Does quasi-local competition lead to pattern formation in metapopulations? An explicit resource competition model

In metapopulations, competitive interactions may extend beyond the confines of the local population such that members of neighbouring habitat patches affect each other adversely (quasi-local competition). We derive a model for quasi-local competition from first principles, assuming that individuals compete for shared resources and members of a population spend a certain fraction of their foraging time in the adjacent populations. Contrary to the results of Doebeli and Killingback [2003. Theor. Popul. Biol. 64, 397-416], our model does not produce spatial patterns of population densities in homogeneous environments. Quasi-local competition nevertheless contributes to pattern formation by amplifying the effect of heterogeneities in the external environment, and this amplification can be extremely strong when dispersal is absent. We discuss why apparently similar models lead to contrasting results.     

The stability of cooperation involving variable investment

In this paper, we attempt to reconcile the results of several studies which have investigated the evolution of cooperation between non-relatives in systems where investment in partners can vary. In contrast to previous proposals, we show for the first time that variable-investment cooperation can be readily maintained in inter-species mutualistic relationships even in the absence of spatial structure, but that the stability of this interaction is dependent on the particular investment-response rule that is employed. By allowing the evolution of investment-response parameters in both inter- and intra-specific versions of the continuous variable-investment Prisoners' Dilemma we show that, in the absence of further factors, the raise-the stakes (RTS) strategy is likely to evolve into a simpler, variable investment form of Give-as-Good-as-you-Get that initially offers a high fixed amount and subsequently matches its partner's investment. Nevertheless, we demonstrate that genuine RTS-like strategies will still be selected if two intuitively reasonable conditions hold: if individuals are limited in terms of the total they can invest in cooperative actions over their lifetimes, and if there are always some individuals in a population that cannot cooperate.     

Hunter–Gatherer population structure and the evolution of contingent cooperation

Unlike other vertebrates, humans cooperate in large groups with unrelated individuals. Many authors have argued that the evolution of such cooperation has resulted from reciprocity and other forms of contingent cooperation. This argument is not well supported by existing theory. The theory of contingent cooperation in pairs is well developed: reciprocating strategies are stable when common, and can increase when rare as long as population structure leads to modest levels of relatedness. In larger groups, however, it is not clear whether contingent cooperation can increase when rare. Existing work suggests that contingent strategies cannot increase unless relatedness is high, but depends on unrealistic assumptions about the effects of population structure. Here we develop and analyze a model incorporating a two level population structure that captures important features of human hunter–gatherer societies. This model suggests that previous work underestimates the range of conditions under which contingent cooperation can evolve, but also predicts that cooperation will not evolve unless (1) social groups are small, and (2) the relatedness within ethnolinguistic groups is at the high end of the range of empirical estimates.     

Cooperation and Stability through Periodic Impulses

Basic games, where each individual chooses between two strategies, illustrate several issues that immediately emerge from the standard approach that applies strategic reasoning, based on rational decisions, to predict population behavior where no rationality is assumed. These include how mutual cooperation (which corresponds to the best outcome from the population perspective) can evolve when the only individually rational choice is to defect, illustrated by the Prisoner''s Dilemma (PD) game, and how individuals can randomize between two strategies when neither is individually rational, illustrated by the Battle of the Sexes (BS) game that models male-female conflict over parental investment in offspring. We examine these questions from an evolutionary perspective where the evolutionary dynamics includes an impulsive effect that models sudden changes in collective population behavior. For the PD game, we show analytically that cooperation can either coexist with defection or completely take over the population, depending on the strength of the impulse. By extending these results for the PD game, we also show that males and females each evolve to a single strategy in the BS game when the impulsive effect is strong and that weak impulses stabilize the randomized strategies of this game.     

Spatial effects in social dilemmas

Social dilemmas and the evolutionary conundrum of cooperation are traditionally studied through various kinds of game theoretical models such as the prisoner's dilemma, public goods games, snowdrift games or by-product mutualism. All of them exemplify situations which are characterized by different degrees of conflicting interests between the individuals and the community. In groups of interacting individuals, cooperators produce a common good benefitting the entire group at some cost to themselves, whereas defectors attempt to exploit the resource by avoiding the costly contributions. Based on synergistic or discounted accumulation of cooperative benefits a unifying theoretical framework was recently introduced that encompasses all games that have traditionally been studied separately (Hauert, Michor, Nowak, Doebeli, 2005. Synergy and discounting of cooperation in social dilemmas. J. Theor. Biol., in press.). Within this framework we investigate the effects of spatial structure with limited local interactions on the evolutionary fate of cooperators and defectors. The quantitative effects of space turn out to be quite sensitive to the underlying microscopic update mechanisms but, more general, we demonstrate that in prisoner's dilemma type interactions spatial structure benefits cooperation-although the parameter range is quite limited-whereas in snowdrift type interactions spatial structure may be beneficial too, but often turns out to be detrimental to cooperation.     

Selective feedback between dispersal distance and the stability of mutualism

The evolution and maintenance of mutually beneficial interactions has been one of the oldest problems for evolutionary theory. For cooperation to be stable, mechanisms such as spatial population structure must exist that prevent non‐cooperative individuals from invading cooperative groups. Selection for certain traits like increased dispersal can erode that structure. Here, I used a spatially explicit individual based dual lattice computer simulation to investigate how the evolution of dispersal interacts with the evolution of mutualism and how this interaction affects the stability of mutualism in the face of non‐mutualists. I ran simulations manipulating the self‐structuring phenotype, dispersal distance, over a range of environmental conditions, as well as letting both dispersal and mutualism evolve independently, with and without a cost of dispersal. I found that environmental productivity is negatively correlated with the stability of mutualism, and that the stability of mutualism relied on the ability of mutualists to evolve shorter dispersal distances than non‐mutualists. The inclusion of a dispersal cost essentially fixed the upper limit of dispersal, and therefore limits the ability of non‐mutualists to evolve higher average dispersal than mutualists, but as costs are relaxed, the differences are recovered. These results show how selection on seemingly unrelated traits can align suites of traits into holistic life history strategies.     

Cooperation in animals: An evolutionary overview

Evolutionary biologists have grappled with the question of the emergenceand maintenance of cooperation since Darwin first listed animal cooperation asapotential problem for his theory of natural selection. Here I review four pathsthat have been delineated in the study of intra-specific cooperation amonganimals. These paths – kinship, reciprocity, byproduct mutualism andgroupselection – serve as a starting point for behavioral ecologistsinterestedstudying the initiation and maintenance of cooperation. After reviewing theempirical and theoretical underpinnings of these paths to cooperation, I touchupon some recent work that has attempted to examine (or reexamine) the role ofphylogeny, punishment and morality in the light of cooperative behavior.     

Social experiments in the mesoscale: humans playing a spatial prisoner's dilemma

Background

The evolutionary origin of cooperation among unrelated individuals remains a key unsolved issue across several disciplines. Prominent among the several mechanisms proposed to explain how cooperation can emerge is the existence of a population structure that determines the interactions among individuals. Many models have explored analytically and by simulation the effects of such a structure, particularly in the framework of the Prisoner''s Dilemma, but the results of these models largely depend on details such as the type of spatial structure or the evolutionary dynamics. Therefore, experimental work suitably designed to address this question is needed to probe these issues.

Methods and Findings

We have designed an experiment to test the emergence of cooperation when humans play Prisoner''s Dilemma on a network whose size is comparable to that of simulations. We find that the cooperation level declines to an asymptotic state with low but nonzero cooperation. Regarding players'' behavior, we observe that the population is heterogeneous, consisting of a high percentage of defectors, a smaller one of cooperators, and a large group that shares features of the conditional cooperators of public goods games. We propose an agent-based model based on the coexistence of these different strategies that is in good agreement with all the experimental observations.

Conclusions

In our large experimental setup, cooperation was not promoted by the existence of a lattice beyond a residual level (around 20%) typical of public goods experiments. Our findings also indicate that both heterogeneity and a “moody” conditional cooperation strategy, in which the probability of cooperating also depends on the player''s previous action, are required to understand the outcome of the experiment. These results could impact the way game theory on graphs is used to model human interactions in structured groups.     

Signalling and the evolution of cooperative foraging in dynamic environments

Understanding cooperation in animal social groups remains a significant challenge for evolutionary theory. Observed behaviours that benefit others but incur some cost appear incompatible with classical notions of natural selection; however, these behaviours may be explained by concepts such as inclusive fitness, reciprocity, intra-specific mutualism or manipulation. In this work, we examine a seemingly altruistic behaviour, the active recruitment of conspecifics to a food resource through signalling. Here collective, cooperative behaviour may provide highly nonlinear benefits to individuals, since group functionality has the potential to be far greater than the sum of the component parts, for example by enabling the effective tracking of a dynamic resource. We show that due to this effect, signalling to others is an evolutionarily stable strategy under certain environmental conditions, even when there is a cost associated to this behaviour. While exploitation is possible, in the limiting case of a sparse, ephemeral but locally abundant nutrient source, a given environmental profile will support a fixed number of signalling individuals. Through a quantitative analysis, this effective carrying capacity for cooperation is related to the characteristic length and time scales of the resource field.     

Evolutionary Dynamics of Nitrogen Fixation in the Legume–Rhizobia Symbiosis

The stabilization of host–symbiont mutualism against the emergence of parasitic individuals is pivotal to the evolution of cooperation. One of the most famous symbioses occurs between legumes and their colonizing rhizobia, in which rhizobia extract nutrients (or benefits) from legume plants while supplying them with nitrogen resources produced by nitrogen fixation (or costs). Natural environments, however, are widely populated by ineffective rhizobia that extract benefits without paying costs and thus proliferate more efficiently than nitrogen-fixing cooperators. How and why this mutualism becomes stabilized and evolutionarily persists has been extensively discussed. To better understand the evolutionary dynamics of this symbiosis system, we construct a simple model based on the continuous snowdrift game with multiple interacting players. We investigate the model using adaptive dynamics and numerical simulations. We find that symbiotic evolution depends on the cost–benefit balance, and that cheaters widely emerge when the cost and benefit are similar in strength. In this scenario, the persistence of the symbiotic system is compatible with the presence of cheaters. This result suggests that the symbiotic relationship is robust to the emergence of cheaters, and may explain the prevalence of cheating rhizobia in nature. In addition, various stabilizing mechanisms, such as partner fidelity feedback, partner choice, and host sanction, can reinforce the symbiotic relationship by affecting the fitness of symbionts in various ways. This result suggests that the symbiotic relationship is cooperatively stabilized by various mechanisms. In addition, mixed nodule populations are thought to encourage cheater emergence, but our model predicts that, in certain situations, cheaters can disappear from such populations. These findings provide a theoretical basis of the evolutionary dynamics of legume–rhizobia symbioses, which is extendable to other single-host, multiple-colonizer systems.     

EXPLAINING MUTUALISM VARIATION: A NEW EVOLUTIONARY PARADOX?

The paradox of mutualism is typically framed as the persistence of interspecific cooperation, despite the potential advantages of cheating. Thus, mutualism research has tended to focus on stabilizing mechanisms that prevent the invasion of low‐quality partners. These mechanisms alone cannot explain the persistence of variation for partner quality observed in nature, leaving a large gap in our understanding of how mutualisms evolve. Studying partner quality variation is necessary for applying genetically explicit models to predict evolution in natural populations, a necessary step for understanding the origins of mutualisms as well as their ongoing dynamics. An evolutionary genetic approach, which is focused on naturally occurring mutualist variation, can potentially synthesize the currently disconnected fields of mutualism evolution and coevolutionary genetics. We outline explanations for the maintenance of genetic variation for mutualism and suggest approaches necessary to address them.     

Food Transfer in Sichuan Snub-nosed Monkeys (<Emphasis Type="Italic">Rhinopithecus roxellana</Emphasis>)

Food transfer behavior provides a way to distribute food resources among individuals. It is not confined to kin, but also occurs among genetically unrelated individuals. Food transfer among nonkin may result from byproduct mutualism, reciprocal altruism (RA), or tolerated scrounging (TS). Sichuan snub-nosed monkeys (Rhinopithecus roxellana) exhibit a high level of social tolerance, and researchers have observed food transfer behavior in the wild. However, little is known about how tolerant social relations influence food transfer in this species. We recorded food-related interactions and social behavior in a group of captive Sichuan snub-nosed monkeys. Our findings suggest that the monkeys develop partner preference in food transfer behaviors. Moreover, individuals rely primarily on nonharassed approaches to claim food, suggesting that the TS model alone cannot explain their food transfer. Food transfer in this species may be a form of mutualism, in which an individual benefits on an immediate basis by fostering a preferred and tolerant relationship. However, we cannot rule out the possibility of reciprocal altruism. Future studies should record the temporal delay of social exchange to distinguish between mutualism and reciprocal altruism.     

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.     

Cooperation beyond the dyad: on simple models and a complex society

Players in Axelrod and Hamilton''s model of cooperation were not only in a Prisoner''s Dilemma, but by definition, they were also trapped in a dyad. But animals are rarely so restricted and even the option to interact with third parties allows individuals to escape from the Prisoner''s Dilemma into a much more interesting and varied world of cooperation, from the apparently rare ‘parcelling’ to the widespread phenomenon of market effects. Our understanding of by-product mutualism, pseudo-reciprocity and the snowdrift game is also enriched by thinking ‘beyond the dyad’. The concepts of by-product mutualism and pseudo-reciprocity force us to think again about our basic definitions of cooperative behaviour (behaviour by a single individual) and cooperation (the outcome of an interaction between two or more individuals). Reciprocity is surprisingly rare outside of humans, even among large-brained ‘intelligent’ birds and mammals. Are humans unique in having extensive cooperative interactions among non-kin and an integrated cognitive system for mediating reciprocity? Perhaps, but our best chance for finding a similar phenomenon may be in delphinids, which also live in large societies with extensive cooperative interactions among non-relatives. A system of nested male alliances in bottlenose dolphins illustrates the potential and difficulties of finding a complex system of cooperation close to our own.     

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.     

Speciation through competition: a critical review

We examined causes of speciation in asexual populations in both sympatry and parapatry, providing an alternative explanation for the speciation patterns reported by Dieckmann and Doebeli (1999) and Doebeli and Dieckmann (2003). Both in sympatry and parapatry, they find that speciation occurs relatively easily. We reveal that in the sympatric clonal model, the equilibrium distribution is continuous and the disruptive selection driving evolution of discrete clusters is only transient. Hence, if discrete phenotypes are to remain stable in the sympatric sexual model, there should be some source of nontransient disruptive selection that will drive evolution of assortment. We analyze sexually reproducing populations using the Bulmer's infinitesimal model and show that cost-free assortment alone leads to speciation and disruptive selection only arises when the optimal distribution cannot be matched--in this example, because the phenotypic range is limited. In addition, Doebeli and Dieckmann's analyses assumed a high genetic variance and a high mutation rate. Thus, these theoretical models do not support the conclusion that sympatric speciation is a likely outcome of competition for resources. In their parapatric model (Doebeli and Dieckmann 2003), clustering into distinct phenotypes is driven by edge effects, rather than by frequency-dependent competition.     

ASSORTMENT AND THE EVOLUTION OF GENERALIZED RECIPROCITY

Reciprocity is often invoked to explain cooperation. Reciprocity is cognitively demanding, and both direct and indirect reciprocity require that individuals store information about the propensity of their partners to cooperate. By contrast, generalized reciprocity, wherein individuals help on the condition that they received help previously, only relies on whether an individual received help in a previous encounter. Such anonymous information makes generalized reciprocity hard to evolve in a well‐mixed population, as the strategy will lose out to pure defectors. Here we analyze a model for the evolution of generalized reciprocity, incorporating assortment of encounters, to investigate the conditions under which it will evolve. We show that, in a well‐mixed population, generalized reciprocity cannot evolve. However, incorporating assortment of encounters can favor the evolution of generalized reciprocity in which indiscriminate cooperation and defection are both unstable. We show that generalized reciprocity can evolve under both the prisoner's dilemma and the snowdrift game.     

Avoiding the bullies: The resilience of cooperation among unequals

Can egalitarian norms or conventions survive the presence of dominant individuals who are ensured of victory in conflicts? We investigate the interaction of power asymmetry and partner choice in games of conflict over a contested resource. Previous models of cooperation do not include both power inequality and partner choice. Furthermore, models that do include power inequalities assume a static game where a bully’s advantage does not change. They have therefore not attempted to model complex and realistic properties of social interaction. Here, we introduce three models to study the emergence and resilience of cooperation among unequals when interaction is random, when individuals can choose their partners, and where power asymmetries dynamically depend on accumulated payoffs. We find that the ability to avoid bullies with higher competitive ability afforded by partner choice mostly restores cooperative conventions and that the competitive hierarchy never forms. Partner choice counteracts the hyper dominance of bullies who are isolated in the network and eliminates the need for others to coordinate in a coalition. When competitive ability dynamically depends on cumulative payoffs, complex cycles of coupled network-strategy-rank changes emerge. Effective collaborators gain popularity (and thus power), adopt aggressive behavior, get isolated, and ultimately lose power. Neither the network nor behavior converge to a stable equilibrium. Despite the instability of power dynamics, the cooperative convention in the population remains stable overall and long-term inequality is completely eliminated. The interaction between partner choice and dynamic power asymmetry is crucial for these results: without partner choice, bullies cannot be isolated, and without dynamic power asymmetry, bullies do not lose their power even when isolated. We analytically identify a single critical point that marks a phase transition in all three iterations of our models. This critical point is where the first individual breaks from the convention and cycles start to emerge.     

Joint Evolution of Kin Recognition and Cooperation in Spatially Structured Rhizobium Populations

In the face of costs, cooperative interactions maintained over evolutionary time present a central question in biology. What forces maintain this cooperation? Two potential ways to explain this problem are spatially structured environments (kin selection) and kin-recognition (directed benefits). In a two-locus population genetic model, we investigated the relative roles of spatial structure and kin recognition in the maintenance of cooperation among rhizobia within the rhizobia-legume mutualism. In the case where the cooperative and kin recognition loci are independently inherited, spatial structure alone maintains cooperation, while kin recognition decreases the equilibrium frequency of cooperators. In the case of co-inheritance, spatial structure remains a stronger force, but kin recognition can transiently increase the frequency of cooperators. Our results suggest that spatial structure can be a dominant force in maintaining cooperation in rhizobium populations, providing a mechanism for maintaining the mutualistic nodulation trait. Further, our model generates unique and testable predictions that could be evaluated empirically within the legume-rhizobium mutualism.     

On the evolution of non-specific mutualism

It has been argued that mutualisms are non-specific when mutualistic interactions are weak and transient, and become more specific as interactions increase in strength. However, this runs counter to the observation that there exist tightly linked mutualisms of great antiquity that are highly nonspecific. Here we argue that mutualism generates positive, interspecific, frequency-dependent selection, which acts as a cohesive evolutionary force, discouraging evolution of specificity. A simple mathematical model is constructed to analyse the evolution of a community consisting of two guilds of species with mutualistic between-guild interactions, two competing species in each guild and two genetically distinct phenotypes within each species. With some simplifying assumptions, the trajectories in the neighbourhood of the only interior equilibrium point are determined analytically in terms of interactions between individuals. These show that the equilibrium is locally stable (no evolution) when there is little differentiation between phenotypes in mutualistic and interspecific, competitive interactions. On the other hand, when there is strong differentiation between phenotypes in their mutualistic interactions, the equilibrium is unstable and the community starts to evolve towards non-specificity. There are, however, two forces counteracting this tendency which, if sufficiently potent, cause evolution towards specificity. The first is generated by strong differentiation between phenotypes in interspecific competition; the second is caused by specificity which already exists between species in their mutualistic interactions. Thus, the tendency for non-specificity or specificity to evolve depends on the interplay between antagonistic and mutualistic interactions in the community. We illustrate these results with some numerical examples and, finally, survey some data on specificity of mutualisms in the light of the analysis.