Patrik Waldmann* and Johann Sölkner

Patrik Waldmann* and Johann Sölkner
Division of Livestock Sciences,
University of Natural Resources and Applied Life Sciences (BOKU),
Vienna, Austria

Introduction
Two approaches to obtain genomic breeding values
1. The genome-wide association approach using (penalized) multiple regression
-> GEBVs sums of regression coefficients
2. The genomic relationship approach using the mixed model with a structured
covariance matrix -> GEBVs random effects

Calculation of genomic relationship matrices (G)
- Three approaches presented in VanRaden (2008)
1. where
2. where
3. where

Linear mixed model as a GMRF

- REML
only point estimates and approximate SE
difficult to perform model comparison
- Bayesian methods (MCMC)
full posterior distributions
Statistical inference
computationally demanding because of the dense G - matrix

Integrated nested Laplace approximation (INLA)

Analysis of QTLMAS 2011 data
- Selection of SNPs with MAF > 0.01
- Calculation of G using approach 1. of VanRaden (2008)
- Make G positive-definite adding part of A, i.e. G* = 0.95G + 0.05A
- Calculate the inverse of G*
- Use the INLA library in R (http://www.r-inla.org/) to obtain estimates of the
genetic and error variances, and to perform predictions of the GEBVs

Results
- Computations took around 45 minutes (Linux server)
- Genetic variance = 21.9 (95% CI: 16.8 – 29.1)
- Error variance = 59.3 (95 % CI: 55.4 – 63.6)
- Heritability = 0.27
- Deviance information criteria (DIC) = 14065.11
- Effective number of parameters = 222.59

Individuals with highest GEBV:
1610 GEBV = 14.6 (95% CI: 9.26 – 20.0)
473 GEBV = 13.0 (95% CI: 7.64 – 18.4)
2582 GEBV = 12.0 (95% CI: 6.84 – 17.2)
1380 GEBV = 11.9 (95% CI: 6.86 – 17.0)
451 GEBV = 11.8 (95% CI: 6.76 – 17.0)
365 individuals with 95% CI of GEBV > 0