Reputation-based conditional interaction supports cooperation in well-mixed prisoner's dilemmas

In the well-mixed prisoner's dilemma game, individuals are typically assumed to have no choice about whether to interact with other individuals in the population. In this paper, we instead consider reputation-based conditional interaction and its consequences for the evolution of cooperation. Each individual has a tolerance range, and only interacts with other individuals whose reputation lies within its tolerance range in a chosen sample of the population. Reputation contains information about the number of interaction partners an individual has just cooperated with. We find that the introduction of conditional interaction promotes cooperation in well-mixed populations, and there exist moderate tolerance ranges for which this effect is maximized. For a given tolerance range, there is a critical cost-to-benefit ratio below which cooperation can be promoted. Interestingly, we find that if cooperation evolves, different cooperators' interaction clusters are typically maintained in the population, each around a different reputation level. We further investigate some properties of these cooperators' clusters. Moreover, we examine the effects of the sample number on the evolution of cooperation. Our results highlight the importance of the detailed consideration of modes of interaction for the evolution of cooperation in well-mixed populations.     

Evolutionary dynamics of continuous strategy games on graphs and social networks under weak selection

Understanding the emergence of cooperation among selfish individuals has been a long-standing puzzle, which has been studied by a variety of game models. Most previous studies presumed that interactions between individuals are discrete, but it seems unrealistic in real systems. Recently, there are increasing interests in studying game models with a continuous strategy space. Existing research work on continuous strategy games mainly focuses on well-mixed populations. Especially, little theoretical work has been conducted on their evolutionary dynamics in a structured population. In the previous work (Zhong et al., BioSystems, 2012), we showed that under strong selection, continuous and discrete strategies have significantly different equilibrium and game dynamics in spatially structured populations. In this paper, we further study evolutionary dynamics of continuous strategy games under weak selection in structured populations. By using the fixation probability based stochastic dynamics, we derive exact conditions of natural selection favoring cooperation for the death–birth updating scheme. We also present a network gain decomposition of the game equilibrium, which might provide a new view of the network reciprocity in a quantitative way. Finally, we make a detailed comparison between games using discrete and continuous strategies. As compared to the former, we find that for the latter (i) the same selection conditions are derived for the general 2 × 2 game; especially, the rule b/c > k in a simplified Prisoner's Dilemma is valid as well; however, (ii) for a coordination game, interestingly, the risk-dominant strategy is disfavored. Numerical simulations have also been conducted to validate our results.     

The evolution of payoff matrices: providing incentives to cooperate

Most of the work in evolutionary game theory starts with a model of a social situation that gives rise to a particular payoff matrix and analyses how behaviour evolves through natural selection. Here, we invert this approach and ask, given a model of how individuals behave, how the payoff matrix will evolve through natural selection. In particular, we ask whether a prisoner's dilemma game is stable against invasions by mutant genotypes that alter the payoffs. To answer this question, we develop a two-tiered framework with goal-oriented dynamics at the behavioural time scale and a diploid population genetic model at the evolutionary time scale. Our results are two-fold: first, we show that the prisoner's dilemma is subject to invasions by mutants that provide incentives for cooperation to their partners, and that the resulting game is a coordination game similar to the hawk-dove game. Second, we find that for a large class of mutants and symmetric games, a stable genetic polymorphism will exist in the locus determining the payoff matrix, resulting in a complex pattern of behavioural diversity in the population. Our results highlight the importance of considering the evolution of payoff matrices to understand the evolution of animal social systems.     

Evolution of equal division among unequal partners

One of the hallmarks of human fairness is its insensitivity to power: although strong individuals are often in a position to coerce weak individuals, fairness requires them to share the benefits of cooperation equally. The existence of such egalitarianism is poorly explained by current evolutionary models. We present a model based on cooperation and partner choice that can account for the emergence of a psychological disposition toward fairness, whatever the balance of power between the cooperative partners. We model the evolution of the division of a benefit in an interaction similar to an ultimatum game, in a population made up of individuals of variable strength. The model shows that strong individuals will not receive any advantage from their strength, instead having to share the benefits of cooperation equally with weak individuals at the evolutionary equilibrium, a result that is robust to variations in population size and the proportion of weak individuals. We discuss how this model suggests an explanation for why egalitarian behaviors toward everyone, including the weak, should be more likely to evolve in humans than in any other species.     

Synergy and discounting of cooperation in social dilemmas

The emergence and maintenance of cooperation by natural selection is an enduring conundrum in evolutionary biology, which has been studied using a variety of game theoretical models inspired by different biological situations. The most widely studied games are the Prisoner's Dilemma, the Snowdrift game and by-product mutualism for pairwise interactions, as well as Public Goods games in larger groups of interacting individuals. Here, we present a general framework for cooperation in social dilemmas in which all the traditional scenarios can be recovered as special cases. In social dilemmas, cooperators provide a benefit to the group at some cost, while defectors exploit the group by reaping the benefits without bearing the costs of cooperation. Using the concepts of discounting and synergy for describing how benefits accumulate when more than one cooperator is present in a group of interacting individuals, we recover the four basic scenarios of evolutionary dynamics given by (i) dominating defection, (ii) coexistence of defectors and cooperators, (iii) dominating cooperation and (iv) bi-stability, in which cooperators and defectors cannot invade each other. Generically, for groups of three or more interacting individuals further, more complex, dynamics can occur. Our framework provides the first unifying approach to model cooperation in different kinds of social dilemmas.     

Evolutionary dynamics in structured populations

Evolutionary dynamics shape the living world around us. At the centre of every evolutionary process is a population of reproducing individuals. The structure of that population affects evolutionary dynamics. The individuals can be molecules, cells, viruses, multicellular organisms or humans. Whenever the fitness of individuals depends on the relative abundance of phenotypes in the population, we are in the realm of evolutionary game theory. Evolutionary game theory is a general approach that can describe the competition of species in an ecosystem, the interaction between hosts and parasites, between viruses and cells, and also the spread of ideas and behaviours in the human population. In this perspective, we review the recent advances in evolutionary game dynamics with a particular emphasis on stochastic approaches in finite sized and structured populations. We give simple, fundamental laws that determine how natural selection chooses between competing strategies. We study the well-mixed population, evolutionary graph theory, games in phenotype space and evolutionary set theory. We apply these results to the evolution of cooperation. The mechanism that leads to the evolution of cooperation in these settings could be called ‘spatial selection’: cooperators prevail against defectors by clustering in physical or other spaces.     

Social structure of primate interaction networks facilitates the emergence of cooperation

Animal cooperation has puzzled biologists for a long time as its existence seems to contravene the basic notion of evolutionary biology that natural selection favours ‘selfish’ genes that promote only their own well-being. Evolutionary game theory has shown that cooperators can prosper in populations of selfish individuals if they occur in clusters, interacting more frequently with each other than with the selfish. Here we show that social networks of primates possess the necessary social structure to promote the emergence of cooperation. By simulating evolutionary dynamics of cooperative behaviour on interaction networks of 70 primate groups, we found that for most groups network reciprocity augmented the fixation probability for cooperation. The variation in the strength of this effect can be partly explained by the groups’ community modularity—a network measure for the groups’ heterogeneity. Thus, given selective update and partner choice mechanisms, network reciprocity has the potential to explain socially learned forms of cooperation in primate societies.     

Active linking in evolutionary games

In the traditional approach to evolutionary game theory, the individuals of a population meet each other at random, and they have no control over the frequency or duration of interactions. Here we remove these simplifying assumptions. We introduce a new model, where individuals differ in the rate at which they seek new interactions. Once a link between two individuals has formed, the productivity of this link is evaluated. Links can be broken off at different rates. In a limiting case, the linking dynamics introduces a simple transformation of the payoff matrix. We outline conditions for evolutionary stability. As a specific example, we study the interaction between cooperators and defectors. We find a simple relationship that characterizes those linking dynamics which allow natural selection to favour cooperation over defection.     

Cooperation and the scale of competition in humans

Explaining cooperation is one of the greatest challenges for evolutionary biology. It is particularly a problem in species such as humans, where there is cooperation between nonrelatives. Numerous possible solutions have been suggested for the problem of cooperation between nonrelatives, including punishment, policing, and various forms of reciprocity. Here, we suggest that local competition for resources can pose a problem for these hypotheses, analogous to how it can select against cooperation between relatives. We extend the prisoner's dilemma (PD) game to show that local competition between interacting individuals can reduce selection for cooperation between nonrelatives. This is because, with local competition, fitness is relative to social partners, and cooperation benefits social partners. We then test whether nonrelated humans adjust their level of cooperation facultatively in response to the scale of competition when playing the PD for cash prizes. As predicted, we found that individuals were less likely to cooperate when competition was relatively local. Cooperation between humans will therefore be most likely when repeated interactions take place on a local scale between small numbers of people, and competition for resources takes place on a more global scale among large numbers of people.     

Evolutionary game dynamics in a finite asymmetric two-deme population and emergence of cooperation

We consider evolutionary game dynamics in a finite population subdivided into two demes with both unequal deme sizes and different migration rates. Assuming viability differences in the population according to a linear game within each deme as a result of pairwise interactions, we specify conditions for weak selection favoring a mutant strategy to go to fixation, under the structured-coalescent assumptions, and their connections with evolutionary stability concepts. In the framework of the Iterated Prisoner's Dilemma with strategy ‘tit-for-tat’ as mutant strategy and ‘always defect’ as resident strategy, we deduce a condition under which the emergence of cooperation is favored by selection, when the game matrix is the same in both demes. We show how this condition extends the one-third law for a panmictic population and when an asymmetry in the spatial structure of a two-deme population facilitates the emergence of the cooperative tit-for-tat strategy in comparison with both its symmetric and panmictic population structure counterparts. We find that the condition is less stringent in the asymmetric scenario versus the symmetric scenario if both the fraction of the population in the deme where the mutant was initially introduced, and the expected proportion of migrant offspring in this deme among all migrant offspring after population regulation, are smaller than, or equal to, , provided they are not too small. On the other hand, the condition is less stringent than the one-third law, which holds in the panmictic case, if the latter proportion remains not too close to 1.     

The evolution of reciprocity in sizable groups

Recently, several authors have investigated the evolution of reciprocal altruism using the repeated prisoner's dilemma game. These models suggest that natural selection is likely to favor behavioral strategies leading to reciprocal cooperation when pairs of individuals interact repeatedly in potentially cooperative situations. Using the repeated n-person prisoner's dilemma game, we consider whether reciprocal altruism is also likely to evolve when social interactions involve more individuals. We show that the conditions that allow the evolution of reciprocal cooperation become extremely restrictive as group size increases.     

Stochastic sampling of interaction partners versus deterministic payoff assignment

Evolutionary game dynamics describes how successful strategies spread in a population. In well-mixed populations, the usual assumption, e.g. underlying the replicator dynamics, is that individuals obtain a payoff from interactions with a representative sample of the population. This determines their fitness. Here, we analyze a situation in which payoffs are obtained through a single interaction, so that individuals of the same type can have different payoffs. We show analytically that for weak selection, this scenario is identical to the usual approach in which an individual interacts with the whole population. For strong selection, however, differences arise that are reflected in the fixation probabilities and lead to deviating evolutionary dynamics.     

Direct Reciprocity in Spatial Populations Enhances R-Reciprocity As Well As ST-Reciprocity

As is well-known, spatial reciprocity plays an important role in facilitating the emergence of cooperative traits, and the effect of direct reciprocity is also obvious for explaining the cooperation dynamics. However, how the combination of these two scenarios influences cooperation is still unclear. In the present work, we study the evolution of cooperation in 2×2 games via considering both spatial structured populations and direct reciprocity driven by the strategy with 1-memory length. Our results show that cooperation can be significantly facilitated on the whole parameter plane. For prisoner''s dilemma game, cooperation dominates the system even at strong dilemma, where maximal social payoff is still realized. In this sense, R-reciprocity forms and it is robust to the extremely strong dilemma. Interestingly, when turning to chicken game, we find that ST-reciprocity is also guaranteed, through which social average payoff and cooperation is greatly enhanced. This reciprocity mechanism is supported by mean-field analysis and different interaction topologies. Thus, our study indicates that direct reciprocity in structured populations can be regarded as a more powerful factor for the sustainability of cooperation.     

Animal movement in the absence of predation: environmental drivers of movement strategies in a partial migration system

Animal movement strategies including migration, dispersal, nomadism, and residency are shaped by broad‐scale spatial‐temporal structuring of the environment, including factors such as the degrees of spatial variation, seasonality and inter‐annual predictability. Animal movement strategies, in turn, interact with the characteristics of individuals and the local distribution of resources to determine local patterns of resource selection with complex and poorly understood implications for animal fitness. Here we present a multi‐scale investigation of animal movement strategies and resource selection. We consider the degree to which spatial variation, seasonality, and inter‐annual predictability in resources drive migration patterns among different taxa and how movement strategies in turn shape local resource selection patterns. We focus on adult Galapagos giant tortoises Chelonoidis spp. as a model system since they display many movement strategies and evolved in the absence of predators of adults. Specifically, our analysis is based on 63 individuals among four taxa tracked on three islands over six years and almost 10⁶ tortoise re‐locations. Tortoises displayed a continuum of movement strategies from migration to sedentarism that were linked to the spatio‐temporal scale and predictability of resource distributions. Movement strategies shaped patterns of resource selection. Specifically, migratory individuals displayed stronger selection toward areas where resources were more predictable among years than did non‐migratory individuals, which indicates a selective advantage for migrants in seasonally structured, more predictable environments. Our analytical framework combines large‐scale predictions for movement strategies, based on environmental structuring, with finer‐scale analysis of space‐use. Integrating different organizational levels of analysis provides a deeper understanding of the eco‐evolutionary dynamics at play in the emergence and maintenance of migration and the critical role of resource predictability. Our results highlight that assessing the potential benefits of differential behavioral responses first requires an understanding of the interactions among movement strategies, resource selection and individual characteristics.     

Emergence of cooperative linkages by random intensity of selection on a network

By assuming the random intensity of selection, the emergence of cooperation on a network is studied. We constructed an evolutionary model in which an individual plays the prisoner's dilemma game, and updates both its strategy and neighbor connections in response to its relative success in the game. The constant (strong or weak) and random intensities of selection are compared. The random intensities of selection are introduced to realize complex environmental effects on the fitness of each individual. Breaking the links on the network is realized according to fixed global parameters. We found that cooperative clusters emerged when cooperators unilaterally broke the link with defectors. The emergent networks under these conditions had a high clustering coefficient and shared some properties with a scale-free network. In addition, after a cooperator with high fitness emerged circumstantially under the random intensity of selection, we observed that the cooperative linkages emerged and spread rapidly through the network. This situation frequently occurred because of the stochastic effect on the fitness of cooperators. Thus, the origin of such phenomena is qualitatively different from the Lotka-Volterra system in which deterministic processes control the system. Cooperative linkages spread more when defectors maintained many links with cooperators.     

When can ecological speciation be detected with neutral loci?

It is not yet clear under what conditions empirical studies can reliably detect progress toward ecological speciation through the analysis of allelic variation at neutral loci. We use a simulation approach to investigate the range of parameter space under which such detection is, and is not, likely. We specifically test for the conditions under which divergent natural selection can cause a ‘generalized barrier to gene flow’ that is present across the genome. Our individual‐based numerical simulations focus on how population divergence at neutral loci varies in relation to recombination rate with a selected locus, divergent selection on that locus, migration rate and population size. We specifically test whether genetic differences at neutral markers are greater between populations in different environments than between populations in similar environments. We find that this expected signature of ecological speciation can be detected under part of the parameter space, most consistently when divergent selection is strong and migration is intermediate. By contrast, the expected signature of ecological speciation is not reliably detected when divergent selection is weak or migration is low or high. These findings provide insights into the strengths and weaknesses of using neutral markers to infer ecological speciation in natural systems.     

Perfect reciprocity is the only evolutionarily stable strategy in the continuous iterated prisoner's dilemma

Theoretical studies have shown that cooperation tends to evolve when interacting individuals have positively correlated phenotypes. In the present article, we explore the situation where this correlation results from information exchange between social partners, and behavioral flexibility. We consider the game 'continuous iterated prisoner's dilemma'. The level of cooperation expressed by individuals in this game, together with their ability to respond to one another, both evolve as two aspects of their behavioral strategy. The conditions for a strategy to be evolutionarily stable in this game are degenerate, and earlier works were thus unable to find a single ESS. However, a detailed invasion analysis, together with the study of evolution in finite populations, reveals that natural selection favors strategies whereby individuals respond to their opponent's actions in a perfectly mirrored (i.e., correlated) fashion. As a corollary, the overall payoff of social interactions (i.e., the amount of cooperation) is maximized because couples of correlated partners effectively become the units of selection.     

具资源效应的非对称“鹰鸽博弈”进化稳定分析

解释合作行为的演化一直是生命科学及社会学研究的重要问题之一。经典理论研究大都关注于合作双方对等的情况。然而,在合作系统中的合作双方通常是不对等的,由此可带来博弈双方支付的非对称并影响合作双方的合作行为。该文基于经典的"鹰鸽博弈"模型,同时考虑非对称性相互关系和资源压力的影响,建立了具有强弱之分的四策略(实力强且合作、实力强且不合作、实力弱且合作和实力弱且不合作)非对称博弈模型。结合演化博弈理论及动力系统稳定性理论分析发现:在系统达到稳定状态时,四种策略的比例变化显著地依赖于博弈双方的强弱之比、资源压力及冲突的单位成本收益。对模型的进一步分析显示,当资源充足时,实力强且合作的比例与冲突的单位成本收益负相关;而实力强且不合作、实力弱且不合作的比例都与冲突的单位成本收益正相关,并且随着系统强弱对比增加,实力强且合作及实力强且不合作的比例均增加,而实力弱且不合作的比例将减小。当资源短缺时,模型得出一个有趣的结论,即随着博弈双方的强弱之比的变化,经典的"智猪博弈"与"鹰鸽博弈"可相互转化,该结论将能为不同均衡状态之间的相互转化给出一个动力学解释。     

Stern-judging: A simple, successful norm which promotes cooperation under indirect reciprocity

We study the evolution of cooperation under indirect reciprocity, believed to constitute the biological basis of morality. We employ an evolutionary game theoretical model of multilevel selection, and show that natural selection and mutation lead to the emergence of a robust and simple social norm, which we call stern-judging. Under stern-judging, helping a good individual or refusing help to a bad individual leads to a good reputation, whereas refusing help to a good individual or helping a bad one leads to a bad reputation. Similarly for tit-for-tat and win-stay-lose-shift, the simplest ubiquitous strategies in direct reciprocity, the lack of ambiguity of stern-judging, where implacable punishment is compensated by prompt forgiving, supports the idea that simplicity is often associated with evolutionary success.     

Geographical patterns of adaptation within a species' range: interactions between drift and gene flow

We use individual-based stochastic simulations and analytical deterministic predictions to investigate the interaction between drift, natural selection and gene flow on the patterns of local adaptation across a fragmented species' range under clinally varying selection. Migration between populations follows a stepping-stone pattern and density decreases from the centre to the periphery of the range. Increased migration worsens gene swamping in small marginal populations but mitigates the effect of drift by replenishing genetic variance and helping purge deleterious mutations. Contrary to the deterministic prediction that increased connectivity within the range always inhibits local adaptation, simulations show that low intermediate migration rates improve fitness in marginal populations and attenuate fitness heterogeneity across the range. Such migration rates are optimal in that they maximize the total mean fitness at the scale of the range. Optimal migration rates increase with shallower environmental gradients, smaller marginal populations and higher mutation rates affecting fitness.