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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.
Reciprocity, whether direct or indirect, is thought to be the key to establishing cooperation among non-relatives. But Riolo et al. have presented a model in which cooperation is instead based on similarity: agents donate only when their partner's 'tag' lies within a 'tolerance' range around their own. Here we point out that their model requires individuals with identical tags to cooperate with each other, and show that cooperation tends to collapse when individuals bearing identical tags are given the option of not donating. We therefore question their mechanism for maintaining cooperation without reciprocity.
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To explain the evolution of cooperation by natural selection has been a major goal of biologists since Darwin. Cooperators help others at a cost to themselves, while defectors receive the benefits of altruism without providing any help in return. The standard game dynamical formulation is the 'Prisoner's Dilemma', in which two players have a choice between cooperation and defection. In the repeated game, cooperators using direct reciprocity cannot be exploited by defectors, but it is unclear how such cooperators can arise in the first place. In general, defectors are stable against invasion by cooperators. This understanding is based on traditional concepts of evolutionary stability and dynamics in infinite populations. Here we study evolutionary game dynamics in finite populations. We show that a single cooperator using a strategy like 'tit-for-tat' can invade a population of defectors with a probability that corresponds to a net selective advantage. We specify the conditions required for natural selection to favour the emergence of cooperation and define evolutionary stability in finite populations.
The theory of indirect reciprocation explains the evolution of cooperation among unrelated individuals, engaging in one-shot interaction. Using reputation, a player acquires information on who are worth cooperating and who are not. In a previous paper, we formalized the reputation dynamics, a rule to assign a binary reputation (good or bad) to each player when his action, his current reputation, and the opponent's reputation are given. We then examined all the possible reputation dynamics, and found that there exist only eight reputation dynamics named "leading eight" that can maintain the ESS with a high level of cooperation, even if errors are included in executing intended cooperation and in reporting the observation to the public. In this paper, we study the nature of these successful social norms. First, we characterize the role of each pivot of the reputation dynamics common to all of the leading eight. We conclude that keys to the success in indirect reciprocity are to be nice (maintenance of cooperation among themselves), retaliatory (detection of defectors, punishment, and justification of punishment), apologetic, and forgiving. Second, we prove the two basic properties of the leading eight, which give a quantitative evaluation of the ESS condition and the level of cooperation maintained at the ESS.
The evolution of cooperation among nonrelated individuals is one of the fundamental problems in biology and social sciences. Reciprocal altruism fails to provide a solution if interactions are not repeated often enough or groups are too large. Punishment and reward can be very effective but require that defectors can be traced and identified. Here we present a simple but effective mechanism operating under full anonymity. Optional participation can foil exploiters and overcome the social dilemma. In voluntary public goods interactions, cooperators and defectors will coexist. We show that this result holds under very diverse assumptions on population structure and adaptation mechanisms, leading usually not to an equilibrium but to an unending cycle of adjustments (a Red Queen type of evolution). Thus, voluntary participation offers an escape hatch out of some social traps. Cooperation can subsist in sizable groups even if interactions are not repeated, defectors remain anonymous, players have no memory, and assortment is purely random.
Inclusive fitness benefits have been suggested to be a major selective force behind the evolution of cooperative breeding. We investigated the fitness benefits selecting for cooperative breeding in the Seychelles warbler, Acrocephalus sechellensis. A microsatellite-based genotyping method was used to determine the relatedness of subordinates to group offspring in an isolated population of Seychelles warblers. The indirect and direct breeding benefits accruing to individual subordinates were then calculated for every successful breeding event over a three-year period. We show that female subordinates frequently gained parentage and that this, combined with high levels of extragroup paternity, resulted in low levels of relatedness between subordinates and nondescendent offspring within a territory. Direct breeding benefits were found to be significantly higher than indirect kin benefits for both female and male subordinates. As predicted, female subordinates gained significantly more direct breeding opportunities and therefore higher inclusive fitness benefits by being a subordinate within a group than did males. This may explain why most subordinates in the Seychelles warbler are female.
Consider a two-player game in which each player contributes a costly resource to the common good of the pair. For such contests, the Nash equilibrium contribution, x*, is one for which neither player can increase its pay-off by unilaterally altering its contribution from x*. We study an elaboration of this game, which allows the players to exchange x-offers back and forth in a negotiation phase until they converge to a final pair of contributions, x1 and x2. A significant feature of such negotiation games, hitherto unrecognized, is the existence of a set of neutrally stable equilibrium points in negotiation phase space. To explore the long-term evolutionary outcome of such games, we simulate populations containing various mixtures of negotiation strategies and, contrary to previous results, we often find convergence to a contribution that is more cooperative than the Nash equilibrium. Mathematical analysis suggests why this might be happening, and provides a novel and robust explanation for cooperation, that negotiation can facilitate the evolution of cooperative behaviour.
Explaining the emergence of cooperative behaviours in a selfish world remains a major challenge for sociobiology. The iterated prisoner's dilemma offers a well-studied metaphor with which to explore theoretically the evolution of cooperation by reciprocation. Our current understanding is that 'tit-for-tat' should be the very first step (if not the aim) of evolution towards cooperation, but that mobility of the players in space seems to raise a devastating obstacle to the spread of tit-for-tat, by allowing egoists to exploit cooperation and escape retaliation. The second point is based on models that represent mobility only implicitly (in terms of travelling costs) and assume random interactions. Here we develop a more explicit theory of spatial iterated games: individual mobility is represented in terms of a diffusion process and interactions--defined locally--are inherently non-random. Our model reveals the existence of critical levels of individual mobility allowing for the evolution of cooperation. In fact, tit-for-tat can spread and take over among mobile players even when originating from extreme rarity. The dynamics of invasion of tit-for-tat develop as a travelling wave which propagates the cooperative strategy through space. Significant mobility is required to make the pioneering moves of cooperators towards the front of invasion less hazardous; it also contributes to neutralizing those defectors who may intrude the core of a cluster of cooperative players.
In the few species of birds in which males form display partnerships to attract females, one male secures most or all of the copulations. This leads to the question of why subordinate males help in the absence of observable reproductive benefits. Hamilton's concept of kin selection, whereby individuals can benefit indirectly by helping a relative, was a crucial breakthrough for understanding apparently altruistic systems. However in the only direct test of kin selection in coordinated display partnerships, partners were unrelated, discounting kin selection as an explanation for the evolution of cooperation. Here I show, using genetic measures of relatedness and reproductive success, that kin selection can explain the evolution of cooperative courtship in wild turkeys. Subordinate (helper) males do not themselves reproduce, but their indirect fitness as calculated by Hamilton's rule more than offsets the cost of helping. This result confirms a textbook example of kin selection that until now has been controversial and also extends recent findings of male relatedness on avian leks by quantifying the kin-selected benefits gained by non-reproducing males.
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The iterated Prisoner's Dilemma reflects the essence of repeated cooperative interactions with selfish incentives. However, the classical form of this game assumes that individuals either cooperate or defect, whereas in practice different degrees of cooperation are usually possible. To overcome this limitation, we present a model of alternating cooperative trade in which individuals controlled the costs they incurred in benefiting their partners. Since the range of possible strategies is enormous, competitively successful solutions were identified using a genetic algorithm, a powerful search technique in which good performers are iteratively selected and recombined from an initial "strategy soup". Beginning with a population of asocial individuals, altruistic behaviour readily emerged. Like the pre-defined strategy of "Raise-the-Stakes", the emerging strategies evolved protection from cheats by investing relatively little in strangers and subsequently responding quantitatively to a partner's altruism. Unlike "Raise-the-Stakes", they began trading relations at intermediate levels and, when the benefit-to-cost ratio of cooperation was relatively low, mean investment was considerably below the maximum level. Our approach is novel in allowing us to predict not just whether cooperation will occur, but how cooperative individuals will be, in relation to factors such as the number of rounds and the cost effectiveness of cooperative trade.
The main obstacle for the evolution of cooperation is that natural selection favors defection in most settings. In the repeated prisoner's dilemma, two individuals interact several times, and, in each round, they have a choice between cooperation and defection. We analyze the evolutionary dynamics of three simple strategies for the repeated prisoner's dilemma: always defect (ALLD), always cooperate (ALLC), and tit-for-tat (TFT). We study mutation-selection dynamics in finite populations. Despite ALLD being the only strict Nash equilibrium, we observe evolutionary oscillations among all three strategies. The population cycles from ALLD to TFT to ALLC and back to ALLD. Most surprisingly, the time average of these oscillations can be entirely concentrated on TFT. In contrast to the classical expectation, which is informed by deterministic evolutionary game theory of infinitely large populations, stochastic evolution of finite populations need not choose the strict Nash equilibrium and can therefore favor cooperation over defection.
The evolutionary form of the iterated prisoner's dilemma (IPD) is a repeated game where players strategically choose whether to cooperate with or exploit opponents and reproduce in proportion to game success. It has been widely used to study the evolution of cooperation among selfish agents. In the past 15 years, researchers proved over a series of papers that there is no evolutionarily stable strategy (ESS) in the IPD when players maintain long-term relationships. This makes it difficult to make predictions about what strategies can actually persist as prevalent in a population over time. Here, we show that this no ESS finding may be a mathematical technicality, relying on implausible players who are "too perfect" in that their probability of cooperating on any move is arbitrarily close to either 0 or 1. Specifically, in the no ESS proof, all strategies were allowed, meaning that after a strategy X experiences any history H, X cooperates with an unrestricted probability p (X, H) where 0< or =p (X, H)< or =1. Here, we restrict strategies to the set S in which X is a member of S [corrected] if after any H, X cooperates with a restricted probability p (X, H) where e< or =p (X, H)< or =1-e and 0<e<1/2. The variables e and 1-e may be thought of as the biological limits to how perfect (pure) a strategy can be. In S, we first prove that an ESS must be a Nash equilibrium and boundary strategy of S where a boundary strategy has allowable probabilities of cooperating of e or 1-e after any history. We then prove that X is an ESS in S if and only if X is a Nash equilibrium in the set consisting of only S's boundary strategies. Thus, in searching for ESSs in S, we only need to consider what happens when boundary strategies interact with one another. This greatly simplifies the search for ESSs. Using these results, we finally show that when e is sufficiently small, exactly three one-move memory ESSs exist in S: [1] Pavlov-e which generally cooperates (i.e. cooperates with maximum probability 1-e) after both players either simultaneously cooperated or simultaneously defected; otherwise, Pavlov-e generally defects (i.e. cooperates with minimum probability e). [2] Grudge-e which generally cooperates after both players simultaneously cooperated; otherwise, Grudge-e generally defects. [3] ALLD-e which generally defects after all histories.
The evolution of cooperation and altruistic behaviour where individuals forego their own reproduction to help others reproduce can be explained by kin selection. Depending on the costs and benefits provided, altruism can be evolutionarily favoured if it is directed at close relatives. A considerable body of data supports the role of relatedness as a key determinant of cooperation and conflict within societies. However, the role of ecological factors and, in particular, how these costs and benefits interact with relatedness remains poorly understood. By studying 16 colonies, here I show that in a drywood termite ecological factors determine the importance of relatedness. In colonies with limited food supply, nestmates restrict cooperative interactions mainly to close relatives, while non-discriminative cooperation occurs when food is abundant. This shows for the first time directly the interaction between ecological conditions and relatedness in shaping cooperation.
Cooperative breeding is comparatively rare among birds in the mainly temperate and boreal Northern Hemisphere. Here we test if the distribution of breeding systems reflects a response to latitude by means of a phylogenetic analysis using correlates with geographical range among the corvids (crows, jays, magpies and allied groups). The corvids trace their ancestry to the predominantly cooperative 'Corvida' branch of oscine passerines from the Australo-Papuan region on the ancient Gondwanaland supercontinent, but we could not confirm the ancestral state of the breeding system within the family, while family cohesion may be ancestral. Initial diversification among pair-breeding taxa that are basal in the corvid phylogeny, represented by genera such as Pyrrhocorax and Dendrocitta, indicates that the corvid family in its current form could have evolved from pair-breeding ancestors only after they had escaped the Australo-Papuan shield. Within the family, cooperative breeding (alloparental care/family cohesion) is strongly correlated to latitude and its predominance in species maintaining a southerly distribution indicates a secondary evolution of cooperative breeding in the lineage leading away from the basal corvids. Multiple transitions show plasticity in the breeding system, indicating a response to latitude rather than evolutionary inertia. The evolutionary background to the loss of cooperative breeding among species with a northerly distribution is complex and differs between species, indicating a response to a variety of selection forces. Family cohesion where the offspring provide alloparental care is a main route to cooperatively breeding groups among corvids. Some corvid species lost only alloparental care, while maintaining coherent family groups. Other species lost family cohesion and, as a corollary, they also lost the behaviour where retained offspring provide alloparental care.
Spotted hyenas (Crocuta crocuta) are gregarious carnivores that live in multigenerational social groups, called clans, containing one to several matrilines. Members of multiple matrilines within a clan cooperate during dangerous interactions with inter- and intraspecific competitors. The evolution of cooperation may be influenced by relatedness between individuals, which in turn is influenced by reproductive skew and mate choice, dispersal and territorial behaviours. Behavioural data exist for spotted hyenas, but corresponding data on patterns of relatedness are unavailable; this lack of data makes it difficult to assess the relative importance of selection pressures favouring cooperative behaviour within and among groups. Therefore we conducted a longitudinal analysis of relatedness within a single large clan of spotted hyenas, as well as a cross-sectional analysis of relatedness among hyenas from multiple clans. Within a clan, patterns of relatedness reflected known pedigree relationships, and relatedness was higher within than among matrilines, even across generations. Although mean within-matriline relatedness varied among matrilines, it did not decline with matriline rank. On average, clan members were not related closely, due to high levels of male-mediated gene flow among clans, and relatedness declined very slightly across clan borders. Low mean relatedness within clans suggests that spotted hyenas cooperate with unrelated clan-mates against close paternal kin in other clans. Our data also suggest that spotted hyenas must derive large net direct fitness benefits from group living and cooperation.