Spatial structure and interspecific cooperation: theory and an empirical test using the mycorrhizal mutualism

Explaining mutualistic cooperation between species remains a major challenge for evolutionary biology. Why cooperate if defection potentially reaps greater benefits? It is commonly assumed that spatial structure (limited dispersal) aligns the interests of mutualistic partners. But does spatial structure consistently promote cooperation? Here, we formally model the role of spatial structure in maintaining mutualism. We show theoretically that spatial structure can actually disfavor cooperation by limiting the suite of potential partners. The effect of spatial structuring depends on the scale (fine or coarse level) at which hosts reward their partners. We then test our predictions by using molecular methods to track the abundance of competing, closely related, cooperative, and less cooperative arbuscular mycorrhizal (AM) fungal symbionts on host roots over multiple generations. We find that when spatial structure is reduced by mixing soil, the relative success of the more cooperative AM fungal species increases. This challenges previous suggestions that high spatial structuring is critical for stabilizing cooperation in the mycorrhizal mutualism. More generally, our results show, both theoretically and empirically, that contrary to expectations, spatial structuring can select against cooperation.     

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.     

Siderophore-mediated cooperation and virulence in Pseudomonas aeruginosa

Why should organisms cooperate with each other? Helping close relatives that are likely to share the same genes (kin selection) is one important explanation that is likely to apply across taxa. The production of metabolically costly extracellular iron-scavenging molecules (siderophores) by microorganisms is a cooperative behaviour because it benefits nearby conspecifics. We review experiments focusing on the production of the primary siderophore (pyoverdin) of the opportunistic bacterial pathogen, Pseudomonas aeruginosa, which test kin selection theories that seek to explain the evolution of cooperation. First, cooperation is indeed favoured when individuals interact with their close relatives and when there is competition between groups of cooperators and noncooperators, such that the benefit of cooperation can be realized. Second, the relative success of cheats and cooperators is a function of their frequencies within populations. Third, elevated mutation rates can confer a selective disadvantage under conditions when cooperation is beneficial, because high mutation rates reduce how closely bacteria are related to each other. Fourth, cooperative pyoverdin production is also shown to be favoured by kin selection in vivo (caterpillars), and results in more virulent infections. Finally, we briefly outline ongoing and future work using this experimental system.     

从合作的进化探讨植物与传粉者的相互作用

合作的进化为研究植物–传粉者相互关系提供了新的视角。植物与传粉者通过"报酬换服务"建立种间合作关系。这一合作关系从建立、维持到解体面临着3个关键问题:(1)在植物和传粉者不了解对方质量信息时,双方如何选择出最适伙伴,进而建立合作关系;(2)合作方如何限制欺骗策略(比如,盗蜜和欺骗性传粉)的扩散以维持合作关系;(3)什么过程可导致传粉合作关系的解体。植物与传粉者间信号博弈或筛选博弈可促进二者合作关系的建立。面对欺骗策略,传粉者和植物分别采用伙伴选择机制和防御机制加以应对。合作者与欺骗者的稳定共存也有助于植物–传粉者合作的维持。从合作转向对抗、转向新的伙伴和合作放弃3个过程可导致植物–传粉者的合作关系的解体。植物与传粉者合作关系的理论预期已经得到了部分实验结果支持,深化了我们对植物与传粉者合作过程中关键机制的理解。在今后的研究中,需要进一步探讨以下问题:(1)传粉者对植物信号诚实性的选择作用和植物对传粉者的筛选作用;(2)植物与传粉者各自应对欺骗策略的可能机制及其相对重要性;(3)合作者与欺骗者稳定共存的机制;(4)植物与传粉者合作系统对全球变化的响应。     

The durability of public goods changes the dynamics and nature of social dilemmas

An implicit assumption underpins basic models of the evolution of cooperation, mutualism and altruism: The benefits (or pay-offs) of cooperation and defection are defined by the current frequency or distribution of cooperators. In social dilemmas involving durable public goods (group resources that can persist in the environment-ubiquitous from microbes to humans) this assumption is violated. Here, we examine the consequences of relaxing this assumption, allowing pay-offs to depend on both current and past numbers of cooperators. We explicitly trace the dynamic of a public good created by cooperators, and define pay-offs in terms of the current public good. By raising the importance of cooperative history in determining the current fate of cooperators, durable public goods cause novel dynamics (e.g., transient increases in cooperation in Prisoner's Dilemmas, oscillations in Snowdrift Games, or shifts in invasion thresholds in Stag-hunt Games), while changes in durability can transform one game into another, by moving invasion thresholds for cooperation or conditions for coexistence with defectors. This enlarged view challenges our understanding of social cheats. For instance, groups of cooperators can do worse than groups of defectors, if they inherit fewer public goods, while a rise in defectors no longer entails a loss of social benefits, at least not in the present moment (as highlighted by concerns over environmental lags). Wherever durable public goods have yet to reach a steady state (for instance due to external perturbations), the history of cooperation will define the ongoing dynamics of cooperators.     

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.     

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.     

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     

Effect of Initial Fraction of Cooperators on Cooperative Behavior in Evolutionary Prisoner's Dilemma Game

We investigate the influence of initial fraction of cooperators on the evolution of cooperation in spatial prisoner''s dilemma games. Compared with the results of heterogeneous networks, we find that there is a relatively low initial fraction of cooperators to guarantee higher equilibrium cooperative level. While this interesting phenomenon is contrary to the commonly shared knowledge that higher initial fraction of cooperators can provide better environment for the evolution of cooperation. To support our outcome, we explore the time courses of cooperation and find that the whole course can be divided into two sequent stages: enduring (END) and expanding (EXP) periods. At the end of END period, thought there is a limited number of cooperator clusters left for the case of low initial setup, these clusters can smoothly expand to hold the whole system in the EXP period. However, for high initial fraction of cooperators, superfluous cooperator clusters hinder their effective expansion, which induces many remaining defectors surrounding the cooperator clusters. Moreover, through intensive analysis, we also demonstrate that when the tendency of three cooperation cluster characteristics (cluster size, cluster number and cluster shape) are consistent within END and EXP periods, the state that maximizes cooperation can be favored.     

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 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.     

Constraints on the origin and maintenance of genetic kin recognition

Kin-recognition mechanisms allow helping behaviors to be directed preferentially toward related individuals, and could be expected to evolve in many cases. However, genetic kin recognition requires a genetic polymorphism on which recognition is based, and kin discriminating behaviors will affect the evolution of such polymorphism. It is unclear whether genetic polymorphisms used in kin recognition should be maintained by extrinsic selection pressures or not, as opposite conclusions have been reached by analytical one-locus models and simulations exploring different population structures. We analyze a two-locus model in a spatially subdivided population following the island model of dispersal between demes of finite size. We find that in the absence of mutation, selection eliminates polymorphism in most cases, except with extreme spatial structure and low recombination. With mutation, the population may reach a stable limit cycle over which both loci are polymorphic; however, the average frequency of conditional helping can be high only under strong structure and low recombination. Finally, we review evidence for extrinsic selection maintaining polymorphism on which kin recognition is based.     

Resource and competitive dynamics shape the benefits of public goods cooperation in a plant pathogen

Cooperative benefits depend on a variety of ecological factors. Many cooperative bacteria increase the population size of their groups by making a public good available. Increased local population size can alleviate the constraints of kin competition on the evolution of cooperation by enhancing the between-group fitness of cooperators. The cooperative pathogenesis of Agrobacterium tumefaciens causes infected plants to exude opines--resources that provide a nearly exclusive source of nutrient for the pathogen. We experimentally demonstrate that opines provide cooperative A. tumefaciens cells a within-group fitness advantage over saprophytic agrobacteria. Our results are congruent with a resource-consumer competition model, which predicts that cooperative, virulent agrobacteria are at a competitive disadvantage when opines are unavailable, but have an advantage when opines are available at sufficient levels. This model also predicts that freeloading agrobacteria that catabolize opines but cannot infect plants competitively displace the cooperative pathogen from all environments. However, we show that these cooperative public goods also promote increased local population size. A model built from the Price Equation shows that this effect on group size can contribute to the persistence of cooperative pathogenesis despite inherent kin competition for the benefits of pathogenesis.     

Kin selection and the Evolution of Mutualisms between Species

Hamilton's theory of kin selection has revolutionized and inspired fifty years of additional theories and experiments on social evolution. Whereas Hamilton's broader intent was to explain the evolutionary stability of cooperation, his focus on shared genetic history appears to have limited the application of his theory to populations within a single species rather than across interacting species. The evolutionary mechanisms for cooperation between species require both spatial and temporal correlations among interacting partners for the benefits to be not only predictable but of sufficient duration to be reliably delivered. As a consequence when the benefits returned by mutualistic partners are redirected to individuals other than the original donor, cooperation usually becomes unstable and parasitism may evolve. However, theoretically, such redirection of mutualistic benefits may actually reinforce, rather than undermine, mutualisms between species when the recipients of these redirected benefits are genetically related to the original donor. Here, I review the few mathematical models that have used Hamilton's theory of kin selection to predict the evolution of mutualisms between species. I go on to examine the applicability of these models to the most well‐studied case of mutualism, pollinating seed predators, where the role of kin selection may have been previously overlooked. Future detailed studies of the direct, and indirect, benefits of mutualism are likely to reveal additional possibilities for applying Hamilton's theory of kin selection to mutualisms between species.     

Temporal Structure in Cooperative Interactions: What Does the Timing of Exploitation Tell Us about Its Cost?

Exploitation in cooperative interactions both within and between species is widespread. Although it is assumed to be costly to be exploited, mechanisms to control exploitation are surprisingly rare, making the persistence of cooperation a fundamental paradox in evolutionary biology and ecology. Focusing on between-species cooperation (mutualism), we hypothesize that the temporal sequence in which exploitation occurs relative to cooperation affects its net costs and argue that this can help explain when and where control mechanisms are observed in nature. Our principal prediction is that when exploitation occurs late relative to cooperation, there should be little selection to limit its effects (analogous to “tolerated theft” in human cooperative groups). Although we focus on cases in which mutualists and exploiters are different individuals (of the same or different species), our inferences can readily be extended to cases in which individuals exhibit mixed cooperative-exploitative strategies. We demonstrate that temporal structure should be considered alongside spatial structure as an important process affecting the evolution of cooperation. We also provide testable predictions to guide future empirical research on interspecific as well as intraspecific cooperation.     

Meta-community selection favours reciprocal cooperation but depresses exploitation between competitors

The evolution of cooperation and mutualism has mainly been explored through individual- and group-level processes. However, community-level processes could also impose selection pressure on species interactions. By using a dome-shaped nonmonotonic interaction (DS interaction) with cooperation at low-density and competition at high-density, we studied how cooperation and exploitation are selected at the meta-community level. Our results showed that population densities of species and communities were both significantly associated with the number of DS interactions and the species interaction modes. The more cooperation a species received via DS interactions, the higher its density was. A community with more DS interactions, especially more reciprocal cooperation, showed a higher total population density. Both reciprocal cooperators and exploiters in a local community were more favoured than unidirectional cooperators within a closed community. When facing competition from a community without cooperators (with only competitors), both reciprocal cooperators and exploiters were favoured in a local community, but only reciprocal cooperators were more favoured when facing competition from another community with cooperators. Our results suggest that selection at the meta-community level could be an alternative mechanism for the evolution of cooperation and the depression of exploitation between competitors.     

Cooperative nest defence in red-winged blackbirds: reciprocal altruism,kinship or by-product mutualism?

Male red-winged blackbirds (Agelaius phoeniceus) often cooperate with their neighbours in defending nests against predators. Some studies have suggested that this is an example of by-product mutualism, whereas others have suggested the possibility of reciprocal altruism. No study has addressed the possibility of kin-selected cooperation in nest defence in this species. Reciprocal altruism, kin selection and by-product mutualism are not mutually exclusive alternatives, but few studies of territorial neighbours have tested for multiple mechanisms simultaneously. We test for these three possibilities in a population of red-winged blackbirds. We used simulated defections to test for reciprocal altruism. We used analysis of microsatellite loci to test for kin selection between adult male neighbours. We also used microsatellite loci to test for by-product mutualism resulting from nest defence of offspring sired on neighbouring territories. We found that male red-winged blackbirds cooperate in nest defence primarily as a form of reciprocal altruism. Experimental males reduced their level of nest defence relative to controls following simulated defection by a neighbour. In contrast to some earlier studies, we found no evidence for by-product mutualism: males did not defend nests where they had sired extra-pair offspring. We also found no evidence for kin selection: males were no more cooperative with more closely related neighbours. Considered alongside the results from other studies, our study suggests that mechanisms stabilizing cooperation in red-winged blackbirds may vary among populations.     

Cooperative boundary populations: the evolution of cooperation on mortality risk gradients

Cooperative or altruistic behavior is known to be vulnerable to destructive exploitation in the absence of spatial segregation and perceptual discrimination on the part of cooperators. In this study, a non-standard, agent-based, spatially explicit model of the evolution of cooperation shows that spatial gradients of increasing individual mortality risk can allow cooperative subpopulations to persist among players randomly matched for one-shot Prisoner's Dilemma. Further, the dynamically stable cooperator population formed on the gradient at the boundary of the survivable non-cooperative range provides ideal conditions for the evolution of discriminating strategies such as tit-for-tat. It is suggested that such gradients may commonly exist at the boundaries of the ranges of existing populations, providing a new basic mechanism for the evolution of cooperation.     

Population dynamics of microbial cross-feeding are determined by co-localization probabilities and cooperation-independent cheater growth

As natural selection acts on individual organisms the evolution of costly cooperation between microorganisms is an intriguing phenomenon. Introduction of spatial structure to privatize exchanged molecules can explain the evolution of cooperation. However, in many natural systems cells can also grow to low cell concentrations in the absence of these exchanged molecules, thus showing “cooperation-independent background growth”. We here serially propagated a synthetic cross-feeding consortium of lactococci in the droplets of a water-in-oil emulsion, essentially mimicking group selection with varying founder population sizes. The results show that when the growth of cheaters completely depends on cooperators, cooperators outcompete cheaters. However, cheaters outcompete cooperators when they can independently grow to only ten percent of the consortium carrying capacity. This result is the consequence of a probabilistic effect, as low founder population sizes in droplets decrease the frequency of cooperator co-localization. Cooperator-enrichment can be recovered by increasing the founder population size in droplets to intermediate values. Together with mathematical modelling our results suggest that co-localization probabilities in a spatially structured environment leave a small window of opportunity for the evolution of cooperation between organisms that do not benefit from their cooperative trait when in isolation or form multispecies aggregates.Subject terms: Community ecology, Microbial ecology, Evolution, Microbial ecology     

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.