Runaway selection for cooperation and strict-and-severe punishment

Punishing defectors is an important means of stabilizing cooperation. When levels of cooperation and punishment are continuous, individuals must employ suitable social standards for defining defectors and for determining punishment levels. Here we investigate the evolution of a social reaction norm, or psychological response function, for determining the punishment level meted out by individuals in dependence on the cooperation level exhibited by their neighbors in a lattice-structured population. We find that (1) cooperation and punishment can undergo runaway selection, with evolution towards enhanced cooperation and an ever more demanding punishment reaction norm mutually reinforcing each other; (2) this mechanism works best when punishment is strict, so that ambiguities in defining defectors are small; (3) when the strictness of punishment can adapt jointly with the threshold and severity of punishment, evolution favors the strict-and-severe punishment of individuals who offer slightly less than average cooperation levels; (4) strict-and-severe punishment naturally evolves and leads to much enhanced cooperation when cooperation without punishment would be weak and neither cooperation nor punishment are too costly; and (5) such evolutionary dynamics enable the bootstrapping of cooperation and punishment, through which defectors who never punish gradually and steadily evolve into cooperators who punish those they define as defectors.     

Defectors Can Create Conditions That Rescue Cooperation

Cooperation based on the production of costly common goods is observed throughout nature. This is puzzling, as cooperation is vulnerable to exploitation by defectors which enjoy a fitness advantage by consuming the common good without contributing fairly. Depletion of the common good can lead to population collapse and the destruction of cooperation. However, population collapse implies small population size, which, in a structured population, is known to favor cooperation. This happens because small population size increases variability in cooperator frequency across different locations. Since individuals in cooperator-dominated locations (which are most likely cooperators) will grow more than those in defector-dominated locations (which are most likely defectors), cooperators can outgrow defectors globally despite defectors outgrowing cooperators in each location. This raises the possibility that defectors can lead to conditions that sometimes rescue cooperation from defector-induced destruction. We demonstrate multiple mechanisms through which this can occur, using an individual-based approach to model stochastic birth, death, migration, and mutation events. First, during defector-induced population collapse, defectors occasionally go extinct before cooperators by chance, which allows cooperators to grow. Second, empty locations, either preexisting or created by defector-induced population extinction, can favor cooperation because they allow cooperator but not defector migrants to grow. These factors lead to the counterintuitive result that the initial presence of defectors sometimes allows better survival of cooperation compared to when defectors are initially absent. Finally, we find that resource limitation, inducible by defectors, can select for mutations adaptive to resource limitation. When these mutations are initially present at low levels or continuously generated at a moderate rate, they can favor cooperation by further reducing local population size. We predict that in a structured population, small population sizes precipitated by defectors provide a “built-in” mechanism for the persistence of cooperation.     

Quorum sensing provides a molecular mechanism for evolution to tune and maintain investment in cooperation

As selection frequently favors noncooperating defectors in mixed populations with cooperators, mechanisms that promote cooperation stability clearly exist. One potential mechanism is bacterial cell-to-cell communication, quorum sensing (QS), which can allow cooperators to prevent invasion by defectors. However, the impact of QS on widespread maintenance of cooperation in well-mixed conditions has not been experimentally demonstrated over extended evolutionary timescales. Here, we use wild-type (WT) Vibrio campbellii that regulates cooperation with QS and an unconditional cooperating (UC) mutant to examine the evolutionary origins and dynamics of novel defectors during a long-term evolution experiment. We found that UC lineages were completely outcompeted by defectors, whereas functioning QS enabled the maintenance of cooperative variants in most WT populations. Sequencing evolved populations revealed multiple luxR mutations that swept the UC lineages. However, the evolution of mutant lineages with reduced levels of bioluminescence (dims) occurred in many WT lineages. These dim variants also decreased other cooperative phenotypes regulated by QS, including protease production, indicating they result from changes to QS regulation. This diminished investment phenotype optimizes a tradeoff between cooperative input and growth output and suggests that decreasing the cost of QS could be a favorable strategy for maintaining the cooperative behaviors it regulates.Subject terms: Bacterial evolution, Microbial ecology, Molecular evolution     

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.     

Collective Chasing Behavior between Cooperators and Defectors in the Spatial Prisoner’s Dilemma

Cooperation is one of the essential factors for all biological organisms in major evolutionary transitions. Recent studies have investigated the effect of migration for the evolution of cooperation. However, little is known about whether and how an individuals’ cooperativeness coevolves with mobility. One possibility is that mobility enhances cooperation by enabling cooperators to escape from defectors and form clusters; the other possibility is that mobility inhibits cooperation by helping the defectors to catch and exploit the groups of cooperators. In this study we investigate the coevolutionary dynamics by using the prisoner’s dilemma game model on a lattice structure. The computer simulations demonstrate that natural selection maintains cooperation in the form of evolutionary chasing between the cooperators and defectors. First, cooperative groups grow and collectively move in the same direction. Then, mutant defectors emerge and invade the cooperative groups, after which the defectors exploit the cooperators. Then other cooperative groups emerge due to mutation and the cycle is repeated. Here, it is worth noting that, as a result of natural selection, the mobility evolves towards directional migration, but not to random or completely fixed migration. Furthermore, with directional migration, the rate of global population extinction is lower when compared with other cases without the evolution of mobility (i.e., when mobility is preset to random or fixed). These findings illustrate the coevolutionary dynamics of cooperation and mobility through the directional chasing between cooperators and defectors.     

For whom is it more beneficial to stop interactions with defectors: Cooperators or defectors?

Cooperation is a mysterious evolutionary phenomenon and its mechanisms require elucidation. When cooperators can stop interactions with defectors, the evolution of cooperation becomes possible; this is one mechanism that facilitates the evolution of cooperation. Here, stopping interactions with defectors is beneficial not only for cooperators but also for defectors. The question then arises, for whom is stopping interactions with defectors more beneficial: cooperators or defectors? By utilizing evolutionary game theory, I addressed this question using a two-player game involving four strategies: (1) cooperators who stop the interaction if the current partner is a defector, (2) cooperators who attempt to maintain a relationship with anyone, (3) defectors who stop the interaction if the current partner is a defector, and (4) defectors who attempt to maintain a relationship with anyone. Our results show that, at equilibrium, the ratio of cooperators who stop the interaction if the current partner is a defector to cooperators who attempt to maintain a relationship with anyone is larger than the ratio of defectors who stop the interaction if the current partner is a defector to defectors who attempt to maintain a relationship with anyone. Thus, cooperators rather than defectors are more likely to stop interactions with defectors at equilibrium. This result is consistent with a previous experimental study in which a positive correlation was detected between the degree of individuals’ cooperativeness and how accurately the individuals recognize whether other individuals are cooperators or defectors. Thus, the theoretical work presented in this study provides relevant insights into the natural phenomena of cooperation and recognition.     

Joint evolution of altruistic cooperation and dispersal in a metapopulation of small local populations

We investigate the joint evolution of public goods cooperation and dispersal in a metapopulation model with small local populations. Altruistic cooperation can evolve due to assortment and kin selection, and dispersal can evolve because of demographic stochasticity, catastrophes and kin selection. Metapopulation structures resulting in assortment have been shown to make selection for cooperation possible. But how does dispersal affect cooperation and vice versa, when both are allowed to evolve as continuous traits? We found four qualitatively different evolutionary outcomes. (1) Monomorphic evolution to full defection with positive dispersal. (2) Monomorphic evolution to an evolutionarily stable state with positive cooperation and dispersal. In this case, parameter changes selecting for increased cooperation typically also select for increased dispersal. (3) Evolutionary branching can result in the evolutionarily stable coexistence of defectors and cooperators. Although defectors could be expected to disperse more than cooperators, here we show that the opposite case is also possible: Defectors tend to disperse less than cooperators when the total amount of cooperation in the dimorphic population is low enough. (4) Selection for too low cooperation can cause the extinction of the evolving population. For moderate catastrophe rates dispersal needs to be initially very frequent for evolutionary suicide to occur. Although selection for less dispersal in principle could prevent such evolutionary suicide, in most cases this rescuing effect is not sufficient, because selection in the cooperation trait is typically much stronger. If the catastrophe rate is large enough, a part of the boundary of viability can be evolutionarily attracting with respect to both strategy components, in which case evolutionary suicide is expected from all initial conditions.     

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.     

Transforming the dilemma

How does natural selection lead to cooperation between competing individuals? The Prisoner's Dilemma captures the essence of this problem. Two players can either cooperate or defect. The payoff for mutual cooperation, R, is greater than the payoff for mutual defection, P. But a defector versus a cooperator receives the highest payoff, T, where as the cooperator obtains the lowest payoff, S. Hence, the Prisoner's Dilemma is defined by the payoff ranking T > R > P > S . In a well‐mixed population, defectors always have a higher expected payoff than cooperators, and therefore natural selection favors defectors. The evolution of cooperation requires specific mechanisms. Here we discuss five mechanisms for the evolution of cooperation: direct reciprocity, indirect reciprocity, kin selection, group selection, and network reciprocity (or graph selection). Each mechanism leads to a transformation of the Prisoner's Dilemma payoff matrix. From the transformed matrices, we derive the fundamental conditions for the evolution of cooperation. The transformed matrices can be used in standard frameworks of evolutionary dynamics such as the replicator equation or stochastic processes of game dynamics in finite populations.     

The Effect of Ostracism and Optional Participation on the Evolution of Cooperation in the Voluntary Public Goods Game

Not only animals, plants and microbes but also humans cooperate in groups. The evolution of cooperation in a group is an evolutionary puzzle, because defectors always obtain a higher benefit than cooperators. When people participate in a group, they evaluate group member’s reputations and then decide whether to participate in it. In some groups, membership is open to all who are willing to participate in the group. In other groups, a candidate is excluded from membership if group members regard the candidate’s reputation as bad. We developed an evolutionary game model and investigated how participation in groups and ostracism influence the evolution of cooperation in groups when group members play the voluntary public goods game, by means of computer simulation. When group membership is open to all candidates and those candidates can decide whether to participate in a group, cooperation cannot be sustainable. However, cooperation is sustainable when a candidate cannot be a member unless all group members admit them to membership. Therefore, it is not participation in a group but rather ostracism, which functions as costless punishment on defectors, that is essential to sustain cooperation in the voluntary public goods game.     

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.     

Evolution of cooperation under -person snowdrift games

In the animal world, performing a given task which is beneficial to an entire group requires the cooperation of several individuals of that group who often share the workload required to perform the task. The mathematical framework to study the dynamics of collective action is game theory. Here we study the evolutionary dynamics of cooperators and defectors in a population in which groups of individuals engage in N-person, non-excludable public goods games. We explore an N-person generalization of the well-known two-person snowdrift game. We discuss both the case of infinite and finite populations, taking explicitly into consideration the possible existence of a threshold above which collective action is materialized. Whereas in infinite populations, an N-person snowdrift game (NSG) leads to a stable coexistence between cooperators and defectors, the introduction of a threshold leads to the appearance of a new interior fixed point associated with a coordination threshold. The fingerprints of the stable and unstable interior fixed points still affect the evolutionary dynamics in finite populations, despite evolution leading the population inexorably to a monomorphic end-state. However, when the group size and population size become comparable, we find that spite sets in, rendering cooperation unfeasible.     

Repeated games and direct reciprocity under active linking

Direct reciprocity relies on repeated encounters between the same two individuals. Here we examine the evolution of cooperation under direct reciprocity in dynamically structured populations. Individuals occupy the vertices of a graph, undergoing repeated interactions with their partners via the edges of the graph. Unlike the traditional approach to evolutionary game theory, where individuals meet at random and have no control over the frequency or duration of interactions, we consider a model in which individuals differ in the rate at which they seek new interactions. Moreover, once a link between two individuals has formed, the productivity of this link is evaluated. Links can be broken off at different rates. Whenever the active dynamics of links is sufficiently fast, population structure leads to a simple transformation of the payoff matrix, effectively changing the game under consideration, and hence paving the way for reciprocators to dominate defectors. We derive analytical conditions for evolutionary stability.     

Maintenance affects the stability of a two-tiered microbial 'food chain'?

Recent studies have shown that constraints on available resources may play an important role in the evolution of cooperation, especially when individuals do not posses the capacity to recognize other individuals, memory or other developed abilities, as it is the case of most unicellular organisms, algae or even plants. We analyze the evolution of cooperation in the case of a limiting resource, which is necessary for reproduction and survival. We show that, if the strategies determine a prisoner's dilemma, the outcome of the interactions may be modified by the limitation of resources allowing cooperators to invade the entire population. Analytic expressions for the region of cooperation are provided. Furthermore we derive expressions for the connection between fitness, as understood in evolutionary game theory, and resource exchanges, which may be of help to link evolutionary game theoretical results with resource based models.     

Spatial Patterns of Prisoner’s Dilemma Game in Metapopulations

Because to defect is the evolutionary stable strategy in the prisoner’s dilemma game (PDG), understanding the mechanism generating and maintaining cooperation in PDG, i.e. the paradox of cooperation, has intrinsic significance for understanding social altruism behaviors. Spatial structure serves as the key to this dilemma. Here, we build the model of spatial PDG under a metapopulation framework: the sub-populations of cooperators and defectors obey the rules in spatial PDG as well as the colonization–extinction process of metapopulations. Using the mean-field approximation and the pair approximation, we obtain the differential equations for the dynamics of occupancy and spatial correlation. Cellular automaton is also built to simulate the spatiotemporal dynamics of the spatial PDG in metapopulations. Join-count statistics are used to measure the spatial correlation as well as the spatial association of the metapopulation. Simulation results show that the distribution is self-organized and that it converges to a static boundary due to the boycotting of cooperators to defectors. Metapopulations can survive even when the colonization rate is lower than the extinction rate due to the compensation of cooperation rewards for extinction debt. With a change of parameters in the model, a metapopulation can consist of pure cooperators, pure defectors, or cooperator–defector coexistence. The necessary condition of cooperation evolution is the local colonization of a metapopulation. The spatial correlation between the cooperators tends to be weaker with the increase in the temptation to defect and the habitat connectivity; yet the spatial correlation between defectors becomes stronger. The relationship between spatial structure and the colonization rate is complicated, especially for cooperators. The metapopulation may undergo a temporary period of prosperity just before the extinction, even while the colonization rate is declining. An erratum to this article can be found at     

Incentives and opportunism: from the carrot to the stick

Cooperation in public good games is greatly promoted by positive and negative incentives. In this paper, we use evolutionary game dynamics to study the evolution of opportunism (the readiness to be swayed by incentives) and the evolution of trust (the propensity to cooperate in the absence of information on the co-players). If both positive and negative incentives are available, evolution leads to a population where defectors are punished and players cooperate, except when they can get away with defection. Rewarding behaviour does not become fixed, but can play an essential role in catalysing the emergence of cooperation, especially if the information level is low.     

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.     

Cooperation prevails when individuals adjust their social ties

Conventional evolutionary game theory predicts that natural selection favours the selfish and strong even though cooperative interactions thrive at all levels of organization in living systems. Recent investigations demonstrated that a limiting factor for the evolution of cooperative interactions is the way in which they are organized, cooperators becoming evolutionarily competitive whenever individuals are constrained to interact with few others along the edges of networks with low average connectivity. Despite this insight, the conundrum of cooperation remains since recent empirical data shows that real networks exhibit typically high average connectivity and associated single-to-broad–scale heterogeneity. Here, a computational model is constructed in which individuals are able to self-organize both their strategy and their social ties throughout evolution, based exclusively on their self-interest. We show that the entangled evolution of individual strategy and network structure constitutes a key mechanism for the sustainability of cooperation in social networks. For a given average connectivity of the population, there is a critical value for the ratio W between the time scales associated with the evolution of strategy and of structure above which cooperators wipe out defectors. Moreover, the emerging social networks exhibit an overall heterogeneity that accounts very well for the diversity of patterns recently found in acquired data on social networks. Finally, heterogeneity is found to become maximal when W reaches its critical value. These results show that simple topological dynamics reflecting the individual capacity for self-organization of social ties can produce realistic networks of high average connectivity with associated single-to-broad–scale heterogeneity. On the other hand, they show that cooperation cannot evolve as a result of “social viscosity” alone in heterogeneous networks with high average connectivity, requiring the additional mechanism of topological co-evolution to ensure the survival of cooperative behaviour.     

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.     

Spatial invasion of cooperation

The evolutionary puzzle of cooperation describes situations where cooperators provide a fitness benefit to other individuals at some cost to themselves. Under Darwinian selection, the evolution of cooperation is a conundrum, whereas non-cooperation (or defection) is not. In the absence of supporting mechanisms, cooperators perform poorly and decrease in abundance. Evolutionary game theory provides a powerful mathematical framework to address the problem of cooperation using the prisoner's dilemma. One well-studied possibility to maintain cooperation is to consider structured populations, where each individual interacts only with a limited subset of the population. This enables cooperators to form clusters such that they are more likely to interact with other cooperators instead of being exploited by defectors. Here we present a detailed analysis of how a few cooperators invade and expand in a world of defectors. If the invasion succeeds, the expansion process takes place in two stages: first, cooperators and defectors quickly establish a local equilibrium and then they uniformly expand in space. The second stage provides good estimates for the global equilibrium frequencies of cooperators and defectors. Under hospitable conditions, cooperators typically form a single, ever growing cluster interspersed with specks of defectors, whereas under more hostile conditions, cooperators form isolated, compact clusters that minimize exploitation by defectors. We provide the first quantitative assessment of the way cooperators arrange in space during invasion and find that the macroscopic properties and the emerging spatial patterns reveal information about the characteristics of the underlying microscopic interactions.