An evolutionarily stable strategy for aggressiveness in feeding groups

Animals searching for food in groups display highly variabledegrees of aggressiveness. In this paper I present an individual-basedgame theoretical model of how gregarious animals should adjusttheir level of aggressiveness to their environmental conditions.In accordance with behavioral observations, the predicted levelof aggressiveness increases progressively with decreasing foodavailability and increasing animal density. The proposed modelalso predicts a positive influence of food energy value andhandling time on the level of aggressiveness within the group.In addition, the model provides information about the influenceof aggressive behavior on individual foraging success, interference,and population dynamics. Adaptive behavioral rules for aggressivenessin consumers are predicted to respond to both competitors andfood density in a way that contributes to stabilization of thedynamics of population systems.     

Evolutionarily stable stealing: game theory applied to kleptoparasitism

We present an individual-based model of a group of foraginganimals. Individuals can obtain food either by discovering itthemselves or by stealing it from others (kleptoparasitism).Given that challenging another individual for a discovered fooditem costs time (which could otherwise be spent searching foran undiscovered item), attempting to steal from another maynot always be efficient We show that there is generally a uniquestrategy that maximizes uptake rate—always or never challengingothers. For any combination of parameter values, we can identifywhich strategy is appropraite. As a corollary to this, we predictthat small changes in ecolgical conditions can, under some circumstances,cause a dramatic change in the aggressive behavior of individuals.Further, we investigate situations where searching for undiscoveredfood and searching for potential opportunities for stealingare mutually exclusive activities (i.e., success at one canonly be improved at the expense of the other). Using game theory,we are able to find the evolutionarily stable strategy for investmentin these two activities in terms of the ecological parametersof the model.     

Evolution of kleptoparasitism as a war of attrition

Previous models of kleptoparasitism (resource stealing) assume that contests over resource items are of fixed duration. Here we suggest that such contests will often be well represented as a war of attrition, with the winner being the individual who is prepared to contest for the longer time. Given that time spent in contests cannot be used to search for other resource items, we provide an analytical expression for the evolutionarily stable distribution of contest times. This can be used to investigate the circumstances under which we would expect kleptoparasitism to evolve. In particular, we focus on situations where searching for conspecifics to kleptoparasitize can only be achieved at a cost of reduced resource discovery by other means; under such circumstances we show that kleptoparasitism is not evolutionarily stable.     

Biological auctions with multiple rewards

The competition for resources among cells, individuals or species is a fundamental characteristic of evolution. Biological all-pay auctions have been used to model situations where multiple individuals compete for a single resource. However, in many situations multiple resources with various values exist and single reward auctions are not applicable. We generalize the model to multiple rewards and study the evolution of strategies. In biological all-pay auctions the bid of an individual corresponds to its strategy and is equivalent to its payment in the auction. The decreasingly ordered rewards are distributed according to the decreasingly ordered bids of the participating individuals. The reproductive success of an individual is proportional to its fitness given by the sum of the rewards won minus its payments. Hence, successful bidding strategies spread in the population. We find that the results for the multiple reward case are very different from the single reward case. While the mixed strategy equilibrium in the single reward case with more than two players consists of mostly low-bidding individuals, we show that the equilibrium can convert to many high-bidding individuals and a few low-bidding individuals in the multiple reward case. Some reward values lead to a specialization among the individuals where one subpopulation competes for the rewards and the other subpopulation largely avoids costly competitions. Whether the mixed strategy equilibrium is an evolutionarily stable strategy (ESS) depends on the specific values of the rewards.     

Adaptive dynamics of cooperation may prevent the coexistence of defectors and cooperators and even cause extinction

It has recently been demonstrated that ecological feedback mechanisms can facilitate the emergence and maintenance of cooperation in public goods interactions: the replicator dynamics of defectors and cooperators can result, for example, in the ecological coexistence of cooperators and defectors. Here we show that these results change dramatically if cooperation strategy is not fixed but instead is a continuously varying trait under natural selection. For low values of the factor with which the value of resources is multiplied before they are shared among all participants, evolution will always favour lower cooperation strategies until the population falls below an Allee threshold and goes extinct, thus evolutionary suicide occurs. For higher values of the factor, there exists a unique evolutionarily singular strategy, which is convergence stable. Because the fitness function is linear with respect to the strategy of the mutant, this singular strategy is neutral against mutant invasions. This neutrality disappears if a nonlinear functional response in receiving benefits is assumed. For strictly concave functional responses, singular strategies become uninvadable. Evolutionary branching, which could result in the evolutionary emergence of cooperators and defectors, can occur only with locally convex functional responses, but we illustrate that it can also result in coevolutionary extinction.     

Is it better to give information, receive it, or be ignorant in a two-player game?

The standard approach in a biological two-player game is toassume both players choose their actions independently of oneanother, having no information about their opponent's action(simultaneous game). However, this approach is not realisticin some circumstances. In many cases, one player chooses hisaction first and then the second player chooses her action withinformation about his action (Stackelberg game). We comparethese two games, which can be mathematically analyzed into twotypes, depending on the direction of the best response function(BRF) at the evolutionarily stable strategy in the simultaneousgame (ESS_sim). We subcategorize each type of game into two cases,depending on the change in payoff to one player, when both playersare at the ESS_sim, and the other player increases his action.Our results show that in cases where the BRF is decreasing atthe ESS_sim, the first player in the Stackelberg game receivesthe highest payoff, followed by both players in the simultaneousgame, followed by the second player in the Stackelberg game.In these cases, it is best to be the first Stackelberg player.In cases where the BRF is increasing at the ESS_sim, both Stackelbergplayers receive a higher payoff than players in a simultaneousgame. In these cases, it is better for both players to playa Stackelberg game rather than a simultaneous game. However,in some cases the first Stackelberg player receives a higherpayoff than the second Stackelberg player, and in some casesthe opposite is true.     

Why Darwin would have loved evolutionary game theory

Humans have marvelled at the fit of form and function, the way organisms'' traits seem remarkably suited to their lifestyles and ecologies. While natural selection provides the scientific basis for the fit of form and function, Darwin found certain adaptations vexing or particularly intriguing: sex ratios, sexual selection and altruism. The logic behind these adaptations resides in frequency-dependent selection where the value of a given heritable phenotype (i.e. strategy) to an individual depends upon the strategies of others. Game theory is a branch of mathematics that is uniquely suited to solving such puzzles. While game theoretic thinking enters into Darwin''s arguments and those of evolutionists through much of the twentieth century, the tools of evolutionary game theory were not available to Darwin or most evolutionists until the 1970s, and its full scope has only unfolded in the last three decades. As a consequence, game theory is applied and appreciated rather spottily. Game theory not only applies to matrix games and social games, it also applies to speciation, macroevolution and perhaps even to cancer. I assert that life and natural selection are a game, and that game theory is the appropriate logic for framing and understanding adaptations. Its scope can include behaviours within species, state-dependent strategies (such as male, female and so much more), speciation and coevolution, and expands beyond microevolution to macroevolution. Game theory clarifies aspects of ecological and evolutionary stability in ways useful to understanding eco-evolutionary dynamics, niche construction and ecosystem engineering. In short, I would like to think that Darwin would have found game theory uniquely useful for his theory of natural selection. Let us see why this is so.     

Individual variation and the resolution of conflict over parental care in penduline tits

Eurasian penduline tits (Remiz pendulinus) have an unusually diverse breeding system consisting of frequent male and female polygamy, and uniparental care by the male or the female. Intriguingly, 30 to 40 per cent of all nests are deserted by both parents. To understand the evolution of this diverse breeding system and frequent clutch desertion, we use 6 years of field data to derive fitness expectations for males and females depending on whether or not they care for their offspring. The resulting payoff matrix corresponds to an asymmetric Snowdrift Game with two alternative evolutionarily stable strategies (ESSs): female-only and male-only care. This, however, does not explain the polymorphism in care strategies and frequent biparental desertion, because theory predicts that one of the two ESSs should have spread to fixation. Using a bootstrapping approach, we demonstrate that taking account of individual variation in payoffs explains the patterns of care better than a model based on the average population payoff matrix. In particular, a model incorporating differences in male attractiveness closely predicts the observed frequencies of male and female desertion. Our work highlights the need for a new generation of individual-based evolutionary game-theoretic models.     

Resource defense in a group-foraging context

When foraging in groups, animals frequently use either scrambleor contest tactics to obtain food at clumps found by others.The question of which competitive tactic should be used hasbeen addressed from two different perspectives: a simple optimalityapproach and a game theoretic approach. Surprisingly, both approachesmake strikingly different predictions about how per-capita frequencyof aggression within groups should change as a function of foodabundance and competitor density. Resource defense theory typicallypredicts dome-shaped relationships between the per-capita frequencyof aggression and both food abundance and competitor density,whereas game theoretic models predict an increase in aggressionwith competitor density and a decline in aggression with increasedfood abundance. We developed a game theoretic model to explorewhether the predictions of resource defense theory and the gametheoretic approach can be reconciled. Our model assumes thatplayers have different competitive abilities and can adopt rolesof either finder or joiner that affect the quantity of foodthat can be gained from a food clump. In accordance with earliergame theoretic models, we predict an increase in aggressionwith competitor density when animals compete by pair-wise contests.However, when food clumps can be challenged by more than onecompetitor, both the costs and benefits of defending increasewith competitor density, which results in a dome-shaped relationshipbetween the two variables. Our model predicts that aggressionshould always decrease as the density of food clumps increases.