A game theoretical approach to conspecific brood parasitism

We constructed a game theoretical model to predict optimal patternsof egg laying in systems where individuals lay in the nestsof others as well as in their own nests. We show that decreasingthe effect of position within an egg-laying sequence on theworth of an egg should lead to reduced parasitism. Indeed,parasitism can only flourish if the worth of an egg to its biological parent declines with the total number of eggs laid in that nest.Further, we found that increasing the intrinsic costs of eggproduction should lead to an increased propensity for conspecificbrood parasitism. The model also predicts that variation inhosts' ability to reject parasitic eggs has little effect on parasitism until this ability is well developed.     

Relatedness and the evolution of conspecific brood parasitism

In conspecific brood parasitism (CBP), a parasitic female takes advantage of the parental care performed by a host female by laying eggs in the nest of the host. The host female raises the offspring of the parasitic female as well as her own. In species where local females are related, direct costs for the host might be more than compensated for by gains in inclusive fitness through increased reproduction of a related parasite, but the role of relatedness in CBP is debated. This inclusive-fitness model of parasitism, structured as a game between host and parasite, suggests that both females can gain inclusive fitness and that host-parasite relatedness can therefore facilitate the evolution of CBP. Crucial assumptions are that there is kin discrimination and a potential for host resistance to parasitism by unrelated females but close relatives are accepted. The cost of parasitism in terms of reduced clutch size or offspring survival for the host must not be large; otherwise, parasitism will reduce her inclusive fitness. Therefore, if these costs are high, it does not benefit a host to accept a parasite, even if the parasite is closely related. The secondary female may still have higher fitness from parasitism, but if the costs are high, she should parasitize an unrelated host, not a relative. This requires that the reduction in parasite success that a host can cause by resistance is not too large; otherwise, it will be better for the secondary female to parasitize an accepting related host or to nest solitarily. For these reasons, host-parasite relatedness is most likely to occur in animals where costs of being parasitized are low and host resistance can markedly reduce the success of an unrelated parasite. When costs are higher, parasitism of unrelated hosts may be better, and if host resistance strongly reduces parasite success, solitary breeding is preferable. In some cases, CBP is directly advantageous for the host, and it may sometimes evolve in close connection with cooperative breeding, which is also considered in the model. Some but not all empirical results support these ideas, and more detailed studies of behavior, relatedness, and reproduction of host and parasite are needed for critical tests.     

The relative role of relatives in conspecific brood parasitism

Conspecific brood parasites lay their eggs in the nests of other females in the same population, leading to a fascinating array of possible ‘games’ among parasites and their hosts ( Davies 2000 ; Lyon & Eadie 2008 ). Almost 30 years ago, Andersson & Eriksson (1982) first suggested that perhaps this form of parasitism was not what it seemed—indeed, perhaps it was not parasitism at all! Andersson & Eriksson (1982) observed that conspecific brood parasitism (CBP) was disproportionally common in waterfowl (Anatidae), a group of birds for which natal philopatry is female‐biased rather than the more usual avian pattern of male‐biased natal philopatry. Accordingly, Andersson (1984) reasoned (and demonstrated in an elegantly simple model) that relatedness among females might facilitate the evolution of CBP—prodding us to reconsider it as a kin‐selected and possibly cooperative breeding system rather than a parasitic interaction. The idea was much cited but rarely tested empirically until recently—a number of new studies, empowered with a battery of molecular techniques, have now put Andersson’s hypothesis to the test ( Table 1 ). The results are tantalizing, but also somewhat conflicting. Several studies, focusing on waterfowl, have found clear evidence that hosts and parasites are often related ( Andersson & Åhlund 2000 ; Roy Nielsen et al. 2006 ; Andersson & Waldeck 2007 ; Waldeck et al. 2008 ; Jaatinen et al. 2009 ; Tiedemann et al. 2011 ). However, this is not always the case ( Semel & Sherman 2001 ; Anderholm et al. 2009 ; and see Pöysa 2004 ). In a new study reported in this issue of Molecular Ecology, Jaatinen et al. (2011a) provide yet another twist to this story that might explain not only why such variable results have been obtained, but also suggests that the games between parasites and their hosts—and the role of kinship in these games—may be even more complex than Andersson (1984) imagined. Indeed, the role of kinship in CBP may be very much one of relative degree!

Table 1. A summary of recent studies that have tested for evidence of relatedness between hosts and parasites in avian conspecific brood parasites

The unavoidable costs and unexpected benefits of parasitism: population and metapopulation models of parasite-mediated competition

When faced with limited resources, organisms have to determine how to allocate their resources to maximize fitness. In the presence of parasites, hosts may be selected for their ability to balance between the two competing needs of reproduction and immunity. These decisions can have consequences not only for host fitness, but also for the ability of parasites to persist within the population, and for the competitive dynamics between different host species. We develop two mathematical models to investigate how resource allocation strategies evolve at both population and metapopulation levels. The evolutionarily stable strategy (ESS) at the population level is a balanced investment between reproduction and immunity that maintains parasites, even though the host has the capacity to eliminate parasites. The host exhibiting the ESS can always invade other host populations through parasite-mediated competition, effectively using the parasites as biological weapons. At the metapopulation level, the dominant strategy is sometimes different from the population-level ESS, and depends on the ratio of local extinction rate to host colonization rate. This study may help to explain why parasites are as common as they are, and can serve as a modeling framework for investigating parasite-mediated ecological invasions. Furthermore, this work highlights the possibility that the ‘introduction of enemies’ process may facilitate species invasion.     

Costs and response to conspecific brood parasitism by colonial red-breasted mergansers

Costs of conspecific brood parasitism (CBP) are expected to be influenced by a species’ life history traits. Precocial birds lay large clutches, and clutches that have been enlarged by CBP can affect host fitness through a longer incubation period, displaced eggs, and lower hatching success. We examined costs and response to CBP by hosts in a population of colonial red-breasted mergansers (Mergus serrator; n?=?400 nests over 8 years) within which 29% of parasitized clutches were enlarged considerably (≥?15 eggs). Length of the incubation period did not increase with clutch size. The mean number of eggs displaced from a parasitized nest during incubation (2.8) was 2×?greater than at an unparasitized nest (1.4). Hatching success declined by 2% for each additional egg in the nest. Thus, for a nest with?≥?15 eggs, one or more fewer host eggs hatch relative to an unparasitized nest with the same number of host eggs, assuming equal probability of success for all eggs. Hosts were 40% more likely to desert nests receiving 2 or 6 experimental eggs relative to unparasitized control nests, although it is unknown whether hens deserting a nest renested elsewhere. Our study indicates that costs of CBP to hosts during nesting may be limited to those red-breasted mergansers incubating the largest clutches (≥?15 eggs), and it raises questions about the adaptive significance of deserting a parasitized clutch.     

Fighting for food: a dynamic version of the Hawk-Dove game

Summary The Hawk-Dove game (Maynard Smith, 1982) has been used to analyse conflicts over resources such as food. At the evolutionarily stable strategy (ESS), either a proportionp* of animals always play Hawk, or each animal has a probabilityp* of playing Hawk. We modify the standard Hawk-Dove game to include a state variable,x, that represents the animal's level of energy reserves. A strategy is now a rule for choosing an action as a function ofx and time of day. We consider a non-reproductive period and adopt the criterion of minimizing mortality over this period. We find the ESS, which has the form play Hawk if reserves are belowc* (t) at timet, otherwise play Dove. This ESS is very different from the ESS in the standard Hawk-Dove game. It is a pure ESS that depends on the animal's state and on time. Furthermore, it is characterized by the strong condition that any single mutant that does not adopt the ESS suffers a reduction in fitness. The standard Hawk-Dove game assumes pay-offs that are related to fitness; our approach starts from a definition of fitness and derives the pay-offs in the process of finding the ESS. When the environment becomes worse (e.g. food becomes less reliable or energy expenditure increases) the ESS changes in such a way as to increase the proportion of animals that will play Hawk.     

A mixed strategy model for the emergence and intensification of social learning in a periodically changing natural environment

Based on a population genetic model of mixed strategies determined by alleles of small effect, we derive conditions for the evolution of social learning in an infinite-state environment that changes periodically over time. Each mixed strategy is defined by the probabilities that an organism will commit itself to individual learning, social learning, or innate behavior. We identify the convergent stable strategies (CSS) by a numerical adaptive dynamics method and then check the evolutionary stability (ESS) of these strategies. A strategy that is simultaneously a CSS and an ESS is called an attractive ESS (AESS). For certain parameter sets, a bifurcation diagram shows that the pure individual learning strategy is the unique AESS for short periods of environmental change, a mixed learning strategy is the unique AESS for intermediate periods, and a mixed learning strategy (with a relatively large social learning component) and the pure innate strategy are both AESS's for long periods. This result entails that, once social learning emerges during a transient era of intermediate environmental periodicity, a subsequent elongation of the period may result in the intensification of social learning, rather than a return to innate behavior.     

A large population parental care game: Polymorphisms and feedback between patterns of care and the operational sex ratio

This article presents a game theoretic model of parental care which models the feedback between patterns of care and the operational sex ratio. It is assumed here that males can be in one of two states: searching for a mate or breeding (including caring for their offspring). Females can be in one of three states: receptive (searching), non-receptive or breeding. However, these sets of states can be adapted to the physiology of a particular species. The length of time that an individual remains in the breeding state depends on the level of care an individual gives. When in the searching state, individuals find partners at a rate dependent on the proportion of members of the opposite sex searching. These rates are defined to satisfy the Fisher condition that the total number of offspring of males equals the total number of offspring of females. The operational sex ratio is not defined exogenously, but can be derived from the adult sex ratio and the pattern of parental care. Pure strategy profiles and so-called single sex stable polymorphisms, in which behaviour is varied within one sex, are derived analytically. The difference between mixed evolutionarily stable strategies and stable polymorphisms within this framework is highlighted. The effects of various physiological and demographic parameters on patterns of care are considered.     

Relatedness and the evolution of conspecific brood parasitism: parameterizing a model with data for a precocial species

Conspecific brood parasitism (CBP) is a common reproductive tactic in several animal taxa, especially in precocial birds. It has been suggested that host-parasite relatedness can facilitate the evolution of CBP. A recent model showed that the existence and accuracy of the kin recognition system is crucial for this to occur. I used field data to parameterize the model for the common goldeneye, Bucephala clangula, a precocial species in which CBP frequently occurs and in which a recent finding of nonrandom host-parasite relatedness has been interpreted to support the idea that relatedness and kin selection influence CBP. It turned out that possibilities to detect brood parasitism and accurately discriminate between kin and nonkin parasites are negligible in the species. The empirically parameterized model exercise revealed that relatedness and kin selection are unlikely explanations of CBP in the species.     

Nest predation and the evolution of conspecific brood parasitism: from risk spreading to risk assessment

Conspecific brood parasitism (CBP) is a taxonomically widespread reproductive tactic. One of the earliest hypotheses put forward to explain the evolution of CBP was "risk spreading"; that is, by laying eggs in more than one nest, parasites may increase the likelihood that at least one offspring will survive to independence. However, the risk spreading hypothesis, based on the assumptions of random nest predation and random selection of target nests by parasites, was theoretically refuted soon after its appearance. New results from the common goldeneye (Bucephala clangula) have revealed that nests are not predated at random and that parasites preferentially lay in safe nests. By taking into account these findings and by modifying accordingly the basic assumptions of the earlier model that refuted the risk spreading hypothesis, we built a model to address the role of nest predation in the evolution of CBP. Model simulations revealed that the selective advantage of parasitic laying, related to nest predation, is much higher than previously thought. Furthermore, the invasion probability of parasitic tactic when initially rare was reasonably high within our model framework. We show that the use of risk assessing, instead of random risk spreading, makes parasitic laying evolutionarily advantageous.     

Rapid convergence to an equilibrium state in kleptoparasitic populations

Previous papers have modelled the behaviour of populations which are subject to kleptoparasitism, and found those ecological situations in which kleptoparasitism should occur. Individuals were considered to be in one of several states, and an equilibrium distribution for the population was found. It was then assumed, for analytical purposes but without proof, that the population was actually in that equilibrium. In this paper, we show that the equilibrium is a stable one, and that it is reached in a relatively short time for all reasonable values of the ecological parameters. Thus, a population may be expected to spend most of the time in equilibrium, and this assumption of these previous works is justified.Research of the first author supported by EPSRC.The authors are also members of The Centre for the Study of Evolution, at the University of Sussex.     

A novel fitness proxy in structured locally finite metapopulations with diploid genetics, with an application to dispersal evolution

Many studies of evolutionarily stable strategies (ESS) for technical reasons make the simplification that reproduction is clonal. A post-hoc justification is that in the simplest eco-evolutionary models more realistic genetic assumptions, such as haploid sexual or diploid sexual cases, yield results compatible with the clonal ones. For metapopulations the technical reasons were even more poignant thanks to the lack of accessible fitness proxies for the diploid case. However, metapopulations are also precisely the sort of ecological backdrop for which one expect discrepancies between the evolutionary outcomes derived from clonal reproduction and diploid genetics, because substantially many mutant homozygotes appear locally even though the mutant is rare globally. In this paper we devise a fitness proxy applicable to the haploid sexual and diploid sexual case, in the style of Metz and Gyllenberg [Metz, J.A.J., Gyllenberg, M., 2001. How should we define fitness in structured metapopulation models? Including an application to the calculation of ES dispersal strategies. Proc. R. Soc. Lond. B 268, 499-508], that can cope with local population fluctuations due to environmental and demographic stochasticity. With the use of this fitness proxy we find that in dispersal evolution the studied clonal model is equivalent with the haploid sexual model, and that there are indeed many differences between clonal and diploid ESS dispersal rates. In a homogenous landscape the discrepancy is but minor (less than 2%), but the situation is different in a heterogeneous landscape: Not only is the quantitative discrepancy between the two types of ESSs appreciable (around 10%-20%), but more importantly, at the same parameter values, evolutionarily stability properties may differ. It is possible, that the singular strategy is evolutionarily stable in the clonal case but not in the diploid case, and vice versa.     

The patch distributed producer-scrounger game

Grouping in animals is ubiquitous and thought to provide group members antipredatory advantages and foraging efficiency. However, parasitic foraging strategy often emerges in a group. The optimal parasitic policy has given rise to the producer-scrounger (PS) game model, in which producers search for food patches, and scroungers parasitize the discovered patches. The N-persons PS game model constructed by Vickery et al. (1991. Producers, scroungers, and group foraging. American Naturalist 137, 847-863) predicts the evolutionarily stable strategy (ESS) of frequency of producers that depends on the advantage of producers and the number of foragers in a group. However, the model assumes that the number of discovered patches in one time unit never exceeds one. In reality, multiple patches could be found in one time unit. In the present study, we relax this assumption and assumed that the number of discovered patches depends on the producers’ variable encounter rate with patches (λ). We show that strongly depends on λ within a feasible range, although it still depends on the advantage of producer and the number of foragers in a group. The basic idea of PS game is the same as the information sharing (parasitism), because scroungers are also thought to parasitize informations of locations of food patches. Horn (1968) indicated the role of information-parasitism in animal aggregation (Horn, H.S., 1968. The adaptive significance of colonial nesting in the Brewer's blackbird (euphagus cyanocephalus). Ecology 49, 682-646). Our modified PS game model shows the same prediction as the Horn's graphical animal aggregation model; the proportion of scroungers will increase or animals should adopt colonial foraging when resource is spatiotemporally clumped, but scroungers will decrease or animals should adopt territorial foraging if the resource is evenly distributed.