000 markers rather than 50 000. However, 

the accuracy may not improve as much as one would have expected (Meuwissen and 

Goddard, 2010). In most, widely used dairy cattle populations the markers are in LD with the 

QTL over long distances and the level of LD does not increase a lot as the distances between 

the markers and the QTL decrease unless the distance is very small (de Roos et al., 2008). 

This LD pattern results from the fact that the effective population size of these populations 

has decreased rapidly during the recent past because of domestication, breed formation, and 

artificial breeding techniques (de Roos et al., 2008). Based on the results from de Roos et al. 

(2008) we would expect that the accuracy of the DGV will only increase considerably with a 

chip containing at least 100 000 markers. 

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Effective population size 


Hayes et al. (2009c) compared results from Australian and US field data with results from the 

deterministic prediction model from Goddard (2009). The accuracies of the DGV that were 

based on field data were in most cases a bit higher than the accuracies of the DGV that were 

based on the deterministic prediction when the effective population size was assumed to be 

100 for the two Holstein populations and 30 for the two Jersey populations (Hayes et al., 

2009c). Nevertheless the results agreed well with one another. We would have expected that 

the difference between the accuracies would have been larger because the accuracies based on 

field data are a result of the markers capturing the effect of relationship as well as the effect of 

LD between markers and QTL, whereas the accuracies based on the deterministic prediction 

are solely a result of the markers capturing the effect of LD between markers and QTL. In the 

deterministic prediction model, the accuracy of the DGV increases as the effective population 

size decreases. Consequently, the small difference between the accuracies based on the 

deterministic prediction and the accuracies based on field data may be due to the use of a 

current effective population size rather than a historical effective population size (Hayes et al., 

2009c). This expectation is based on the fact that the amount of LD in a given population is a 

function of the historical effective population size, and not only the recent effective 

population size. 

Persistence of the accuracy of the DGV 

Some simulation studies show that the accuracy of the DGV decreases as the number of 

generations between the animals in the reference population and the selection candidates 

increases (e.g. Habier et al., 2007) whereas others do not (e.g. Meuwissen and Goddard, 

2010). The reason may be that the marker density differ between the studies by Habier et al. 

(2007) and Meuwissen and Goddard (2010) (100 SNP per Morgan vs. ~33 000 SNP per 

Morgan, respectively). Another important factor may be the genetic relationship among the 

animals in the reference population. The population size is larger in the study by Meuwissen 

and Goddard (2010) than in the study by Habier et al. (2007). For that reason the animals in 

the reference population will be less related and the markers will capture less of the genetic 

relationship among the genotyped animals (Meuwissen and Goddard, 2010). Thus, for the 

accuracy of the DGV to persist across generations it seems as if the marker density needs to 

be high and the reference population needs to contain animals that are as distantly related to 

each other as possible (Meuwissen and Goddard, 2010). In Paper IV, it is difficult to give an 

104


estimate of whether the most recent information is worth more than the information that was 

collected long ago when predicting marker effects, because we do not know the combined 

effect of using a relatively low marker density (38 000 informative markers) and a relatively 

high effective population size (900 animals) on the accuracy of the DGV. 

Genomic prediction models 

More evaluation centres, including the evaluation centre in the Nordic countries, use a 

genome-wide best linear unbiased prediction model (GWBLUP model) when they predict 

DGV because it requires less computation time and yields as high accuracies of the DGV as 

the Bayesian models in many cases (Hayes et al., 2009a). At least this is true if the animals in 

the reference population are genotyped with a chip containing 50 000 markers. Meuwissen 

and Goddard (2010) showed in a simulation study that it is necessary to use more 

sophisticated statistical models to make the best of a high marker density if the number of 

causative SNP is limited. However, if the number of causative SNP is very large, the 

GWBLUP model may result in as accurate predictions as the Bayesian models (Meuwissen 

and Goddard, 2010). This seems reasonable, as the assumptions underlying GWBLUP are 

closer to be fulfilled if there are many genes each with a small effect. 

If animals are selected on the basis of a correlated trait, unbiased evaluations can only be 

obtained from multi-trait models that include information on the correlated trait on which the 

selection was based (Mrode, 2005). Selection for female fertility as well as milk production is 

just one example out of many in dairy cattle breeding. The bias stems from a systematic trend 

in the average of the trait. This trend is due to selection on a correlated trait and the size of 

this trend depends on the selection response for the correlated trait. So speeding up selection, 

e.g. by using genomic selection, may cause a greater need to use multi-trait evaluations to get 

unbiased predicted breeding values. Therefore, it seems reasonable to assume that the bias 

caused by not using multi-trait evaluations is proportional to the annual genetic gain so that 

multi-trait evaluations are more relevant in breeding schemes with genomic selection than in 

breeding schemes without genomic selection because the rate by which the genetic gain is 

achieved will increase. 

Today, young bulls and potential bull dams are pre-selected on the basis of DGV. 

Consequently, the expectation of the Mendelian sampling effect is not zero and this creates a 

bias in the subsequent genetic evaluation. By combining information on pedigree, phenotypic 

105


performance and genotype in a correct manner it is possible to avoid this selection bias. Both 

one-step procedures and multi-step procedures that are able to take pre-selection into account 

are under development (e.g. Christensen and Lund, 2010; Ducrocq and Liu, 2009). Selection 

is based on unbiased genomically enhanced breeding values (GEBV) in the stochastic 

simulation study in Paper III because the DGV are sampled on the basis of known 

correlations between the true breeding values and the DGV. It is not possible to use the same 

approach in the genetic evaluation as we did in the simulation study because the DGV are 

predicted on the basis of daughter yield deviations, deregressed proofs or EBV in practice. 

For the time being, an index combining DGV and parent average breeding values (PABV) 

may equalize the accuracies for selection candidates with different genetic relationship to the 

animals in the reference population. The results from Lund et al. (2009) substantiate this 

argument as they found a higher genetic correlation between DGV and PABV if the sire of 

the selection candidate was included in the reference population. For that reason, the selection 

candidates with and without sires in the reference population had the same probability of 

being selected on the basis of a combined index. However, the accuracies of the PABV were 

relatively high in the study by Lund et al. (2009) because the sires and the maternal grandsires 

were progeny tested bulls. If a turbo scheme is going to be used then the sires of the selection 

candidates will not have daughters with phenotypic records. Consequently, the accuracy of 

the PABV will be lower for all selection candidates in the turbo scheme. Because of this, the 

chance of being selected will likely be lower for the selection candidates that are less related 

to the animals in the reference population even though an index combining DGV and PABV 

is constructed. 

Consequences of genomic selection on rate of inbreeding 

Simulation studies have shown that the rate of inbreeding per generation is lower in breeding 

schemes with genomic selection than in breeding schemes without genomic selection (e.g. de 

Roos et al., 2010; Paper III). This result is also reached even if the generation interval is 

reduced. The reduction in the rate of inbreeding is due to the fact that GEBV are based less on 

information from relatives and more on information from the animal itself than EBV. It is 

likely that the advantage of including genomic information in the selection index is greater if 

the selection index contains many functional traits because EBV based on best linear unbiased 

106


prediction build even more on information from relatives when the heritability of the traits is 

low. Whether this will be the case in practice remains to be seen. 

According to Daetwyler et al. (2007) the rate of inbreeding should be presented per generation 

as it is a more suitable measure of the biological risks of inbreeding depression and 

deleterious alleles because the processes that work against inbreeding, e.g. mutation, also take 

place per generation. However, the rate of inbreeding per year indicates the uncertainty of the 

outcome of a breeding scheme. In Paper III and in the study by de Roos et al. (2010), the rate 

of inbreeding per year was higher in turbo schemes than it was in conventional progeny 

testing schemes and in pre-selection schemes. Thus, a turbo scheme is more uncertain than 

breeding schemes using progeny testing. 

The results from Lillehammer et al. (2010) suggest that the accuracies of the DGV will 

decrease over time given that a turbo scheme is used and the reference population is only 

supplemented by sires with proofs. Thus, the genotyping strategy with the purpose of 

selecting breeding animals is not sufficient to maintain the level of information in the 

reference population. Therefore, AI companies have to spend resources on strategies of 

maintaining the level of information in the reference population. The size of the reference 

population and the heritability of the trait have a favorable effect on the proportion of the 

reliability of the DGV that is explained by LD, as mentioned earlier. Thus, commercial 

populations with a small population size and therefore a small reference population may 

suffer from a higher probability of co-selection of relatives than populations with a large 

population size. This would especially be true if the selection index contains many functional 

traits. Therefore, strategies of maintaining the level of information in the reference population 

are even more important for small commercial populations. 

Daetwyler et al. (2007) suggest that optimal contribution selection could be used to handle the 

transition from a breeding scheme where sires are selected on the basis of progeny testing 

results to a breeding scheme where sires are selected directly on the basis of GEBV. Optimal 

contribution selection is a selection method that maximizes the genetic level of the selected 

parents, while controlling the increase of the average kinship in the population (Meuwissen, 

2007). Depending on the data that are available, the kinships between the animals may be 

assessed using pedigree, markers or a combination of both. Sonesson et al. (2010) showed 

that it is possible to achieve the desired rate of inbreeding per generation whether the rate of 

inbreeding based on genomic identical-by-descent is constrained or the pedigree based rate of 

107


inbreeding is constrained. However, the genomic rate of inbreeding was approximately three 

times too high when the pedigree based rate of inbreeding was constrained (Sonesson et al., 

2010). The discrepancy between pedigree based rate of inbreeding and genomic rate of 

inbreeding is larger when the selection decisions are based on genomic information (Pedersen 

et al., 2010). So, using genomic selection it may be necessary to reevaluate the guidelines for 

acceptable rates of inbreeding (Sonesson et al., 2010). 

References 

Christensen, O. F., and M. S. Lund. 2010. Genomic prediction when some animals are not 

genotyped. Genet. Sel. Evol. 42:2. 


selection. J. Anim. Breed. Genet. 124:369-376. 

de Roos, A. P. W, B. J. Hayes, R. J. Spelman, and M. E. Goddard. 2008. Linkage 

disequilibrium and persistence of phase in Holstein-Friesian, Jersey and Angus cattle. 

Genetics 179:1503-1512. 

de Roos, A. P. W., C. Schrooten, R. F. Veerkamp, and J. A. M. van Arendonk. 2010. The 

impact of genomic selection and short generation interval on dairy cattle breeding programs. 


2010. 

Ducrocq, V., and Z. Liu. 2009. Combining genomic and classical information in national 

BLUP evaluations. Proceedings of the Interbull Meeting, Barcelona, Spain, August 21-24, 

2009. Interbull Bulletin 40:172-177. 

Goddard, M. 2009. Genomic selection: prediction of accuracy and maximisation of long term 

response. Genetica 136:245-257. 

Goddard, M. E., and B. J. Hayes. 2009. Mapping genes for complex traits in domestic animals 

and their use in breeding programmes. Nat. Rev. Genet. 10:381-391. 



Harris, B. L., D. L. Johnson, and R. J. Spelman. 2008. Selection in New Zealand and the 

implications for national genetic evaluation. Proceedings of the Interbull Meeting, Niagara 

Falls, Canada, June 16-19. http://wwwinterbull.slu.se/bulletins/bulletin38/presentations/ICAR/Harris- 

Genomic%20selection%20in%20New%20Zealand%20and%20the%20implications%20for% 

20national%20genetic%20evaluation.pdf Accessed December 7, 2010. 

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Hayes, B. J., P. J. Bowman, A. J. Chamberlain, and M. E. Goddard. 2009a. Invited review: 


Hayes, B. J., P. J. Bowman, A. C. Chamberlain, K. Verbyla, and M. E. Goddard. 2009b. 

Accuracy of genomic breeding values in multi-breed dairy cattle populations. Genet. Sel. 

Evol. 41:51. 

Hayes, B. J., H. D. Daetwyler, P. Bowman, G. Moser, B. Tier, R. Crump, M. Khatkar, H. W. 

Raadsma, and M. E. Goddard. 2009c. Accuracy of genomic selection: comparing theory and 

results. In Proc. Assoc. Advmt. Anim. Breed. Genet., Barossa Valley, Australia, September 

28 – October 1, 2009. 18:34-37. 

Laursen, M. V., D. Boelling, and T. Mark. 2009. Genetic parameters for claw and leg health, 

foot and leg conformation, and locomotion in Danish Holsteins. J. Dairy Sci. 92:1770-1777. 

Lillehammer, M., T. H. E. Meuwissen, and A. K. Sonesson. 2010. Effects of alternative 

genomic selection breeding schemes on genetic gain in dairy cattle. No 130 in Proc. 9 th World 

Congr. Genet. Appl. Livest. Prod., Leipzig, Germany, August 1-6, 2010. 

Luan, T., J. A. Woolliams, and T. H. E. Meuwissen. 2010. The contribution of linkage and 

linkage disequilibrium information to the accuracy of genomic selection. No 636 in Proc. 9 th 


Lund, M. S., G. Su, U. S. Nielsen, and G. P. Aamand. 2009. Relation between accuracies of 

genomic predictions and ancestral links to the training data. Proceedings of the Interbull 

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Meuwissen, T., and M. Goddard. 2010. Accurate prediction of genetic values for complex 

traits by whole-genome resequencing. Genetics 185:623 - 631. 



Pedersen, L. D., A. C. Sørensen, and P. Berg. 2010. Marker-assisted selection reduced 

expected inbreeding but can also result in large effects of hitchhiking. J. Anim. Breed. Genet. 

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Sonesson, A. K., and T. H. E. Meuwissen. 2009. Testing strategies for genomic selection in 

aquaculture breeding programs. Genet. Sel. Evol. 41:37. 

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Sonesson, A. K., J. A.Woolliams, and T. H. E. Meuwissen. 2010. Maximising genetic gain 



2010. 

van der Werf, J., and R. G. Banks. 2010. A genomic information nucleus to accelerate rates of 

genetic improvement in sheep. No 46 in Proc. 9 th World Congr. Genet. Appl. Livest. Prod., 

Leipzig, Germany, August 1-6, 2010. 

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Predicting energy balance for dairy cows using high-density single nucleotide polymorphism 

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Conclusions and perspectives 

The implementation of genomic selection in dairy cattle breeding has been a swift process. So 

far, the main focus has been on the development of methods for predicting genetic merit. 

Consequently, breeding schemes with genomic selection is still a relatively new research area. 

Hopefully, this thesis will contribute to the understanding of the potential advantages of 

genomic selection as such and the potential advantages for genetic gain in the functional traits 

in particular. 

The overall conclusion of this thesis is that precise phenotypic measurements that are closer to 

the traits in the proper breeding goal provide the opportunity for higher genetic gain in the 

functional traits, also in breeding schemes with genomic selection. In addition to this, the 

thesis also supports the following findings. 

Main findings 

Breeding schemes with genomic selection result in a larger genetic gain in the functional traits 

than breeding schemes without genomic selection without compromising the genetic gain in 

the milk production traits (Paper III). Several simulation studies support this result, and we 

believe that it also holds true in practice. Today, the accuracies of the direct genomic values 

(DGV) for the functional traits and the milk production traits are almost equally high because 

the estimation of marker effects is based on a large population of well-proven bulls. However, 

precise phenotypic measurements are also needed in the future so the accuracies of the DGV, 

and thus the genetic gains in the functional traits, can maintain the same level as they have 

today. 

Earlier on, a large amount of data had to be collected if a new trait was to be included in the 

genetic evaluation. However, genomic selection enables genetic improvement of new traits 

within a reasonably short period of time (Paper IV). This result is in line with the fact that 

genomic selection allows accurate selection decisions to be made even for traits that are 

recorded on only a few animals due to high costs or other constraints (Paper IV). This is 

especially true if the reference population contains cows instead of sires. 

It is possible to obtain genetic progress for functional traits by including traits in the selection 

index that are less affected by management and resemble the traits in the proper breeding goal 

to a greater extent, e.g. measures of hoof diseases reported by hoof trimmers (Paper II). We 

111


expect that this result also applies for breeding schemes with genomic selection as the 

accuracy of the DGV tends to increase as the heritability of the trait increases (Paper IV). To 

our surprise, the inclusion of an indicator trait in the selection index improves the annual 

genetic gain even if genomic information on the functional trait in the breeding goal is 

available (Paper III). Therefore, indicator traits still play an important role in dairy cattle 

breeding, especially if genomic information on the indicator traits is also included in the 

genetic evaluation. 

On the assumption that the accuracies of the DGV are equally high for all selection 

candidates, the rates of inbreeding are lower in breeding schemes with genomic selection than 

in breeding schemes without genomic selection (Paper III). However, markers are capable of 

capturing the genetic relationship among the genotyped animals so the effect of genomic 

information on the rate of inbreeding may be less markedly in practice or even unfavorable. 

Genomic selection sets the stage for a reconsideration of the existing progeny testing scheme 

because a short generation interval increases the effect of genomic selection on the annual 

genetic gain (Paper III). As a result, it is likely that a genomic selection breeding scheme with 

intensive use of young bulls will be implemented in practice in the medium to long term. 

However, the accuracies of the DGV may decrease over time if the reference population is 

only supplemented by the bulls that are used directly as sires without progeny testing results. 

It is therefore advisable to include test bulls and/or cows as well as sires in the reference 

population (Paper IV). 

Genomic selection may also call for a reconsideration of the use of multi-trait evaluations. In 

a breeding scheme without genomic selection, a multi-trait evaluation will only increase the 

accuracy of selection marginally when the records that are available today are used (Paper I). 

However, multi-trait evaluations may be needed in the future in order to avoid selection bias 

because the rate by which the genetic gain is achieved will increase as a consequence of 

genomic selection. Besides being necessary for multi-trait evaluations, genetic correlations 

may also contribute to the understanding of the biology of dairy cattle. This is especially true 

if the traits we are able to measure resemble the traits in the proper breeding goal. 

112

Use of genomic information in dairy cattle breeding has been assigned a high priority in recent years. 

So far the main focus has been on the development of methods for predicting genetic merit. The next 

step is to study the effects of genomic selection on future breeding schemes. Based on field data as well 

as simulated data, this thesis contributes to the understanding of the potential advantages of genomic 

selection on genetic gain in the functional traits. Three main conclusions of this thesis are: 1) a breeding 

scheme with genomic selection and with intensive use of young bull results in a greater contribution of 

the functional traits to the increase in total merit than a conventional progeny testing scheme, 2) genomic 

selection allows accurate selection decisions also for traits recorded on few animals due to costs or other 

constraints, and 3) the inclusion of more precise measures of the functional traits in the selection index, in 

this case measures of hoof diseases, will improve the genetic gain in the functional traits. 

A primary aim at the Faculty of Agricultural Sciences 

is to educate scientists with extensive knowledge 

within agriculture, food and environment. The Graduate 

School of Agriculture, Food and Environment 

(SAFE) ensures that the PhD programmes offered 

are of high international standard. For more information 

visit our website at www.agrsci.au.dk

Perspectives 


In order for genomic selection to be optimally implemented in dairy cattle breeding there are 

still unresolved issues that need to be addressed in the future. This includes, among others, the 

persistence of DGV accuracies across generations, the effect of genomic selection on 

inbreeding at the genomic level, and the definition of the best traits to include in the proper 

breeding goal as well as the selection index. 

Some simulations studies have found that the accuracy of the DGV decreases as the distance 

between the animals in the reference population and the selection candidates increases (e.g. 

Habier et al., 2007) whereas others have not (e.g. Meuwissen and Goddard, 2010). It is likely 

that the decline in the accuracy of the DGV is less noticeably when the number of markers is 

very high because the models are able to pin point markers that are in very high linkage 

disequilibrium with the quantitative traits loci (Meuwissen and Goddard, 2010). In addition, 

the accuracy of the DGV may persist across generations if the animals in the reference 

population are distantly related to each other because the markers are less capable of 

capturing the genetic relationship among the genotyped animals (Meuwissen and Goddard, 

2010). Little is known about the decline in the accuracy of the DGV in practice as the long- 

term consequences of genomic selection are still uncertain. Therefore, it should be examined 

more closely to what extent the accuracy of the DGV persists across generations in different 

situations. 

Historically, measures of inbreeding have been based solely on pedigree information. 

However, pedigree estimated inbreeding is only correct if all loci across the genome are 

neutral and the alleles at each locus have equal probabilities of being found in selected 

offspring. This is not the case in selective breeding schemes and especially not in breeding 

schemes with genomic selection as genomic information increases selection pressure on 

individual quantitative trait loci that affects the traits in the selection index. Consequently, 

traditional pedigree estimated inbreeding underestimates true inbreeding defined as the actual 

proportion of loci that are identical by descent across the genome (Pedersen et al., 2010). It 

may be possible to prevent the reduction in genetic variability that is caused by strong 

selection for particular chromosomal regions if optimal contribution selection is used in 

combination with genomic selection (Meuwissen, 2007). However, the effect of genomic 

selection on inbreeding should be studied more closely. 

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Today, most applied breeding goals are defined by the traits that are measurable rather than 

by the traits we want to improve (Oldenbroek, 2007). Due to technological developments 

more and more measures that are relevant for the management of cows will be available. 

Some of these measures will be relevant to include in the selection index as well. As a 

consequence of genomic selection, this also applies to measures that are recorded on a small 

scale. Which measures to select will be easier to identify if the proper breeding goal is well- 

defined. For instance, if one of the new measures does not show genetic variation or if it is not 

genetically correlated to the traits in the proper breeding goal then it is not relevant for 

breeding purposes. Thus, it is important to investigate which traits to include in the proper 

breeding goal because it facilitates the decisions on which traits to include in the selection 


In dairy cattle breeding, there is a general wish to maintain the current genetic levels of the 

functional traits or even to increase them. It may be possible to reach that goal as genomic 

selection in combination with precise phenotypic measurements that are closer to the traits in 

the proper breeding goal will lead to higher genetic gain in the functional traits. 

References 






Meuwissen, T., and M. Goddard. 2010. Accurate prediction of genetic values for complex 

traits by whole-genome resequencing. Genetics 185:623 - 631. 

Oldenbroek, K. 2007. Glossary. Pages 215-228 in Utilisation and conservation of farm animal 

genetic resources. Wageningen Academic Publishers, Wageningen, The Netherlands. 

Pedersen, L. D., A. C. Sørensen, and P. Berg. 2010. Marker-assisted selection reduced 

expected inbreeding but can also result in large effects of hitchhiking. J. Anim. Breed. Genet. 

127:189-198. 

114

Genetic improvement of functional traits in dairy cattle

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