Inverse density dependence and the Allee effect - Personal Web ...

PERSPECTIVESPer capitagrowth rate(dN/Ndt)DensitydependenceInverse densitydependence (Allee effect)Box 1. The floury little worldof the TriboliumOne of the earliest illustrations of Allee’s ideasof the existence of an optimal population sizeconcerns his analysis of the laboratory work ofthree different researchers on the flour beetle,Tribolium confusum 35 . This species showed the‘most rapid population growth at an intermediatepopulation size rather than with too few ortoo many present’, as shown in his figure,reproduced below.K —(unstable)Fig. 1. Illustration of the Allee effect, from a very simple mathematical model of population dynamics:dNdtThe per capita growth rate (dN/dt) is negative above the carrying capacity (K) and positive below. However,in the presence of an Allee effect, it also decreases below a given population size, and can even becomenegative below a critical population threshold (K ). When a population displaying this type of populationdynamics is driven below the critical threshold, the low, sometimes negative, per capita growth rate maylead it to extinction.æ N öæN ö= rNç1-÷ -è K øç 1è K÷ø-K(stable)Populationsize (N )fertile), distributed across four islands 7 .A recent breeding program has resultedin the birth of nine chicks, but only two ofthese are female (R. Dennett, pers. commun.).The third category concerns thereduction in cooperative interactionswhen there are fewer individuals.This last mechanism has attractedmost research effort, probably partlybecause Allee himself proposed it, referringto it as ‘proto-cooperation’ or ‘facilitation’1 . Given that cooperation usuallyimplies active participation, we prefer touse the more generalist term of facilitation,except for particular cases. Shortage ofreceptive mate encounters during the matingperiod when density is too low 8 is themost cited factor, although it representsonly a small subset of social causes ofinverse density dependence. Species inwhich fitness is enhanced by any type ofconspecific facilitation might suffer fromreduced density when intraspecific competitiveprocesses are of secondary importance(Box 2). In this context, facilitation istaken in the broadest sense and sometimesincludes sexual reproduction (where twoorganisms can be seen as ‘cooperating’ topass on their genes to the next generation).For example, decreased sexual reproductionowing to a lower probability offinding a mate at very low densities mightgenerate a lower rate of recruitment,which in turn lowers the probability offinding mates in the next generation,thereby creating an extinction vortex,and ultimately the collapse of the population.Additionally, in cooperative animals,reduced recruitment may also becaused by higher juvenile mortality,owing to the cost of feeding or babysittingin small groups 9 as in suricates,Suricata suricatta.The Allee effect might also be generatedby lower survival, such as whenantipredator strategies become inefficientin small groups of prey. Examplesof this include the passive protection ofTrends in Ecology & EvolutionReproduction rate(per female per day)87654311 days2125 days00 2 4 8 16 32 64Initial density(in 32 mg of flour)Trends in Ecology & Evolution(Online: Fig. I)The higher growth rate at an intermediatepopulation size was interpreted as the resultof the interaction between two opposingprocesses. On one hand, ‘adult beetles roamat random through their floury universe. Theyeat the flour, but they also eat their own eggsas they encounter these on their travels’ 35 .Because of this, eggs are less likely to escapeoophagy at high densities. However, femaleslay more eggs, and eggs with a higher percentageof fertility, when they have been stimulatedby successive copulation, which is morelikely to occur at high densities. As a result,there is an intermediate optimal populationdensity, above the possible minimum one, inwhich the growth rate is higher than at lower orhigher population densities. Later, Allee andcollaborators 35 showed that fish are betterable to survive water poisoning if other fishhad previously lived in it, because their secretionshad conditioned the environment. Thisrelationship between fitness and density was,however, positive only until competitionbecame the principal factor influencing populationdynamics. Such an interaction betweentwo processes with an opposing relationshipto density is a reasonably general feature ofthe Allee effect.sea urchin larvae sheltered by adultspine canopies 10 , the early warning orconfusion effects in fish schools andungulate herds 11 , or more active sentinelsystems or defence strategies, as in suricates12 . However, because the extent offacilitation and/or cooperation mightdetermine the strength of the Alleeeffect, many of these processes could berather weak unless the populations areat very low density. In contrast, obligatecooperatively breeding species mightexperience a strong inverse densitydependence, even when close to the carryingcapacity, and may suffer from anAllee effect for most of their normal densityrange 12,13 .406 TREE vol. 14, no. 10 October 1999

PERSPECTIVESFig. 2. Examples of the Allee effect in different taxa. (a) Because of a shortage of fertilization or of mating encounters, Allee effects can cause species extinctionwhen density is too low. This is illustrated by pollination in fig trees (Ficus sp.), where small dispersed patches attract fewer pollinators or dispersers (photo reproduced,with permission, from Corbis/C. Mattison). (b) The Allee effect is important in group living animals, such as schooling fishes (here bluefin tunas Thunnus thynnusin fishing nets). It may also cause a population to collapse if harvesting pressure is too strong, as has happened for fisheries (photo reproduced, with permission,from Corbis/J.L. Rotman). (c) Because fruit flies attack more than 400 crops worldwide, they are considered to be one of the worst insect pests of agriculture. Oneof the techniques used to control them is the release of sterile males to create an Allee effect, as for these fruit flies, Anastrepha ludens (photo reproduced, withpermission, from J. Dykinga, Agricultural Research Service, USDA). Another technique is to release natural enemies, in numbers large enough to ensure the Alleeeffect is avoided. (d) At very small population sizes, some endangered species, such as the Kakapo (Strigops habroptilus), have a low probability of finding receptivemates, and/or have a biased sex-ratio because of demographic stochasticity. There are only 54 individuals surviving of this giant parrot (photo reproduced, withpermission, from D. Merton). (e) Obligate cooperative breeders, such as African wild dogs (Lycaon pictus), may have a critical group size below which the groupwould be very likely to go extinct (photo reproduced, with permission, from J. Ginsberg).Implications for populationdynamicsFor all these phenomena, and others,the major consequence of the Allee effectis the existence of a critical density belowwhich the aggregation unit considered(e.g. population, colony or social group)is likely to go extinct. This has beenshown theoretically both with deterministicand stochastic mathematical models4,13,14 , and although still scarce, empiricalevidence exists from very diverseecological systems (Box 2). Because themechanism is quite straightforward, verybasic population dynamic models (comparablein simplicity to the classicalVerlhust logistic equation) can be usedto mimic the Allee effect (Fig. 1).TREE vol. 14, no. 10 October 1999 407

PERSPECTIVESBox 2. Allee effects, facilitation and cooperationThe Allee effect can be generated by a shortage of interactions among conspecifics at low density. Theseinteractions range from strict cooperation to unconscious facilitation. At one extreme, strong cooperation,are taxa that form colonies (with different degrees of coloniality). For example, because offspringsurvival to maturity increases with colony size, the lifetime reproductive success of female social spiders,Anelosimus eximius, decreases in small colonies 36 . Smaller colonies of reef-building coral populationsare less likely to survive attacks by mucilage coverage 37 or catastrophic climatic events 33 . InDamaraland mole-rats, Cryptomys damarensis, small colonies are more likely to fail because the colonywork force is of insufficient size to locate food 38 . In plants, lower survival can be caused by a lack of conditioningeffects at low densities 39 , and some colonial seabirds need a critical density to establish andreproduce 1,40 .At the other extreme of sociality are individuals of species whose only form of contact with conspecificsis for sexual reproduction (which can in this context be considered as proto-cooperation). They can alsobe subject to Allee effects. For example, pollination of many species of plants (especially by animalvectors), is less efficient when inter-individual distances become too large or patches too small 39,41,42 .Fertilization in benthic invertebrates with free-spawn gametes, or with planktonic larvae, has also beenshown to be insufficient at low population densities 33 . A shortage of encounters with receptive matesduring the mating period 8 can increase the threat to small populations, such as those of the Glanvillefritillary butterfly, Melitaea cinxia 18 , and the northern spotted owl, Strix occidentalis 43 . An Allee effect mayalso delay the beginning of an invasion 32 , or even prevent its success, as seen in the House Finch,Carpodacus mexicanus, in North America. The same is true for species introductions (for their conservationor for biological control of another species), which generally require repeated releases of large numbersof individuals before successful establishment 44,45 .Between these two extremes, the atypical social system of obligate cooperative breeders can generatean Allee effect, potentially responsible for their high rates of group extinction 13 (Box 3).The implications of the Allee effect arepotentially very important in most areasof ecology 15 and evolution 14 , but we willfocus here on population dynamics only.As we will see below, the practical managementof population numbers, whetheraiming to increase or reduce them, isstrongly affected by this effect. The consequencesof Allee effects are also likely tobe significant for the theory of populationdynamics, because most classic modelsimply a linear decrease of growth withdensity, as opposed to the non-linear relationshipassociated with the Allee effect 14 .Similarly, current mathematical modelsseem to overestimate persistence times formetapopulations of species exhibiting anAllee effect, because even when explicitlyconsidering small metapopulation sizes,they carry the implicit assumption thatlocal populations always increase totheir carrying capacity 16 . Other types ofAllee effects have been demonstrated atthe theoretical metapopulation level whenthe spatial dimension and stochasticityare taken into account 4,17 . The importanceof the Allee effect in metapopulationdynamics has also been shown empirically,as for the endangered Glanvillefritillary butterfly (Melitaea cinxia) 18 .Repercussions across trophic levelsAlthough it is an intraspecific phenomenon,some interspecific relationshipsBox 3. The Allee effect in African wild dogs?It has recently been proposed that the high rates of group extinction observed in obligate cooperativebreeders are generated by a need for a critical number of helpers, which produce an Allee effect 13 . As aresult, a social group driven below a critical threshold would have a lower chance of recovery and consequentlybecome even smaller, with an increasing risk of extinction.This can be illustrated by the African wild dog, Lycaon pictus, which is currently facing the threat ofextinction throughout its remaining geographical range. Many causes have been proposed to explain its currentdecline, including human persecution, diseases, habitat fragmentation and competition with otherpredators 46 . Although it has never been proposed, another, nonexclusive, factor is the existence of an Alleeeffect, which would render this species more sensitive to other mortality factors. Wild dogs live in groups ofup to 20 adults and their dependent young 23 . The hunting strategy of the group usually requires a critical sizeto be energetically efficient 23,24,47 . A threshold group size might also be required for hunting because ofkleptoparasitism by hyenas, which can be energetically very costly to small groups of wild dogs 22,47,48 . In addition,helpers are required by the breeding female: litters are very large (up to 20 pups), and the breeding female,then the pups, need to be fed by other members of the group 46,49 . Group members also help by chasingpredators from the den area, and by staying at the den to protect the pups while the pack is hunting 46,49 .Consequently, a critical number of helpers might be needed for wild dog groups to survive. It has beensuggested that groups of less than four adults are unable to reproduce successfully 46 . Furthermore, theimpact of environmental stochasticity (including random catastrophes, such as droughts and epidemics)and of natural enemies (competitors, predators, kleptoparasites) might increase the extinction probabilityof cooperators by driving them closer to or below the critical threshold. Human activities andpathogens might act in the same way, increasing the threat of the Allee effect by decreasing group sizes.For example, because of high contact rates owing to wild dogs’ social structure, a virus can probablyspread rapidly among group members. The disease-induced death of several dogs might then reduce thegroup to insufficient size for survival.are strongly influenced by the Alleeeffect. It is well known that smaller groupsof prey may be more exposed to predationthan larger groups 11 . It has also beenshown, both theoretically and empirically,that if a species is a secondary preyitem of a predator with a type II functionalresponse, its death rate from predationwill be inverse density dependent19 . Similarly, the rate of infection formany parasitoid species has been shownto decrease with increasing host density20 . Other interspecific relationships,such as nest parasitism 21 and kleptoparasitism22 can also be affected (Box 3).The victims of interspecific relationships(e.g. prey or hosts) are not the onlyones prone to the Allee effect: at lowdensity, their natural enemies can alsosuffer inverse density dependence.Indeed, some cooperative hunters arenot as efficient if they have a small huntingparty, because some prey require acertain number of individual hunters ifthey are to be successfully isolatedand attacked 23,24 (Box 3). Other examplesinclude kleptoparasites: hyenas (Crocutacrocuta) form large clans that spread outin search of prey and regroup onceindividuals have located a fresh kill andsignalled to the others. A critical thresholdin the clan size of hyenas is thus likelyto limit the success of this type of foragingstrategy when prey are scarce. Thisalso seems to be true for many birds(whether predatory or not) regrouping inflocks to maximize resource location efficiency.In addition, it is reasonable topredict that inverse density-dependentmechanisms are likely to affect stronglythe population dynamics of species suchas parasitoids 20 , because the difficulty offinding a mate at low densities compoundsthat of finding a host when thehost density is also low.Perhaps among the best known manifestationsof population thresholds forextinction are some infectious pathogens,which do not persist below a critical hostpopulation size, as shown for human 25 aswell as wildlife populations 26 . This is becausethe life history of some pathogens(mostly their rates of transmission andinduced mortality) makes it difficult forthem to infect new hosts before dying outif the host density is too low. Althoughthis is not an Allee effect per se, this criticalcommunity size, which can take differentmathematical forms according tothe system modelled 27 , has interestinganalogies with minimum viable populationsand extinction thresholds generatedby inverse density dependence. At adifferent scale, too few parasites (eithermicro- or macroparasites) in a host areless likely to overcome the host’s immunedefence, resulting in the extinction of the408 TREE vol. 14, no. 10 October 1999

PERSPECTIVESparasite. Consequently, there might be acritical threshold for many internal parasites.Allee effects in more complex interspecificrelationships, involving more thantwo species, have seldom been considered.However, given what is alreadyknown about the importance of thisprocess on ‘simple’ competitive, predatoryor parasitic relationships, it is reasonableto predict that models of processessuch as predator- or parasite-mediatedcompetition (which is an important ecologicalprocess 28 ) will generate differentoutcomes in the presence of inverse densitydependence. At the niche scale, theAllee effect can prevent persistence ofplants that ameliorate physically stressfulhabitats 29 . This environmental conditioningis also important for many associatedplant and animal species because it allowsnew colonization. At a larger scale, theAllee effect is likely to have a detectableinfluence on plant community dynamicsand vegetation succession 29 . It is verylikely that species are affected by inversedensity dependence generated by a combinationof all these ecological forces.Even those species displaying no obviousAllee effect can be affected by others thatdo, which means that most species areprobably influenced, either directly orindirectly, by this dynamic process.Implications for applied ecologySpecies subjected to a strong Alleeeffect might be more susceptible to catastrophicpopulation collapses with only aslight increase in mortality, resulting eitherfrom harvesting or ‘natural’ causes. Twogenerally conflicting interests in ecosystemmanagement, long-term optimal harvestingand biodiversity preservation, whichboth aim to prevent these collapses, havemuch to gain from acknowledging potentialAllee effects. In fisheries, for example,the existence of multiple equilibria hasbeen recognized (in theory at least), andthe existence of a critical threshold forharvested populations has been advancedas a highly plausible explanation for thecollapse of fisheries in several parts of theworld 30 (Fig. 2). As exploited fish speciesare usually schooling species, and a largeschool is generally considered to be adefence against predators 21 , one shouldexpect (and therefore attempt to prevent)Allee effects in these species.Prevention of population collapses isalso a priority in conservation biology 15 ,where it is widely admitted that populationsof small size are often at greaterrisk of extinction. However, even thoughmany conservation programs (includingreintroduction) focus on the extinctionrisks encountered by very small populations,and the existence of a minimumBox 4. Biological control: helped and hindered by Allee effectsThe primary aim of biological control, which is nothing more than a planned biological invasion to get ridof another invasion, is to minimize the establishment and persistence of pests and maximize that of theirenemies. This is one of the few research areas in which the Allee effect is plainly recognized and fullyused. The first successful attempts at biologically controlling a pest insect to meet with success artificiallycreated an Allee effect in the pest population by inundating it with sterile males 50 . This method isstill widely used 50 , as illustrated by the massive releases of sterile male Mediterranean fruit flies, Ceratitiscapitata, last year in the USA. The emerging new concept of mammal control through virus-vectoredimmunocontraception 51 is likely to succeed because it should create an Allee effect.An important issue in biological control programmes (and in the reintroduction of threatened species)concerns the minimum number of individuals that should be released to ensure the establishment ofpopulations of natural enemies of the pest. Indeed, insufficient reproduction at low densities wouldresult in a collapse of these populations because of at least two mechanisms 44 . First, the low probabilityat finding a mate at low density may lead to a lack of recruitment 8 . Second, in arrhenotokous insectspecies (when virgin females produce only males), failure to mate may result in a male-biased sex ratio,and therefore in demographic stochasticity 4 . Both potentially create an Allee effect, and both can resultin the failure of the introduction 44 .population size below which they cannotrecover, the Allee effect is still seldomtaken into account in this area 15 . That theAllee effect is indexed in only five out of 35of the most recent major books on conservationbiology illustrates this deficiencyvery well. Other research areas where theAllee effect plays a critical role are ecosysteminvasions 31,32 (Box 2) and, mostimportantly, biological control (Box 4).What prospects for the Allee effect?The early studies of population biologyhave been largely dominated by the importanceof (negative) density dependence athigh densities. In a time when anthropogenicdisturbance has driven manypopulations to small sizes and/or lowdensities, we must now focus on the otherextreme of population sizes. Indeed, studiesdemonstrating Allee effects and determiningtheir causal mechanisms, eithertheoretically or empirically, ought to bemore numerous in the future. There is arange of logistical problems associatedwith the study of very small natural populations,especially of mobile animals, renderingit difficult to demonstrate an Alleeeffect 14,18,21 . Nevertheless, in several differentareas of ecology, empirical evidence isneeded on this still poorly documented butnonetheless important dynamic process.With the notable exception of biologicalcontrol, which provides excellentopportunities to study experimentally theeffect of population size on establishmentand persistence, experimental studies ofthe Allee effect are both impractical andunethical in natural conditions. Therefore,one has either to rely on ‘natural experiments’,such as catastrophic events 33 , or towork on laboratory populations 1 , whichcan compensate for the lack of replicabilityand control typical of ‘natural experiments’.Although they are less scarcethan empirical studies, theoretical studiesof the consequences of the Allee effect arealso needed, especially concerning thedynamics of interspecific relationships.Future progress in understanding thedynamics of small populations will mostlikely be achieved by creatively combiningthese different scientific approaches.Knowing a given species is prone to astrong Allee effect would not be of muchhelp if the population collapse was inevitable.In many cases, however, it shouldbe possible to artificially reverse the fateof a population that is dangerously closeto, or even below, its critical threshold.For example, densities of some plants ortrees could be increased by dispersingseeds, or by planting individuals obtainedfrom nurseries or from other, more densepopulations. Similarly, social groups ofsome endangered vertebrates could beartificially increased (e.g. during a shortperiod of captivity), thereby avoiding theloss of the smallest groups. More importantly,knowing that an Allee effect threatensa given population would allow theredirection of harvesting pressure towardsless threatened populations. Similarly,protection efforts for an endangered species,if proven sensitive to the Allee effect,should be redefined according to differentpriorities: for many species, densityas much as population size should becomea criterion of endangerment in conservationprogrammes. As the causes ofdecline of many populations still remaina puzzle (as for the recent amphibiandeclines 34 ), a more systematic investigationof potential Allee effects in endangeredpopulations could be crucial to thebetter understanding of their dynamics,as well as efficiently protecting themagainst formally identified threats.AcknowledgementsThe authors would like to thankJan Lindström, Mads Forchammer,Rosie Cooney, Phil Stephen, Ilkka Hanski,Hamish McCallum and an anonymousreferee for critical comments on themanuscript. Financial support wasprovided by a TMR 30 Marie CurieFellowship from the EuropeanCommunity.TREE vol. 14, no. 10 October 1999 409

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Olsen Trends inGenetics 15, 298Ð299 (August 1999)410 TREE vol. 14, no. 10 October 1999