Evolution of cooperation and altruistic punishment when retaliation is possible

Altruistic punishment is suggested to explain observed high levels of cooperation among non-kin related humans. However, laboratory experiments as well as ethnographic evidence suggest that people might retaliate if being punished, and that this reduces the level of cooperation. Building on existing models on the evolution of cooperation and altruistic punishment, we explore the consequences of the option of retaliation. We find that cooperation and altruistic punishment does not evolve with larger population levels if the option of retaliation is included.     

Rewards and the evolution of cooperation in public good games

Properly coordinating cooperation is relevant for resolving public good problems, such as clean energy and environmental protection. However, little is known about how individuals can coordinate themselves for a certain level of cooperation in large populations of strangers. In a typical situation, a consensus-building process rarely succeeds, owing to a lack of face and standing. The evolution of cooperation in this type of situation is studied here using threshold public good games, in which cooperation prevails when it is initially sufficient, or otherwise it perishes. While punishment is a powerful tool for shaping human behaviours, institutional punishment is often too costly to start with only a few contributors, which is another coordination problem. Here, we show that whatever the initial conditions, reward funds based on voluntary contribution can evolve. The voluntary reward paves the way for effectively overcoming the coordination problem and efficiently transforms freeloaders into cooperators with a perceived small risk of collective failure.     

Evolution of contingent altruism when cooperation is expensive

The ubiquity of cooperation has motivated a major research program over the last 50 years to discover ever more minimal conditions for the evolution of altruism. One important line of work is based on favoritism toward those who appear to be close relatives. Another important line is based on continuing interactions, whether between individuals (e.g., reciprocity) or between lines of descent in a viscous population. Here, we use an agent-based model to demonstrate a new mechanism that combines both lines of work to show when and how favoritism toward apparently similar others can evolve in the first place. The mechanism is the joint operation of viscosity and of tags (heritable, observable, and initially arbitrary characteristics), which serve as weak and potentially deceptive indicators of relatedness. Although tags are insufficient to support cooperation alone, we show that this joint mechanism vastly increases the range of environments in which contingent altruism can evolve in viscous populations. Even though our model is quite simple, the subtle dynamics underlying our results are not tractable using formal analytic tools (such as analysis of evolutionarily stable strategies), but are amenable to agent-based simulation.     

The volunteer's dilemma and the optimal size of a social group

If one or few individuals are enough to perform an action that produces a collective good and if this action has a cost, living in group can be beneficial because the cost can be shared with other individuals. Without coordination, however, the production of a collective good by the contribution of one or few individuals is inefficient and can be modelled as a volunteer's dilemma. In the volunteer's dilemma the individuals that pay the cost for the production of the collective good benefit from their action if nobody else volunteers, but the cost is wasted if too many individuals volunteer. Increasing group size reduces the need of volunteering for each member of the group; the overall benefit for the group, however, decreases too because the larger the group is, the less likely it is that the collective good is produced. This problem persists even with a high degree of relatedness between group members; an optimal, intermediate group size exists that maximizes the probability to produce the collective good.     

Stable public goods cooperation and dynamic social interactions in yeast

Despite long-standing theoretical interest in the evolution of cooperation, empirical data on the evolutionary dynamics of cooperative traits remain limited. Here, we investigate the evolutionary dynamics of a simple public goods cooperative trait, invertase secretion, using a long-term selection experiment in Saccharomyces cerevisiae. We show that average investment in cooperation remains essentially constant over a period of hundreds of generations in viscous populations with high relatedness. Average cooperation remains constant despite transient local selection for high and low levels of cooperation that generate dynamic social interactions. Natural populations of yeast show similar variation in social strategies, which is consistent with the existence of similar selective pressures on public goods cooperation in nature.     

The continuous public goods game and the evolution of cooperative sex ratios

Some animals, such as Melittobia wasps and surface-living mites, have extremely female-biased sex ratios that cannot be explained by the existing local mate competition (LMC) theories. The restricted production of sons may entail cooperation among mothers, enabling the production of more daughters and avoiding severe competition among sons for insemination access. These unusual examples are characterized by the long-term cohabitation of egg-layers (foundresses) on resource patches and possible contact with oviposited eggs. By applying the logic of mutual policing, we develop a novel game theoretical model for the evolution of cooperation in sex-ratio traits. This is the first attempt to model the evolution of sex ratios based on iterated games. We assumed that foundresses have two abilities to enable mutual policing: they can monitor the sex ratio in the resource patch, and they can punish defectors that produce an overabundance of males. Numerical analysis and evolutionary simulations demonstrate that cooperative low sex ratios can evolve when the number of foundresses per patch is sufficiently small. Our model predicts a slight, but steady increase in oviposition sex ratios with an increase in the number of foundresses, which mimics the phenomenon observed in several animals with extremely female-biased sex ratios. We also discuss the relationship between our model and other models of sex-ratio evolution.     

Constraining free riding in public goods games: designated solitary punishers can sustain human cooperation

Much of human cooperation remains an evolutionary riddle. Unlike other animals, people frequently cooperate with non-relatives in large groups. Evolutionary models of large-scale cooperation require not just incentives for cooperation, but also a credible disincentive for free riding. Various theoretical solutions have been proposed and experimentally explored, including reputation monitoring and diffuse punishment. Here, we empirically examine an alternative theoretical proposal: responsibility for punishment can be borne by one specific individual. This experiment shows that allowing a single individual to punish increases cooperation to the same level as allowing each group member to punish and results in greater group profits. These results suggest a potential key function of leadership in human groups and provides further evidence supporting that humans will readily and knowingly behave altruistically.     

Natural selection of cooperation and degree hierarchy in heterogeneous populations

One of the current theoretical challenges to the explanatory powers of Evolutionary Theory is the understanding of the observed evolutionary survival of cooperative behavior when selfish actions provide higher fitness (reproductive success). In unstructured populations natural selection drives cooperation to extinction. However, when individuals are allowed to interact only with their neighbors, specified by a graph of social contacts, cooperation-promoting mechanisms (known as lattice reciprocity) offer to cooperation the opportunity of evolutionary survival. Recent numerical works on the evolution of Prisoner's Dilemma in complex network settings have revealed that graph heterogeneity dramatically enhances the lattice reciprocity. Here we show that in highly heterogeneous populations, under the graph analog of replicator dynamics, the fixation of a strategy in the whole population is in general an impossible event, for there is an asymptotic partition of the population in three subsets, two in which fixation of cooperation or defection has been reached and a third one which experiences cycles of invasion by the competing strategies. We show how the dynamical partition correlates with connectivity classes and characterize the temporal fluctuations of the fluctuating set, unveiling the mechanisms stabilizing cooperation in macroscopic scale-free structures.     

One-shot reciprocity under error management is unbiased and fragile

The error management model of altruism in one-shot interactions provides an influential explanation for one of the most controversial behaviors in evolutionary social science. The model posits that one-shot altruism arises from a domain-specific cognitive bias that avoids the error of mistaking a long-term relationship for a one-shot interaction. One-shot altruism is thus, in an intriguingly paradoxical way, a form of reciprocity. We examine the logic behind this idea in detail. In its most general form the error management model is exceedingly flexible, and restrictions about the psychology of agents are necessary for selection to be well-defined. Once these restrictions are in place, selection is well defined, but it leads to behavior that is perfectly consistent with an unbiased rational benchmark. Thus, the evolution of one-shot reciprocity does not require an evoked cognitive bias based on repeated interactions and reputation. Moreover, in spite of its flexibility in terms of psychology, the error management model assumes that behavior is exceedingly rigid when individuals face a new interaction partner. Reciprocity can only take the form of tit-for-tat, and individuals cannot adjust their behavior in response to new information about the duration of a relationship. Zefferman (2014) showed that one-shot reciprocity does not reliably evolve if one relaxes the first restriction, and we show that the behavior does not reliably evolve if one relaxes the second restriction. Altogether, these theoretical results on one-shot reciprocity do not square well with experiments showing increased altruism in the presence of payoff-irrelevant stimuli that suggest others are watching.     

Group selection, kin selection, altruism and cooperation: When inclusive fitness is right and when it can be wrong

Group selection theory has a history of controversy. After a period of being in disrepute, models of group selection have regained some ground, but not without a renewed debate over their importance as a theoretical tool. In this paper I offer a simple framework for models of the evolution of altruism and cooperation that allows us to see how and to what extent both a classification with and one without group selection terminology are insightful ways of looking at the same models. Apart from this dualistic view, this paper contains a result that states that inclusive fitness correctly predicts the direction of selection for one class of models, represented by linear public goods games. Equally important is that this result has a flip side: there is a more general, but still very realistic class of models, including models with synergies, for which it is not possible to summarize their predictions on the basis of an evaluation of inclusive fitness.     

Altruism, sex, and inbreeding when the genotype-phenotype map is additive

Recently published theoretical results suggest that, in a sexual population, when genotypes code for phenotypes in a complex manner, it is possible for altruistic genotypes to spread through a metapopulation (i.e. through a collection of subpopulations). This spread tends to occur during periods when the environment deteriorates throughout the metapopulation. By contrast, under asexual reproduction, non-altruistic genotypes seem to be favoured, at least when subpopulations are substantial in size. The most relevant previous study makes use of Kauffman and Levin's "NK model" as a way to relate genotypes to fitness. Unfortunately, there are both conceptual and technical problems with the application of the NK model to populations that contain many different genotypes (e.g. polymorphic diploid populations with more than a few loci under selection). The present study presents a more tractable and biologically plausible model to study the causal relationship between sexual reproduction and altruism. In particular, phenotypes are determined by additive interactions among alleles at different loci in a diploid genome, with up to 200 loci under selection. In addition, subpopulations are substantially larger than those considered in the most relevant previous work. The results show that, so long as there are multiple "fitness peaks" in "phenotype space", the additive genotype-phenotype map leads to results that are similar to those from the NK model. Various parameters are manipulated in an effort to discover the determinants of altruistic and non-altruistic outcomes. The findings should facilitate further investigations, and they should help to establish the plausibility of the suggested relationship between sexual reproduction and altruism. The results also suggest that inbreeding can lead to a similar result as asexuality. That is, inbreeding seems to enhance the probability that altruistic phenotypes will be eliminated.     

Virulence and transmission modes in metapopulations: when group selection increases virulence

Individuals that are infected by a pathogen can transmit it to unrelated conspecifics (horizontal transmission) or to their progeny when they reproduce (vertical transmission). The mechanisms of these two routes of transmission are different and this difference impacts the way virulence evolves in pathogens. More precisely, horizontal transmission depends on the probability that an infected host contacts susceptible conspecifics, and therefore on its lifespan. Vertical transmission additionally depends on the host's fecundity. This additional dependence in vertically transmitted pathogens results in a decrease in their evolutionarily stable (ES) virulence.Spatial structure is another factor that is often supposed to decrease pathogens’ ES virulence, mostly because it impedes competition for transmission in local populations of hosts. In this paper, using the adaptive dynamics framework, we show that spatial structure can increase ES virulence when pathogens are mostly vertically transmitted. This is due to the difference in how pathogens compete for transmission in local population of hosts, depending on how they are transmitted. We also show that symbionts that are horizontally transmitted should respond more to a change in spatial structure than symbionts that are vertically transmitted.     

Evolution of cooperation in spatial public goods games with common resource dynamics

Investment in a common resource shared by all players is difficult to evolve despite higher returns because a non-investor (free-rider) always receives more than an investor (altruist). This situation is referred to as the Tragedy of the Commons and is often observed in various biological systems including environmental problems of human society. Punishment and reputation are effective mechanisms but require cooperator's ability to identify free-riders. Volunteering can work in anonymous public goods games but this requires voluntary participation, which is not always the case. Here, we show that the evolution of altruism is possible in anonymous and obligate public goods games if we consider the spatiotemporal dynamics of the common resource that incorporate spatial diffusion and internal dynamics of the commons. The investors' strategy to counter free-riders is to increase population density and to outnumber them with the common resource level kept as low as that of the free-riders.     

Viscous medium promotes cooperation in the pathogenic bacterium Pseudomonas aeruginosa

There has been extensive theoretical debate over whether population viscosity (limited dispersal) can favour cooperation. While limited dispersal increases the probability of interactions occurring between relatives, which can favour cooperation, it can also lead to an increase in competition between relatives and this can reduce or completely negate selection for cooperation. Despite much theoretical attention, there is a lack of empirical research investigating these issues. We cultured Pseudomonas aeruginosa bacteria in medium with different degrees of viscosity and examined the fitness consequences for a cooperative trait—the production of iron-scavenging siderophore molecules. We found that increasing viscosity of the growth medium (i) significantly limited bacterial dispersal and the diffusion of siderophore molecules and (ii) increased the fitness of individuals that produced siderophores relative to mutants that did not. We propose that viscosity favours siderophore-producing individuals in this system, because the benefits of siderophore production are more likely to accrue to relatives (i.e. greater indirect benefits), and, at the same time, bacteria are more likely to gain direct fitness benefits by taking up siderophore molecules produced by themselves (i.e. the trait becomes less cooperative). Our results suggest that viscosity of the microbial growth environment is a crucial factor determining the dynamics of wild-type bacteria and siderophore-deficient mutants in natural habitats, such as the viscous mucus in cystic fibrosis lung.     

Evolving learning rules and emergence of cooperation in spatial prisoner's dilemma

In the evolutionary Prisoner's dilemma (PD) game, agents play with each other and update their strategies in every generation according to some microscopic dynamical rule. In its spatial version, agents do not play with every other but, instead, interact only with their neighbours, thus mimicking the existing of a social or contact network that defines who interacts with whom. In this work, we explore evolutionary, spatial PD systems consisting of two types of agents, each with a certain update (reproduction, learning) rule. We investigate two different scenarios: in the first case, update rules remain fixed for the entire evolution of the system; in the second case, agents update both strategy and update rule in every generation. We show that in a well-mixed population the evolutionary outcome is always full defection. We subsequently focus on two-strategy competition with nearest-neighbour interactions on the contact network and synchronised update of strategies. Our results show that, for an important range of the parameters of the game, the final state of the system is largely different from that arising from the usual setup of a single, fixed dynamical rule. Furthermore, the results are also very different if update rules are fixed or evolve with the strategies. In these respect, we have studied representative update rules, finding that some of them may become extinct while others prevail. We describe the new and rich variety of final outcomes that arise from this co-evolutionary dynamics. We include examples of other neighbourhoods and asynchronous updating that confirm the robustness of our conclusions. Our results pave the way to an evolutionary rationale for modelling social interactions through game theory with a preferred set of update rules.     

Invasion of cooperators in lattice populations: Linear and non-linear public good games

A generalized version of the N-person volunteer's dilemma (NVD) Game has been suggested recently for illustrating the problem of N-person social dilemmas. Using standard replicator dynamics it can be shown that coexistence of cooperators and defectors is typical in this model. However, the question of how a rare mutant cooperator could invade a population of defectors is still open.     

Cooperation as a volunteer’s dilemma and the strategy of conflict in public goods games

Conflict and cooperation for the exploitation of public goods are usually modelled as an N‐person prisoner’s dilemma. Many social dilemmas, however, would be described more properly as a volunteer’s dilemma, in which a certain number of individuals are necessary to produce a public good. If volunteering is costly, but so is failure to produce the public good, cheaters can invade and form a stable mixed equilibrium with cooperators. The dilemma is that the benefit for the group decreases with group size because the larger the group is, the less likely it is that someone volunteers. This problem persists even in the presence of a high degree of relatedness between group members. This model provides precise, testable predictions for the stability of cooperation. It also suggests a counterintuitive but practical solution for this kind of social dilemmas: increasing the damage resulting from the failure to produce the public good increases the probability that the public good is actually produced. Adopting a strategy that entails a deliberate risk (brinkmanship), therefore, can lead to a benefit for the society without being detrimental for the individual.     

The paradox of cooperation benefits

It seems obvious that as the benefits of cooperation increase, the share of cooperators in the population should also increase. It is well known that positive assortment between cooperative types, for instance in spatially structured populations, provide better conditions for the evolution of cooperation than complete mixing. This study demonstrates that, assuming positive assortment, under most conditions higher cooperation benefits also increase the share of cooperators. On the other hand, under a specified range of payoff values, when at least two payoff parameters are modified, the reverse is true. The conditions for this paradox are determined for two-person social dilemmas: the Prisoner's Dilemma, the Hawks and Doves game, and the Stag Hunt game, assuming global selection and positive assortment.     

The effect of dispersal and neighbourhood in games of cooperation

The prisoner's dilemma (PD) and the snowdrift (SD) games are paradigmatic tools to investigate the origin of cooperation. Whereas spatial structure (e.g. nonrandom spatial distribution of strategies) present in the spatially explicit models facilitates the emergence of cooperation in the PD game, recent investigations have suggested that spatial structure can be unfavourable for cooperation in the SD game. The frequency of cooperators in a spatially explicit SD game can be lower than it would be in an infinitely large well-mixed population. However, the source of this effect cannot be identified with certainty as spatially explicit games differ from well-mixed games in two aspects: (i) they introduce spatial correlations, (ii) and limited neighbourhood. Here we extend earlier investigations to identify the source of this effect, and thus accordingly we study a spatially explicit version of the PD and SD games with varying degrees of dispersal and neighbourhood size. It was found that dispersal favours selfish individuals in both games. We calculated the frequency of cooperators at strong dispersal limit, which in concordance with the numerical results shows that it is the short range of interactions (i.e. limited neighbourhood) and not spatial correlations that decreases the frequency of cooperators in spatially explicit models of populations. Our results demonstrate that spatial correlations are always beneficial to cooperators in both the PD and SD games. We explain the opposite effect of dispersal and neighbourhood structure, and discuss the relevance of distinguishing the two effects in general.     

A simple learning strategy that realizes robust cooperation better than Pavlov in Iterated Prisoners' Dilemma

Pavlov was proposed as a leading strategy for realizing cooperation because it dominates over a long period in evolutionary computer simulations of the Iterated Prisoners' Dilemma. However, our numerical calculations reveal that Pavlov and also any other cooperative strategy are not evolutionarily stable among all stochastic strategies with memory of only one previous move. We propose simple learning based on reinforcement. The learner changes its internal state, depending on an evaluation of whether the score in the previous round is larger than a critical value (aspiration level), which is genetically fixed. The current internal state decides the learner's move, but we found that the aspiration level determines its final behavior. The cooperative variant, having an intermediate aspiration level, is not an evolutionarily stable strategy (ESS) when evaluation is binary (good or bad). However, when the evaluation is quantified some cooperative variants can invade not only All-C, Tit-For-Tat (TFT), and Pavlov but also noncooperative variants with different aspiration levels. Moreover, they establish robust cooperation, which is evolutionarily stable against invasion by All-C, All-D, TFT, Pavlov, and noncooperative variants, and they receive a high score even when the error rate is high. Our results suggest that mutual cooperation can be maintained when players have a primitive learning ability. Received: June 23, 2000 / Accepted: October 1, 2000