Revisiting “The Evolution of Reciprocity in Sizable Groups”: Continuous reciprocity in the repeated n-person prisoner's dilemma

For many years in evolutionary science, the consensus view has been that while reciprocal altruism can evolve in dyadic interactions, it is unlikely to evolve in sizable groups. This view had been based on studies which have assumed cooperation to be discrete rather than continuous (i.e., individuals can either fully cooperate or else fully defect, but they cannot continuously vary their level of cooperation). In real world cooperation, however, cooperation is often continuous. In this paper, we re-examine the evolution of reciprocity in sizable groups by presenting a model of the n-person prisoner's dilemma that assumes continuous rather than discrete cooperation. This model shows that continuous reciprocity has a dramatically wider basin of attraction than discrete reciprocity, and that this basin's size increases with efficiency of cooperation (marginal per capita return). Further, we find that assortative interaction interacts synergistically with continuous reciprocity to a much greater extent than it does with discrete reciprocity. These results suggest that previous models may have underestimated reciprocity's adaptiveness in groups. However, we also find that the invasion of continuous reciprocators into a population of unconditional defectors becomes realistic only within a narrow parameter space in which the efficiency of cooperation is close to its maximum bound. Therefore our model suggests that continuous reciprocity can evolve in large groups more easily than discrete reciprocity only under unusual circumstances.     

The evolution of reciprocity in sizable human groups

The scale and complexity of human cooperation is an important and unresolved evolutionary puzzle. This article uses the finitely repeated n person Prisoners’ Dilemma game to illustrate how sapience can greatly enhance group-selection effects and lead to the evolutionary stability of cooperation in large groups. This affords a simple and direct explanation of the human “exception.”     

Bet hedging based cooperation can limit kin selection and form a basis for mutualism

Mutualism is a mechanism of cooperation in which partners that differ help each other. As such, mutualism opposes mechanisms of kin selection and tag-based selection (for example the green beard mechanism), which are based on giving exclusive help to partners that are related or carry the same tag. In contrast to kin selection, which is a basis for parochialism and intergroup warfare, mutualism can therefore be regarded as a mechanism that drives peaceful coexistence between different groups and individuals. Here the competition between mutualism and kin (tag) selection is studied. In a model where kin selection and tag-based selection are dominant, mutualism is promoted by introducing environmental fluctuations. These fluctuations cause reduction in reproductive success by the mechanism of variance discount. The best strategy to counter variance discount is to share with agents who experience the most anticorrelated fluctuations, a strategy called bet hedging. In this way, bet hedging stimulates cooperation with the most unrelated partners, which is a basis for mutualism. Analytic results and simulations reveal that, if this effect is large enough, mutualistic strategies can dominate kin selective strategies. In addition, mutants of these mutualistic strategies that experience fluctuations that are more anticorrelated to their partner, can outcompete wild type, which can lead to the evolution of specialization. In this way, the evolutionary success of mutualistic strategies can be explained by bet hedging-based cooperation.     

Modeling reciprocation and cooperation in primates: evidence for a punishing strategy

Experiments in which animals strategically interact with one another or search over some controlled domain are becoming common. While these experiments often promise to illuminate sophisticated animal behavior, the analyses brought to bear on these data are often quite coarse. For example, many papers simply tally the number of observations consistent with a behavioral theory. This analysis is simple, but ignores a potentially rich source of information by failing to take into account patterns and systematic variation among observations inconsistent with the theory. Using a new data set generated by cotton-top tamarin monkeys playing a repeated food-exchange game, we apply a maximum-likelihood estimation technique (more commonly used to study human economic behavior) which utilizes much more of the information in these data, and which uncovers unexpectedly sophisticated cooperative behavior from our subjects. Tamarin cooperation remains stable as long as both actors consistently cooperate, but requires at least two consecutive unexpected acts of cooperation to restart cooperation after it has collapsed, a strategy that resembles two-tits for a tat. We conclude by enumerating the benefits of a maximum-likelihood approach in experimental settings such as ours, and suggest other areas in which these techniques may be fruitful.     

Asymmetries in the Friendship Preferences and Social Styles of Men and Women

Several hypotheses on the form and function of sex differences in social behaviors were tested. The results suggest that friendship preferences in both sexes can be understood in terms of perceived reciprocity potential—capacity and willingness to engage in a mutually beneficial relationship. Divergent social styles may in turn reflect trade-offs between behaviors selected to maintain large, functional coalitions in men and intimate, secure relationships in women. The findings are interpreted from a broad socio-relational framework of the types of behaviors that facilitate selective advertisement and investment of reciprocity potential across individuals and within groups of men and women.

The excuse principle can maintain cooperation through forgivable defection in the Prisoner's Dilemma game

Reciprocal altruism describes a situation in which an organism acts in a manner that temporarily reduces its fitness while increasing another organism''s fitness, but there is an ultimate fitness benefit based on an expectation that the other organism will act in a similar manner at a later time. It creates the obvious dilemma in which there is always a short-term benefit to cheating, therefore cooperating individuals must avoid being exploited by non-cooperating cheaters. This is achieved by following various decision rules, usually variants of the tit-for-tat (TFT) strategy. The strength of TFT, however, is also its weakness—mistakes in implementation or interpretation of moves, or the inability to cooperate, lead to a permanent breakdown in cooperation. We show that pied flycatchers (Ficedula hypoleuca) use a TFT with an embedded ‘excuse principle’ to forgive the neighbours that were perceived as unable to cooperate during mobbing of predators. The excuse principle dramatically increases the stability of TFT-like behavioural strategies within the Prisoner''s Dilemma game.     

The iterated continuous prisoner's dilemma game cannot explain the evolution of interspecific mutualism in unstructured populations

The evolutionionary origin of inter- and intra-specific cooperation among non-related individuals has been a great challenge for biologists for decades. Recently, the continuous prisoner's dilemma game has been introduced to study this problem. In function of previous payoffs, individuals can change their cooperative investment iteratively in this model system. Killingback and Doebeli (Am. Nat. 160 (2002) 421-438) have shown analytically that intra-specific cooperation can emerge in this model system from originally non-cooperating individuals living in a non-structured population. However, it is also known from an earlier numerical work that inter-specific cooperation (mutualism) cannot evolve in a very similar model. The only difference here is that cooperation occurs among individuals of different species. Based on the model framework used by Killingback and Doebeli (2002), this Note proves analytically that mutualism indeed cannot emerge in this model system. Since numerical results have revealed that mutualism can evolve in this model system if individuals interact in a spatially structured manner, our work emphasizes indirectly the role of spatial structure of populations in the origin of mutualism.     

The costs and benefits of resource sharing: reciprocity requires resource heterogeneity

The evolution of resource sharing requires that the fitness benefits to the recipients be much higher than the costs to the giver, which requires heterogeneity among individuals in the fitness value of acquiring additional resources. We develop four models of the evolution of resource sharing by either direct or indirect reciprocity, with equal or unequal partners. Evolution of resource sharing by reciprocity requires differences between interacting individuals in the fitness value of the resource, and these differences must reverse although previous acts of giving are remembered and both participants survive. Moreover, inequality in the expected reproductive value of the interacting individuals makes reciprocity more difficult to evolve, but may still allow evolution of sharing by kin selection. These constraints suggest that resource sharing should evolve much more frequently by kin selection than by reciprocity, a prediction that is well supported by observations in the natural world.     

Size,longevity and cancer: age structure

There is significant recent interest in Peto''s paradox and the related problem of the evolution of large, long-lived organisms in terms of cancer robustness. Peto''s paradox refers to the expectation that large, long-lived organisms have a higher lifetime cancer risk, which is not the case: a paradox. This paradox, however, is circular: large, long-lived organisms are large and long-lived because they are cancer robust. Lifetime risk, meanwhile, depends on the age distributions of both cancer and competing risks: if cancer strikes before competing risks, then lifetime risk is high; if not, not. Because no set of competing risks is generally prevalent, it is instructive to temporarily dispose of competing risks and investigate the pure age dynamics of cancer under the multistage model of carcinogenesis. In addition to augmenting earlier results, I show that in terms of cancer-free lifespan large organisms reap greater benefits from an increase in cellular cancer robustness than smaller organisms. Conversely, a higher cellular cancer robustness renders cancer-free lifespan more resilient to an increase in size. This interaction may be an important driver of the evolution of large, cancer-robust organisms.     

Population viscosity can promote the evolution of altruistic sterile helpers and eusociality

Because it increases relatedness between interacting individuals, population viscosity has been proposed to favour the evolution of altruistic helping. However, because it increases local competition between relatives, population viscosity may also act as a brake for the evolution of helping behaviours. In simple models, the kin selected fecundity benefits of helping are exactly cancelled out by the cost of increased competition between relatives when helping occurs after dispersal. This result has lead to the widespread view, especially among people working with social organisms, that special conditions are required for the evolution of altruism. Here, we re-examine this result by constructing a simple population genetic model where we analyse whether the evolution of a sterile worker caste (i.e. an extreme case of altruism) can be selected for by limited dispersal. We show that a sterile worker caste can be selected for even under the simplest life-cycle assumptions. This has relevant consequences for our understanding of the evolution of altruism in social organisms, as many social insects are characterized by limited dispersal and significant genetic population structure.     

Social learning and the replication process: an experimental investigation

Human cultural traits typically result from a gradual process that has been described as analogous to biological evolution. This observation has led pioneering scholars to draw inspiration from population genetics to develop a rigorous and successful theoretical framework of cultural evolution. Social learning, the mechanism allowing information to be transmitted between individuals, has thus been described as a simple replication mechanism. Although useful, the extent to which this idealization appropriately describes the actual social learning events has not been carefully assessed. Here, we used a specifically developed computer task to evaluate (i) the extent to which social learning leads to the replication of an observed behaviour and (ii) the consequences it has for fitness landscape exploration. Our results show that social learning does not lead to a dichotomous choice between disregarding and replicating social information. Rather, it appeared that individuals combine and transform information coming from multiple sources to produce new solutions. As a consequence, landscape exploration was promoted by the use of social information. These results invite us to rethink the way social learning is commonly modelled and could question the validity of predictions coming from models considering this process as replicative.     

Is genomic diversity a useful proxy for census population size? Evidence from a species‐rich community of desert lizards

Species abundance data are critical for testing ecological theory, but obtaining accurate empirical estimates for many taxa is challenging. Proxies for species abundance can help researchers circumvent time and cost constraints that are prohibitive for long‐term sampling. Under simple demographic models, genetic diversity is expected to correlate with census size, such that genome‐wide heterozygosity may provide a surrogate measure of species abundance. We tested whether nucleotide diversity is correlated with long‐term estimates of abundance, occupancy and degree of ecological specialization in a diverse lizard community from arid Australia. Using targeted sequence capture, we obtained estimates of genomic diversity from 30 species of lizards, recovering an average of 5,066 loci covering 3.6 Mb of DNA sequence per individual. We compared measures of individual heterozygosity to a metric of habitat specialization to investigate whether ecological preference exerts a measurable effect on genetic diversity. We find that heterozygosity is significantly correlated with species abundance and occupancy, but not habitat specialization. Demonstrating the power of genomic sampling, the correlation between heterozygosity and abundance/occupancy emerged from considering just one or two individuals per species. However, genetic diversity does no better at predicting abundance than a single day of traditional sampling in this community. We conclude that genetic diversity is a useful proxy for regional‐scale species abundance and occupancy, but a large amount of unexplained variation in heterozygosity suggests additional constraints or a failure of ecological sampling to adequately capture variation in true population size.     

A proximate perspective on reciprocal altruism

The study of reciprocal altruism, or the exchange of goods and services between individuals, requires attention to both evolutionary explanations and proximate mechanisms. Evolutionary explanations have been debated at length, but far less is known about the proximate mechanisms of reciprocity. Our own research has focused on the immediate causes and contingencies underlying services such as food sharing, grooming, and cooperation in brown capuchin monkeys and chimpanzees. Employing both observational and experimental techniques, we have come to distinguish three types of reciprocity. Symmetry-based reciprocity is cognitively the least complex form, based on symmetries inherent in dyadic relationships (e.g., mutual association, kinship). Attitudinal reciprocity, which is more cognitively complex, is based on the mirroring of social attitudes between partners and is exhibited by both capuchin monkeys and chimpanzees. Finally, calculated reciprocity, the most cognitively advanced form, is based on mental scorekeeping and is found only in humans and possibly chimpanzees. Sarah F. Brosnan is a graduate student in the Population Biology, Ecology, and Evolution Program at Emory University. Her interests include proximate mechanisms of cooperation and reciprocity in primates, and social learning in primates and other species. Frans B. M. de Waal is the C. H. Candler Professor of Psychology and the director of the Living Links Center at Emory University. His interests include social behavior and cognition of monkeys and apes, and their relevance for questions on the evolution of human politics, economy, morality, and culture.     

Do aggressive signals evolve towards higher reliability or lower costs of assessment?

It has been suggested that the evolution of signals must be a wasteful process for the signaller, aimed at the maximization of signal honesty. However, the reliability of communication depends not only on the costs paid by signallers but also on the costs paid by receivers during assessment, and less attention has been given to the interaction between these two types of costs during the evolution of signalling systems. A signaller and receiver may accept some level of signal dishonesty by choosing signals that are cheaper in terms of assessment but that are stabilized with less reliable mechanisms. I studied the potential trade‐off between signal reliability and the costs of signal assessment in the corncrake (Crex crex). I found that the birds prefer signals that are less costly regarding assessment rather than more reliable. Despite the fact that the fundamental frequency of calls was a strong predictor of male size, it was ignored by receivers unless they could directly compare signal variants. My data revealed a response advantage of costly signals when comparison between calls differing with fundamental frequencies is fast and straightforward, whereas cheap signalling is preferred in natural conditions. These data might improve our understanding of the influence of receivers on signal design because they support the hypothesis that fully honest signalling systems may be prone to dishonesty based on the effects of receiver costs and be replaced by signals that are cheaper in production and reception but more susceptible to cheating.