Comparative statics of games between relatives

According to Hamilton's theory of kin selection, species tend to evolve behavior such that each organism appears to be attempting to maximize its inclusive fitness. In particular, two neighbors are likely to help each other if the cost of doing so is less than the benefit multiplied by r, their coefficient of relatedness. Since the latter is less than unity, mutual altruism benefits both neighbors. However, is it theoretically possible that acting so as to maximize the inclusive, rather than personal, fitness may harm both parties. This may occur in strategic symmetric pairwise interactions (more specifically, nxn games), in which the outcome depends on both sides' actions. In this case, the equilibrium outcome may be less favorable to the interactants' personal fitness than if each of them acted so as to maximize the latter. This paper shows, however, that such negative effect of relatedness on fitness is incompatible with evolutionary stability. If the symmetric equilibrium strategies are evolutionarily stable, a higher coefficient of relatedness can only entail higher personal fitness for the two neighbors. This suggests that negative comparative statics as above are not likely to occur in nature.     

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.     

An ESS for the Height of a Plant Population, or an Optimal Height for an Individual?—Rethinking Game-Theoretic Models for Plant Height

Plants only interact with neighbors over restricted distances, so local conditions are of great significance for plants. It is therefore important to consider spatial structure and neighborhood effects if we are to understand plants' strategies. We constructed a spatially-explicit, game theory model to explore optimal height growth at the individual-level. In the model, there is no ESS for height growth at the population level, because there is an “instantaneous” optimal height growth strategy for the individual plant that changes depending on the local light environment. The optimal strategy is plasticity in response to local conditions. Game-theoretic models for plant phenotypic traits should move from “mean-field approximations” towards explicit modeling of local interactions.     

进化稳定对策

进化稳定对策（ESS）是对策论的核心概念,在进化生物学研究中有着非常重要的意义,该理论被认为是自Darwin以来进化论最重要的发展之一。阐释进化稳定对策基本理论的产生以及几种重要的进化稳定对策模型,并运用进化稳定对策理论解释一些生物现象。     

Sex allocation in simultaneous hermaphrodites: Trade-offs between sex-specific costs and lifespan

Fitness in self-incompatible simultaneous hermaphrodites incorporates gains and costs from both male and female reproductive function, and evolutionarily stable allocation of gonadal tissue to male or female function depends on these gains and costs. Paradoxically, despite the often equal expected gains but different costs associated with each sex, contributions to expected reproductive success through male and female function must be identical. Whenever allocation costs are unequal and limiting resources are energetically expensive or risky to acquire, these costs must ultimately be paid through reduced survival, resolving the paradox by equally diminishing expected reproductive success as male and as female. Maximizing fitness as lifetime reproductive success – not just reproductive rate alone, as in previous studies – maximizes the product of expected survival time and reproductive rate. The analysis shows how male-biased allocation can thereby arise and generate novel predictions on the relation between intensity of sperm competition and allocation to male function.     

On the non-existence of an optimal migration rate

 We show that an optimal migration rate may not exist in a population distributed over an infinite number of individual living sites if empty sites occur. This is the case when the mean number of offspring per individual μ is finite. We make the assumption of uniform migration to other sites whose rate is determined by the parent’s genotype or the offspring’s genotype at a single locus in a diploid hermaphrodite population undergoing random mating. In both cases, for μ small enough, any population at fixation would go to extinction. Moreover, in the latter case, for intermediate values of μ, the only fixation state that could resist the invasion of any mutant would lead the population to extinction. These are the two conditions for the non-existence of an optimal migration rate. They become less stringent as the cost for migration expressed by a coefficient of selection 1−β becomes larger, that is, closer to 1. The results are obtained assuming that the allele at fixation is either nondominant or dominant. Although the optimal migration rate is the same in both cases when it exists, the optimality properties may differ. Received 14 December 1995; received in revised form 5 April 1996     

Evolutionary matrix games and optimization theory

An evolutionarily stable strategy (ESS) is only required to be capable of resisting invasion by rare mutant strategies. In contrast, an absolute invader strategy (AIS) is a rare mutant strategy that can invade any established strategy. We show that the predictions of the outcome of evolution made by optimization models are compatible with those made by the classical expected payoff comparisons in matrix games. We also show that if a matrix game has an AIS that AIS is unique and is also an ESS. But an ESS need not be an AIS. In pure-strategy submodels, an AIS need not be unique. An AIS of a matrix game has global asymptotic stability property in the game dynamics which involve only pure strategies including the AIS.     

Cooperation in defence against a predator

The origin and the evolutionary stability of cooperation between unrelated individuals is one of the key problems of evolutionary biology. In this paper, a cooperative defence game against a predator is introduced which is based on Hamilton's selfish herd theory and Eshel's survival game models. Cooperation is altruistic in the sense that the individual, which is not the target of the predator, helps the members of the group attacked by the predator and during defensive action the helper individual may also die in any attack. In order to decrease the long term predation risk, this individual has to carry out a high risk action. Here I show that this kind of cooperative behaviour can evolve in small groups. The reason for the emergence of cooperation is that if the predator does not kill a mate of a cooperative individual, then the survival probability of the cooperative individual will increase in two cases. If the mate is non-cooperative, then—according to the dilution effect, the predator confusion effect and the higher predator vigilance—the survival probability of the cooperative individual increases. The second case is when the mate is cooperative, because a cooperative individual has a further gain, the active help in defence during further predator attacks. Thus, if an individual can increase the survival rate of its mates (no matter whether the mate is cooperative or not), then its own predation risk will decrease.