Adaptive Dynamics of Altruistic Cooperation in a Metapopulation: Evolutionary Emergence of Cooperators and Defectors or Evolutionary Suicide?

We investigate the evolution of public goods cooperation in a metapopulation model with small local populations, where altruistic cooperation can evolve due to assortment and kin selection, and the evolutionary emergence of cooperators and defectors via evolutionary branching is possible. Although evolutionary branching of cooperation has recently been demonstrated in the continuous snowdrift game and in another model of public goods cooperation, the required conditions on the cost and benefit functions are rather restrictive, e.g., altruistic cooperation cannot evolve in a defector population. We also observe selection for too low cooperation, such that the whole metapopulation goes extinct and evolutionary suicide occurs. We observed intuitive effects of various parameters on the numerical value of the monomorphic singular strategy. Their effect on the final coexisting cooperator–defector pair is more complex: changes expected to increase cooperation decrease the strategy value of the cooperator. However, at the same time the population size of the cooperator increases enough such that the average strategy does increase. We also extend the theory of structured metapopulation models by presenting a method to calculate the fitness gradient in a general class of metapopulation models, and try to make a connection with the kin selection approach.     

Emergence and resilience of cooperation in the spatial prisoner's dilemma via a reward mechanism

We study the problem of the emergence of cooperation in the spatial Prisoner's Dilemma. The pioneering work by Nowak and May [1992. Evolutionary games and spatial chaos. Nature 415, 424-426] showed that large initial populations of cooperators can survive and sustain cooperation in a square lattice with imitate-the-best evolutionary dynamics. We revisit this problem in a cost-benefit formulation suitable for a number of biological applications. We show that if a fixed-amount reward is established for cooperators to share, a single cooperator can invade a population of defectors and form structures that are resilient to re-invasion even if the reward mechanism is turned off. We discuss analytically the case of the invasion by a single cooperator and present agent-based simulations for small initial fractions of cooperators. Large cooperation levels, in the sustainability range, are found. In the conclusions we discuss possible applications of this model as well as its connections with other mechanisms proposed to promote the emergence of cooperation.     

Effect of the presence of empty sites on the evolution of cooperation by costly punishment in spatial games

Cooperation and spiteful behavior are still evolutionary puzzles. Costly punishment, for which the game payoff is the same as that of spiteful behavior, is one mechanism for promoting the evolution of cooperation. A spatially structured population facilitates the evolution of either cooperation or spite/punishment if cooperation is linked explicitly or implicitly with spite/punishment; a cooperator cooperates with another cooperator and punishes/spites the other type of player. Different updating rules in the evolutionary game produce different evolutionary outcomes: with one updating rule—the score-dependent viability model, in which a player dies with a probability inversely proportional to the game score and the resulting unoccupied site is colonized by one player chosen randomly—the evolution of spite/punishment is promoted more than with the other updating rule—the score-dependent fertility model, in which, after a player dies randomly, the site is colonized by a player with a higher game score. If the population has empty sites, spiteful players or punishers should have less chance to interact with others and then spite/punish others. Thus the presence of empty sites would affect the evolutionary dynamics of spite/punishment. Here, we investigated whether the presence of empty sites discourages the evolution of spite/punishment in both a lattice-structured population and a completely mixing population where players interact with others randomly, especially when the score-dependent viability model is adopted. In the lattice-structured population adopting this viability model, the presence of empty sites promoted the evolution of cooperation and did not reduce the effect of spite/punishment. In the completely mixing population, the presence of empty sites did not promote evolution of cooperation by punishment. The evolutionary dynamics of the score-dependent viability model with empty sites were close to those of the score-dependent fertility model.     

Genetic Architecture Promotes the Evolution and Maintenance of Cooperation

When cooperation has a direct cost and an indirect benefit, a selfish behavior is more likely to be selected for than an altruistic one. Kin and group selection do provide evolutionary explanations for the stability of cooperation in nature, but we still lack the full understanding of the genomic mechanisms that can prevent cheater invasion. In our study we used Aevol, an agent-based, in silico genomic platform to evolve populations of digital organisms that compete, reproduce, and cooperate by secreting a public good for tens of thousands of generations. We found that cooperating individuals may share a phenotype, defined as the amount of public good produced, but have very different abilities to resist cheater invasion. To understand the underlying genetic differences between cooperator types, we performed bio-inspired genomics analyses of our digital organisms by recording and comparing the locations of metabolic and secretion genes, as well as the relevant promoters and terminators. Association between metabolic and secretion genes (promoter sharing, overlap via frame shift or sense-antisense encoding) was characteristic for populations with robust cooperation and was more likely to evolve when secretion was costly. In mutational analysis experiments, we demonstrated the potential evolutionary consequences of the genetic association by performing a large number of mutations and measuring their phenotypic and fitness effects. The non-cooperating mutants arising from the individuals with genetic association were more likely to have metabolic deleterious mutations that eventually lead to selection eliminating such mutants from the population due to the accompanying fitness decrease. Effectively, cooperation evolved to be protected and robust to mutations through entangled genetic architecture. Our results confirm the importance of second-order selection on evolutionary outcomes, uncover an important genetic mechanism for the evolution and maintenance of cooperation, and suggest promising methods for preventing gene loss in synthetically engineered organisms.     

The public and private benefit of an impure public good determines the sensitivity of bacteria to population collapse in a snowdrift game

When cooperation is critical for survival, cheating can lead to population collapse. One mechanism of cooperation that permits the coexistence of cooperators and cheaters is an impure public good, whose public benefits are shared, but with a private benefit retained by the cooperator. It has yet to be determined how the contributions of the public and private benefit affect population survival. Using simulations and experiments with β-lactamase-expressing bacteria, we found that for a given amount of public and private benefit, the population was most sensitive to collapse when initiated from an intermediate fraction of cooperators due to the near-concurrent collapse of the cooperator and cheater populations. We found that increasing the ratio of public to private benefit increased sensitivity to collapse. A low ratio allowed cooperators to survive on their private benefit after the public benefit could not rescue the cheaters. A high ratio allowed the cheaters to survive to high concentrations of ampicillin due to the high public benefit. However, small increases in ampicillin caused a rapid decline in the entire population as the private benefit was insufficient to allow self-rescue of the cooperators. Our findings have implications in the persistence of populations that rely on cooperation for survival.     

Interaction effects of cell diffusion,cell density and public goods properties on the evolution of cooperation in digital microbes

Microbial cooperation typically consists in the sharing of secreted metabolites (referred to as public goods) within the community. Although public goods generally promote population growth, they are also vulnerable to exploitation by cheating mutants, which no longer contribute, but still benefit from the public goods produced by others. Although previous studies have identified a number of key factors that prevent the spreading of cheaters, little is known about how these factors interact and jointly shape the evolution of microbial cooperation. Here, we address this issue by investigating the interaction effects of cell diffusion, cell density, public good diffusion and durability (factors known to individually influence costs and benefits of public goods production) on selection for cooperation. To be able to quantify these effects across a wide parameter space, we developed an individual‐based simulation platform, consisting of digital cooperator and cheater bacteria inhabiting a finite two‐dimensional continuous toroidal surface. Our simulations, which closely mimic microbial microcolony growth, revealed that: (i) either reduced cell diffusion (which keeps cooperators together) or reduced public good diffusion (which keeps the public goods closer to the producer) is not only essential but also sufficient for cooperation to be promoted; (ii) the sign of selection for or against cooperation can change as a function of cell density and in interaction with diffusion parameters; and (iii) increased public goods durability has opposing effects on the evolution of cooperation depending on the level of cell and public good diffusion. Our work highlights that interactions between key parameters of public goods cooperation give rise to complex fitness landscapes, a finding that calls for multifactorial approaches when studying microbial cooperation in natural systems.     

Evolutionary games and population dynamics: maintenance of cooperation in public goods games

The emergence and abundance of cooperation in nature poses a tenacious and challenging puzzle to evolutionary biology. Cooperative behaviour seems to contradict Darwinian evolution because altruistic individuals increase the fitness of other members of the population at a cost to themselves. Thus, in the absence of supporting mechanisms, cooperation should decrease and vanish, as predicted by classical models for cooperation in evolutionary game theory, such as the Prisoner's Dilemma and public goods games. Traditional approaches to studying the problem of cooperation assume constant population sizes and thus neglect the ecology of the interacting individuals. Here, we incorporate ecological dynamics into evolutionary games and reveal a new mechanism for maintaining cooperation. In public goods games, cooperation can gain a foothold if the population density depends on the average population payoff. Decreasing population densities, due to defection leading to small payoffs, results in smaller interaction group sizes in which cooperation can be favoured. This feedback between ecological dynamics and game dynamics can generate stable coexistence of cooperators and defectors in public goods games. However, this mechanism fails for pairwise Prisoner's Dilemma interactions and the population is driven to extinction. Our model represents natural extension of replicator dynamics to populations of varying densities.     

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.     

西双版纳不同斑块望天树种群的密度、结构和生物量

 根据5个不同斑块的野外调查数据,分析了残存分布在西双版纳的国家一级保护稀有树种望天树（Parashorea chinensis）的种群密度与数量、 年龄结构与生物量动态, 组建了不同生长发育阶段的望天树个体生长与年龄的回归模型、个体生物量模型及种群年龄结构模型, 编制了不同 斑块的望天树种群及整个种群的静态生命表、存活曲线和年龄结构图。结果表明,不同斑块的望天树种群因种群年龄及所受到的干扰方式的不 同,其种群密度和年龄结构差异很大,不同年龄阶段的死亡率也不同。面积最小的斑块缺乏成熟个体,并出现龄级结构缺省的现象。不同斑块 局部种群的生物量随林龄的变化近似于Logistic增长,但各斑块局部种群的最大生物量以及生物量随时间的动态变化有所不同。整个种群的年 龄结构为稳定增长型种群,1～60龄的种群个体的死亡率随林龄的增加而下降,60～150龄的个体死亡率随林龄的增加而上升,180 龄后种群呈 现生理衰退,个体出现死亡高峰。种群的生物量在180 龄前呈Logistic 增长,此后,生物量下降。部分斑块受到严重的人为干扰,已严重威胁 其局部种群的生存。     

Evolution of Cooperation in a Heterogeneous Graph: Fixation Probabilities under Weak Selection

It has been shown that natural selection favors cooperation in a homogenous graph if the benefit-to-cost ratio exceeds the degree of the graph. However, most graphs related to interactions in real populations are heterogeneous, in which some individuals have many more neighbors than others. In this paper, we introduce a new state variable to measure the time evolution of cooperation in a heterogeneous graph. Based on the diffusion approximation, we find that the fixation probability of a single cooperator depends crucially on the number of its neighbors. Under weak selection, a cooperator with more neighbors has a larger probability of fixation in the population. We then investigate the average fixation probability of a randomly chosen cooperator. If a cooperator pays a cost for each of its neighbors (the so called fixed cost per game case), natural selection favors cooperation if the benefit-to-cost ratio is larger than the average degree. In contrast, if a cooperator pays a fixed cost and all its neighbors share the benefit (the fixed cost per individual case), cooperation is favored if the benefit-to-cost ratio is larger than the harmonic mean of the degree distribution. Moreover, increasing the graph heterogeneity will reduce the effect of natural selection.     

细菌群体感应“合作-欺骗”研究进展

细菌利用信号分子进行细胞间的交流即为群体感应.群体感应调控着生物膜形成、公共物质合成、基因水平转移等一系列社会性行为.在群体感应过程中,公共物质分泌后可以被群体中任何个体所使用即合作;亦可以被一些不分泌公共物质的个体所使用形成欺骗.群体感应合作-欺骗既可能在种群中稳定维持,也可能由于欺骗子的快速增长造成种群崩溃.欺骗子致种群崩溃为病原菌控制新策略研发带来了希望,是目前群体感应研究方面的前沿和热点.本文在介绍细菌群体感应合作及欺骗的基础上,分析了群体感应合作-欺骗生态关系形成和发展的影响因素,重点从亲缘选择、谨慎代谢、代谢限制(基因多效型)、群体感应监管等方面探讨了细菌群体感应合作-欺骗的稳定维持机制,并对细菌群体感应合作-欺骗的相关研究进行了问题总结和展望,以期为深入理解群体感应、微生物种群生态提供参考.     

On the dynamic persistence of cooperation: how lower individual fitness induces higher survivability

We study a model in which cooperation and defection coexist in a dynamical steady state. In our model, subpopulations of cooperators and defectors inhabit sites on a lattice. The interactions among the individuals at a site, in the form of a prisoner's dilemma (PD) game, determine their fitnesses. The chosen PD payoff allows cooperators, but not defectors, to maintain a homogeneous population. Individuals mutate between types and migrate to neighboring sites with low probabilities. We consider both density-dependent and density-independent versions of the model. The persistence of cooperation in this model can be explained in terms of the life cycle of a population at a site. This life cycle starts when one cooperator establishes a population. Then defectors invade and eventually take over, resulting finally in the death of the population. During this life cycle, single cooperators migrate to empty neighboring sites to found new cooperator populations. The system can reach a steady state where cooperation prevails if the global "birth" rate of populations is equal to their global "death" rate. The dynamic persistence of cooperation ranges over a large section of the model's parameter space. We compare these dynamics to those from other models for the persistence of altruism and to predator-prey models.     

Feedback between Population and Evolutionary Dynamics Determines the Fate of Social Microbial Populations

The evolutionary spread of cheater strategies can destabilize populations engaging in social cooperative behaviors, thus demonstrating that evolutionary changes can have profound implications for population dynamics. At the same time, the relative fitness of cooperative traits often depends upon population density, thus leading to the potential for bi-directional coupling between population density and the evolution of a cooperative trait. Despite the potential importance of these eco-evolutionary feedback loops in social species, they have not yet been demonstrated experimentally and their ecological implications are poorly understood. Here, we demonstrate the presence of a strong feedback loop between population dynamics and the evolutionary dynamics of a social microbial gene, SUC2, in laboratory yeast populations whose cooperative growth is mediated by the SUC2 gene. We directly visualize eco-evolutionary trajectories of hundreds of populations over 50–100 generations, allowing us to characterize the phase space describing the interplay of evolution and ecology in this system. Small populations collapse despite continual evolution towards increased cooperative allele frequencies; large populations with a sufficient number of cooperators “spiral” to a stable state of coexistence between cooperator and cheater strategies. The presence of cheaters does not significantly affect the equilibrium population density, but it does reduce the resilience of the population as well as its ability to adapt to a rapidly deteriorating environment. Our results demonstrate the potential ecological importance of coupling between evolutionary dynamics and the population dynamics of cooperatively growing organisms, particularly in microbes. Our study suggests that this interaction may need to be considered in order to explain intraspecific variability in cooperative behaviors, and also that this feedback between evolution and ecology can critically affect the demographic fate of those species that rely on cooperation for their survival.     

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.     

Stochastic evolutionary dynamics of direct reciprocity

Evolutionary game theory is the study of frequency-dependent selection. The success of an individual depends on the frequencies of strategies that are used in the population. We propose a new model for studying evolutionary dynamics in games with a continuous strategy space. The population size is finite. All members of the population use the same strategy. A mutant strategy is chosen from some distribution over the strategy space. The fixation probability of the mutant strategy in the resident population is calculated. The new mutant takes over the population with this probability. In this case, the mutant becomes the new resident. Otherwise, the existing resident remains. Then, another mutant is generated. These dynamics lead to a stationary distribution over the entire strategy space. Our new approach generalizes classical adaptive dynamics in three ways: (i) the population size is finite; (ii) mutants can be drawn non-locally and (iii) the dynamics are stochastic. We explore reactive strategies in the repeated Prisoner''s Dilemma. We perform ‘knock-out experiments’ to study how various strategies affect the evolution of cooperation. We find that ‘tit-for-tat’ is a weak catalyst for the emergence of cooperation, while ‘always cooperate’ is a strong catalyst for the emergence of defection. Our analysis leads to a new understanding of the optimal level of forgiveness that is needed for the evolution of cooperation under direct reciprocity.     

Quorum-sensing and cheating in bacterial biofilms

The idea from human societies that self-interest can lead to a breakdown of cooperation at the group level is sometimes termed the public goods dilemma. We tested this idea in the opportunistic bacterial pathogen, Pseudomonas aeruginosa, by examining the influence of putative cheats that do not cooperate via cell-to-cell signalling (quorum-sensing, QS). We found that: (i) QS cheating occurs in biofilm populations owing to exploitation of QS-regulated public goods; (ii) the thickness and density of biofilms was reduced by the presence of non-cooperative cheats; (iii) population growth was reduced by the presence of cheats, and this reduction was greater in biofilms than in planktonic populations; (iv) the susceptibility of biofilms to antibiotics was increased by the presence of cheats; and (v) coercing cooperator cells to increase their level of cooperation decreases the extent to which the presence of cheats reduces population productivity. Our results provide clear support that conflict over public goods reduces population fitness in bacterial biofilms, and that this effect is greater than in planktonic populations. Finally, we discuss the clinical implications that arise from altering the susceptibility to antibiotics.     

Selection on non-social traits limits the invasion of social cheats

While the conditions that favour the maintenance of cooperation have been extensively investigated, the significance of non-social selection pressures on social behaviours has received little attention. In the absence of non-social selection pressures, patches of cooperators are vulnerable to invasion by cheats. However, we show both theoretically, and experimentally with the bacterium Pseudomonas fluorescens, that cheats may be unable to invade patches of cooperators under strong non-social selection (both a novel abiotic environment and to a lesser extent, the presence of a virulent parasite). This is because beneficial mutations are most likely to arise in the numerically dominant cooperator population. Given the ubiquity of novel selection pressures on microbes, these results may help to explain why cooperation is the norm in natural populations of microbes.     

The structure of mutations and the evolution of cooperation

Evolutionary game dynamics in finite populations assumes that all mutations are equally likely, i.e., if there are n strategies a single mutation can result in any strategy with probability 1/n. However, in biological systems it seems natural that not all mutations can arise from a given state. Certain mutations may be far away, or even be unreachable given the current composition of an evolving population. These distances between strategies (or genotypes) define a topology of mutations that so far has been neglected in evolutionary game theory. In this paper we re-evaluate classic results in the evolution of cooperation departing from the assumption of uniform mutations. We examine two cases: the evolution of reciprocal strategies in a repeated prisoner's dilemma, and the evolution of altruistic punishment in a public goods game. In both cases, alternative but reasonable mutation kernels shift known results in the direction of less cooperation. We therefore show that assuming uniform mutations has a substantial impact on the fate of an evolving population. Our results call for a reassessment of the "model-less" approach to mutations in evolutionary dynamics.     

Microbial expansion–collision dynamics promote cooperation and coexistence on surfaces

Microbes colonizing a surface often experience colony growth dynamics characterized by an initial phase of spatial clonal expansion followed by collision between neighboring colonies to form potentially genetically heterogeneous boundaries. For species with life cycles consisting of repeated surface colonization and dispersal, these spatially explicit “expansion‐collision dynamics” generate periodic transitions between two distinct selective regimes, “expansion competition” and “boundary competition,” each one favoring a different growth strategy. We hypothesized that this dynamic could promote stable coexistence of expansion‐ and boundary‐competition specialists by generating time‐varying, negative frequency‐dependent selection that insulates both types from extinction. We tested this experimentally in budding yeast by competing an exoenzyme secreting “cooperator” strain (expansion–competition specialists) against nonsecreting “defectors” (boundary–competition specialists). As predicted, we observed cooperator–defector coexistence or cooperator dominance with expansion–collision dynamics, but only defector dominance otherwise. Also as predicted, the steady‐state frequency of cooperators was determined by colonization density (the average initial cell–cell distance) and cost of cooperation. Lattice‐based spatial simulations give good qualitative agreement with experiments, supporting our hypothesis that expansion–collision dynamics with costly public goods production is sufficient to generate stable cooperator–defector coexistence. This mechanism may be important for maintaining public–goods cooperation and conflict in microbial pioneer species living on surfaces.