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PubMed1996

ESS patterns: adding pairs to an ESS.

The notion of a pattern of evolutionarily stable strategies was introduced by Cannings and Vickers in 1988 (J. Theor. Biol. 132:387-420). In this paper a specific class of patterns is considered. Suppose that there is an evolutionarily stable strategy (ESS) on some set of n strategies {1,2,...,n} and that new strategies {n + 1,n + 2,...,n + k} are added. Supposing that for this new enlarged conflict there is still an ESS on {1,2,...,n} and also that there are ESSs on {n + i,j} for 1 < or = i < or = k and j epsilon Si [symbol: see text] {1,2,...,n}, the authors investigate the restrictions on the Si. These restrictions are related to certain properties of strong tournaments introduced by Reid and Beineke. We also specify, given the Si, what ESSs of the form {n + i,n + j} can be added.

Animals↗
PubMed2005

The evolution of strategy variation: will an ESS evolve?

Evolutionarily stable strategy (ESS) models are widely viewed as predicting the strategy of an individual that when monomorphic or nearly so prevents a mutant with any other strategy from entering the population. In fact, the prediction of some of these models is ambiguous when the predicted strategy is "mixed", as in the case of a sex ratio, which may be regarded as a mixture of the subtraits "produce a daughter" and "produce a son." Some models predict only that such a mixture be manifested by the population as a whole, that is, as an "evolutionarily stable state"; consequently, strategy monomorphism or polymorphism is consistent with the prediction. The hawk-dove game and the sex-ratio game in a panmictic population are models that make such a "degenerate" prediction. We show here that the incorporation of population finiteness into degenerate models has effects for and against the evolution of a monomorphism (an ESS) that are of equal order in the population size, so that no one effect can be said to predominate. Therefore, we used Monte Carlo simulations to determine the probability that a finite population evolves to an ESS as opposed to a polymorphism. We show that the probability that an ESS will evolve is generally much less than has been reported and that this probability depends on the population size, the type of competition among individuals, and the number of and distribution of strategies in the initial population. We also demonstrate how the strength of natural selection on strategies can increase as population size decreases. This inverse dependency underscores the incorrectness of Fisher's and Wright's assumption that there is just one qualitative relationship between population size and the intensity of natural selection.

Biological Evolution↗
PubMed2005

Stochastic stability in three-player games.

Animal behavior and evolution can often be described by game-theoretic models. Although in many situations the number of players is very large, their strategic interactions are usually decomposed into a sum of two-player games. Only recently were evolutionarily stable strategies defined for multi-player games and their properties analyzed [Broom, M., Cannings, C., Vickers, G.T., 1997. Multi-player matrix games. Bull. Math. Biol. 59, 931-952]. Here we study the long-run behavior of stochastic dynamics of populations of randomly matched individuals playing symmetric three-player games. We analyze the stochastic stability of equilibria in games with multiple evolutionarily stable strategies. We also show that, in some games, a population may not evolve in the long run to an evolutionarily stable equilibrium.

Animals↗
PubMed2002

Cross-cultural evidence of cognitive adaptations for social exchange among the Shiwiar of Ecuadorian Amazonia.

On the basis of evolutionary game theory, it was hypothesized that humans have an evolved cognitive specialization for reasoning about social exchange, including a subroutine for detecting cheaters. This hypothesis led to a specific prediction: Although humans are known to be poor at detecting potential violations of conditional rules in general, they should nevertheless detect them easily when the rule involves social exchange and looking for violations corresponds to looking for cheaters. This prediction was subsequently confirmed by numerous tests. Evolutionary analyses further predict that: (i) in humans, complex adaptations will be distributed in a species-typical fashion; and (ii) aspects of cognitive organization relevant to performing the evolved function of an adaptation should be more buffered against environmental and cultural variation than function-irrelevant aspects. Here we report experiments testing whether social exchange reasoning exhibits these properties of adaptations. Existing tests of conditional reasoning were adapted for nonliterate experimental subjects and were administered to Shiwiar hunter-horticulturalists of the Ecuadorian Amazon. As predicted, Shiwiar subjects were as highly proficient at cheater detection as subjects from developed nations. Indeed, the frequency of cheater-relevant choices among Shiwiar hunter-horticulturalists was indistinguishable from that of Harvard undergraduates. Also as predicted, cultural variation was confined to those aspects of reasoning that are irrelevant to social exchange algorithms functioning as an evolutionarily stable strategy. Finally, Shiwiar subjects displayed the same low performance on descriptive conditionals as subjects from developed nations. Taken together, these findings support the hypotheses that social exchange algorithms are species-typical and that their evolutionarily stable strategy (ESS)-relevant subroutines are developmentally buffered against cultural variation.

Adaptation, Psychological↗
PubMed1999

A comparison of foraging strategies in a patchy environment.

In this paper we compare foraging strategies that might be used by predators seeking prey in a patchy environment. The strategies differ in the extent to which predators aggregate in response to prey density. The approach to the comparison is suggested by the idea of evolutionarily stable strategies. A strategy is said to be evolutionarily stable if it cannot be invaded by another strategy. Thus we examine scenarios where a small number of individuals using one strategy are introduced into a situation where a large number of individuals using the other strategy are already present. However, our foraging models do not explicitly incorporate predator population dynamics, so we use net energy uptake as a surrogate for reproductive fitness. In cases where all of the patches visited by predators sustain prey populations, we find that for any pair of strategies one of them will have a higher net energy uptake than the other whether it is the resident or the introduced strain. However, which one is higher will typically depend on the total predator population, which is determined by the resident strain. If the predators leave prey densities high, the more aggregative strain will have the advantage. If the predators reduce prey densities to low levels the less aggregative strain will have the advantage. In cases where one strain of predators aggregates in response to prey density and the other does not, then there might be patches which do not contain prey but do contain (non-aggregating) predators. In those cases, there is the possibility that whichever strategy is used by the introduced strain will yield a higher energy uptake than that used by the resident strain. This suggests that if some patches are empty of prey then aggregative and non-aggregative strategies may be able to coexist.

Animals↗
PubMed1986

Hierarchical selection theory and sex ratios. I. General solutions for structured populations.

Models of sex-ratio evolution in structured populations are derived with G.R. Price's covariance form for the hierarchical analysis of natural selection (1970, Nature 227, 520-521). Previous work on competition among related males for mates (local mate competition), competition among related females for a limiting resource (local resource competition), inbreeding, group selection, and asymmetry of genetic inheritance between males and females, are subsumed under a general formulation for sex-ratio biases in structured populations. I found that the evolutionarily stable strategy sex ratio (males:females) for diploids is 1 - rho m:1 - rho f, where rho m is the regression coefficient of relatedness of the controlling genotypes on males competing for mates, rho f is the regression of controlling genotypes on females that compete for a fixed, limiting resource, and there is no inbreeding. For inbreeding and no competition among females, the evolutionarily stable strategy is 1 - rho m:1 + rho mf, where rho mf is the regression of controlling genotypes on females' mates.

Animals↗
PubMed2003

Analysis of disruptive selection in subdivided populations.

BACKGROUND: Analytical methods have been proposed to determine whether there are evolutionarily stable strategies (ESS) for a trait of ecological significance, or whether there is disruptive selection in a population approaching a candidate ESS. These criteria do not take into account all consequences of small patch size in populations with limited dispersal. RESULTS: We derive local stability conditions which account for the consequences of small and constant patch size. All results are derived from considering Rm, the overall production of successful emigrants from a patch initially colonized by a single mutant immigrant. Further, the results are interpreted in term of concepts of inclusive fitness theory. The condition for convergence to an evolutionarily stable strategy is proportional to some previous expressions for inclusive fitness. The condition for evolutionary stability stricto sensu takes into account effects of selection on relatedness, which cannot be neglected. It is function of the relatedness between pairs of genes in a neutral model and also of a three-genes relationship. Based on these results, I analyze basic models of dispersal and of competition for resources. In the latter scenario there are cases of global instability despite local stability. The results are developed for haploid island models with constant patch size, but the techniques demonstrated here would apply to more general scenarios with an island mode of dispersal. CONCLUSIONS: The results allow to identity and to analyze the relative importance of the different selective pressures involved. They bridge the gap between the modelling frameworks that have led to the Rm concept and to inclusive fitness.

Animal Migration↗
PubMed1998

Evolutionarily Stable Reproductive Strategies in Sexual Organisms. Part V-Joint Effects of Parent-offspring Conflict and Sibling Conflict in Perennial Plants.

We develop a general treatment of the joint effects of parent-offspring conflict (conflict between broods) and sibling conflict (conflict within broods) in perennial plants. Parent-offspring conflict as well as sibling conflict are examined in the context of an integrated analysis of reproductive allocation, sex allocation, and the amount of resources invested in each offspring. We find that under a wide range of conditions the selected seed size is independent of reproductive effort or sex allocation. To the extent that the relationships between gamete output and resource investment are linear for both sex functions, the separate treatment of reproductive effort, sex allocation, and offspring size-number compromise in modern life-history theories is well justified, regardless of which side, parents or offspring, controls the allocation to individual seed offspring. We show that incorporation of sibling conflict results in even larger seed size, which in turn leads to even lower reproductive effort, than under pure parent-offspring conflict. If the costs of increased provisioning of selfish offspring are entirely borne by their brood mates, then offspring are selected to solicit parental care as long as they continue to benefit individually from more resources.Copyright 1998 Academic Press Limited

Journal Article↗
PubMed1985

Genetical ESS-models. II. Multi-strategy models and multiple alleles.

The problem of evolutionarily stable strategies (ESS) in sexual populations can be investigated by means of genetical ESS-models which link common sense, phenotypic ESS-models to an underlying genetical system. Thorough results are obtained for multi-strategy models in diploid, panmictic populations on the basis of multi-allelic, one-locus systems. A sexual population will be maintained at a phenotypic ESS if this can possibly be produced by the genotypes currently existing. If there is enough allelic variation, the corresponding gene pool may either be an ESS itself, or belong to an attracting, continuous set of states, which all determine the same evolutionarily stable population. The latter case allows new alleles to enter and spread in the gene pool without disturbing the phenotypic ESS. If a phenotypic ESS cannot be established, ESSs of the genetical model may be found which give rise to stable populations alternatively. Since these depend on the phenotypes determined by the currently existing genotypes, they may be destabilized by the occurrence of new mutations. In this sense, they are less durable than populations maintained at a phenotypic ESS and can be expected to evolve, in the long run, towards a phenotypic ESS.

Alleles↗
PubMed2006

Environmentally induced dispersal under heterogeneous logistic growth.

We consider a single-species model which is composed of several habitats connected by linear migration rates and having logistic growth. A spatially varying, temporally constant environment is introduced by the non-homogeneity of its carrying capacity. Under this condition any type of purely diffusive behavior, characterized in our model by symmetric migration rates, produces an unbalanced population distribution, i.e. some locations receive more individuals than can be supported by the environmental carrying capacity, while others receive less. Using an evolutionarily stable strategy (ESS) approach we show that an asymmetric migration mechanism, induced by the heterogeneous carrying capacity of the environment, will be selected. This strategy balances the inflow and outflow of individuals in each habitat (balanced dispersal), as well as 'balancing' the spatial distribution relative to variation in carrying capacity (the Ideal Free Distribution from habitat selection theory). We show that several quantities are maximized or minimized by the evolutionarily stable dispersal strategy.

Animal Migration↗
PubMed2001

Runaway social games, genetic cycles driven by alternative male and female strategies, and the origin of morphs.

Analysis of evolutionarily stable strategies (ESS) and decade-long field studies indicate that two color morphs of female side-blotched lizards exhibit density- and frequency-dependent strategies. Orange females are r-strategists: they lay large clutches of small progeny that are favored at low density. Conversely, yellow females are K-strategists: they lay small clutches of large progeny that are favored when carrying capacity is exceeded and the population crashes to low density. Interactions among three male morphs resembles a rock-paper-scissors (RPS) game. Fertilization success of males depends on frequency of neighboring morphs. Orange males usurp territory from blue neighbors and thereby mate with many females. However, orange males are vulnerable to cuckoldry by sneaky yellow males that mimic females. The yellow strategy is thwarted in turn by the mate-guarding strategy of blue. Sinervo and Lively (1996) developed a simple asexual model of the RPS game. Here, we model the dynamics of male and female morphs with one- and two-locus genetic models. Male and female games were considered in isolation and modeled as games that were genetically coupled by the same locus. Parameters for payoff matrices, which describe the force of frequency-dependent selection in ESS games, were estimated from free-ranging animals. Period of cycles in nature was 5 years for males and 2 years for females. Only the one locus model with three alleles (o, b, y) was capable of driving rapid cycles in male and female games. Furthermore, the o allele must be dominant to the y allele in females. Finally, the amplitude of male cycles was only reproduced in genetic models which allowed for irreversible plasticity of by genotypes, which is consistent with hormonally-induced changes that transform some males with yellow to dark blue. We also critique experimental designs that are necessary to detect density- and frequency-dependent selection in nature. Finally, runaway ESS games are discussed in the context of self-reinforcing genetic correlations that build and promote the formation of morphotypic variation.

Alleles↗
PubMed2000

The Evolution of Intraspecific Brood Parasitism in Birds and Insects.

Many species of birds and insects engage in intraspecific brood parasitism (IBP), when a female lays eggs in the nest of a conspecific and leaves without providing parental care. These visiting females may also act to cooperate with a primary female, staying to provide parental care. Therefore, IBP and cooperative breeding can be considered extremes on a continuum of parental care provided by a secondary female. When a secondary female abandons a nest, she creates an asymmetry in parental care between herself and the host. While models of asymmetry in reproductive allocation have focused directly on relatedness between females, we lack an appropriate theoretical framework that addresses the effects of relatedness on parental care asymmetry. Here, I present an evolutionarily stable strategy (ESS) model that predicts the conditions under which IBP is favored over cooperation and solitary breeding. Intraspecific brood parasitism is less likely to evolve (relative to cooperation and solitary breeding) as the relatedness between a host and parasite increases. It can evolve, however, if parasites achieve a high overall fecundity relative to solitary females. Constraints on solitary breeding can further promote IBP under some circumstances. Cooperation is favored when relatedness is high and reproductive skew is low. This model makes several predictions regarding the conditions under which IBP may evolve, motivating a variety of experimental approaches.

birds↗
PubMed2000

Reproductive Effort and Reproductive Values in Periodic Environments.

Life-history theory concerns the optimal spread of reproduction over an organism's life span. In variable environments, there may be extrinsic differences between breeding periods within an organism's life, affecting both offspring and parent and giving rise to intergenerational trade-offs. Such trade-offs are often discussed in terms of reproductive value for parent and offspring. Here, we consider parental life-history optimization in response to varying offspring values of a population regulated by territoriality, where the quality of the environment varies periodically. Periods are interpreted as either within-year (seasonality) or between-years variation (cyclicity). The evolutionarily stable strategy in a general model with two-phased periodicity in the environment can generate either higher or lower effort in the more favorable of the two phases; hence knowing survival prospects of offspring does not suffice for predicting reproductive effort-the future of all descendants and the parent must be tracked. We also apply our method to data on the Ural owl Strix uralensis, a species preying on cyclically fluctuating voles. The observed dynamics are best predicted by assuming delayed reproductive costs and Type II functional response. Accounting for varying offspring values can lead to cases where both reproductive effort and recruitment of offspring are higher in the phase when voles are not maximally abundant, a pattern supported by our data.

Ural owl↗
PubMed2000

Cheating as a mixed strategy in a simple model of aggressive communication.

The possibility that frequency-dependent cheating can persist in an evolutionarily stable communication system has frequently been proposed. Although there is empirical evidence for this idea, however, it has not been investigated in terms of game theory. In the present paper I show for a simple symmetric game that cheating can be part of a mixed evolutionarily stable strategy (ESS). Furthermore, despite the widespread assumption that cheaters must be rare, I show that most of the population can be cheaters, while the signalling system remains evolutionarily stable. Consequences for signalling theory and experiments to detect such mixed ESS are discussed. Copyright 2000 The Association for the Study of Animal Behaviour.

Journal Article↗
PubMed2002

Adaptive diversification of germination strategies.

Evolution of the germination rate (the proportion of newly produced and dormant seeds that germinates every year) of annual plants is investigated, when the environment is temporally stochastic and spatially heterogeneous. The environment consists of two habitats with synchronous stochastic variation in the annual yield and permanent difference in constant seed survival rates. Density dependence operates within the habitats, which are connected via restricted seed dispersal. We find that instead of a single common evolutionarily stable strategy the coexistence of several germination strategies is possible and that in an initially monomorphic population evolutionary branching may occur. During evolutionary branching the population undergoes disruptive selection and splits into two branches of different lineages that converge to the evolutionarily stable coalition of different germination strategies. It is shown that spatial heterogeneity and restricted dispersal are essential for evolutionary branching. Disruptive selection on the germination rate presents yet another possibility for parapatric speciation.

Adaptation, Physiological↗
PubMed1997

Sperm competition games: a prospective analysis of risk assessment.

We develop the logic of assessment of sperm competition risk by individual males where the mechanism of sperm competition follows a 'loaded raffle' (first and second inseminates of a female have unequal prospects). Male roles (first or second to mate) are determined randomly. In model 1, males have no information about the risk associated with individual females and ejaculation strategy depends only on the probability, q, that females mate twice. Evolutionarily stable strategy (ESS) ejaculate expenditure increases linearly from zero with q, and reduces with increasing inequality between ejaculates, though the direction of the loading (which role is favoured) is unimportant. In model 2, males have perfect information and can identify each of three risk states: females that will (1) mate just once ('no risk'), (2) mate twice but have not yet mated ('future risk'), and (3) mate twice and have already mated ('past risk'). The ESS is to ejaculate minimally with 'no risk' females, and to expand equally with 'past' and 'future' risk females; the direction of the competitive loading is again unimportant. Expenditure again increases with risk, but is now non-zero at extremely low risk. Model 3 examines three cases of partial information where males can identify only one of the three risk states and cannot distinguish between the other two: they therefore have just two information sets or 'contexts'. Expenditure in both contexts typically rises non-linearly from zero with q, but (whatever the loading direction) expenditure is higher in the context with higher risk (e.g. if contexts are 'mated' and 'virgin', males spend more with mated females). However, in highly loaded raffles, sperm expenditure can decrease over part of the range of risk. Also, the direction of the loading now affects expenditure. Biological evidence for the predictions of the models is summarized and discussed.

Animals↗