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.     

Selfish altruism,fierce cooperation and the predator*

This paper suggests a new way to think about a famous question: what explains cooperation in nature and in particular in humans? I argue that, for an evolutionary biologist as well as a quantitative social scientist, the triangle of two ‘teammates’ in the presence of a predator (passing and shooting in two-on-one situations) is one of the fundamental conceptual building-blocks for understanding these phenomena because in such a situation the fact that life is packaged in many distinct enclosures (and not in one big monolithic blob) can unfold its comparative advantage. I show how, in the presence of a predator, cooperative equilibria emerge among entirely selfish teammates if we infinitesimally bias the lead player in the selfish direction or assign a computational burden on the predator due to the presence of a teammate. I argue that ‘predators’ are common in the biological jungle but also in everyday human settings. Intuitively, this paper builds on the simple idea – a familiar one to a biologist observing the natural world but perhaps less so to social scientists – that everybody has enemies.     

Individual variation and the resolution of conflict over parental care in penduline tits

Eurasian penduline tits (Remiz pendulinus) have an unusually diverse breeding system consisting of frequent male and female polygamy, and uniparental care by the male or the female. Intriguingly, 30 to 40 per cent of all nests are deserted by both parents. To understand the evolution of this diverse breeding system and frequent clutch desertion, we use 6 years of field data to derive fitness expectations for males and females depending on whether or not they care for their offspring. The resulting payoff matrix corresponds to an asymmetric Snowdrift Game with two alternative evolutionarily stable strategies (ESSs): female-only and male-only care. This, however, does not explain the polymorphism in care strategies and frequent biparental desertion, because theory predicts that one of the two ESSs should have spread to fixation. Using a bootstrapping approach, we demonstrate that taking account of individual variation in payoffs explains the patterns of care better than a model based on the average population payoff matrix. In particular, a model incorporating differences in male attractiveness closely predicts the observed frequencies of male and female desertion. Our work highlights the need for a new generation of individual-based evolutionary game-theoretic models.     

Negotiation may lead selfish individuals to cooperate: the example of the collective vigilance game

Game-theoretical models have been highly influential in behavioural ecology. However, these models generally assume that animals choose their action before observing the behaviour of their opponents while, in many natural situations, individuals in fact continuously react to the actions of others. A negotiation process then takes place and this may fundamentally influence the individual attitudes and the tendency to cooperate. Here, I use the classical model system of vigilance behaviour to demonstrate the consequences of such behavioural negotiation among selfish individuals, by predicting patterns of vigilance in a pair of animals foraging under threat of predation. I show that the game played by the animals and the resulting vigilance strategies take radically different forms, according to the way predation risk is shared in the pair. In particular, if predators choose their target at random, the prey respond by displaying moderate vigilance and taking turns scanning. By contrast, if the individual that takes flight later in an attack endures a higher risk of being targeted, vigilance increases and there is always at least one sentinel in the pair. Finally, when lagging behind its companion in fleeing from an attacker becomes extremely risky, vigilance decreases again and the animals scan simultaneously.     

Social structure of primate interaction networks facilitates the emergence of cooperation

Animal cooperation has puzzled biologists for a long time as its existence seems to contravene the basic notion of evolutionary biology that natural selection favours ‘selfish’ genes that promote only their own well-being. Evolutionary game theory has shown that cooperators can prosper in populations of selfish individuals if they occur in clusters, interacting more frequently with each other than with the selfish. Here we show that social networks of primates possess the necessary social structure to promote the emergence of cooperation. By simulating evolutionary dynamics of cooperative behaviour on interaction networks of 70 primate groups, we found that for most groups network reciprocity augmented the fixation probability for cooperation. The variation in the strength of this effect can be partly explained by the groups’ community modularity—a network measure for the groups’ heterogeneity. Thus, given selective update and partner choice mechanisms, network reciprocity has the potential to explain socially learned forms of cooperation in primate societies.     

On evolution under asymmetric competition

The evolutionary consequences of asymmetric competition between species are poorly understood in comparison with symmetric competition. A model for evolution of body size under asymmetric competition within and between species is described. The model links processes operating at the scale of the individual to that of macroscopic evolution through a stochastic mutation–selection process. Phase portraits of evolution in a phenotype space characteristically show character convergence and parallel character shifts, with character divergence being relatively uncommon. The asymptotic states of evolution depend very much on the properties of asymmetric competition. Given relatively weak asymmetries between species, a single equilibrium point exists; this is a local attractor, and its position is determined by the intra- and interspecific asymmetries. When the asymmetries are made stronger, several fixed points may come about, creating further equilibrium points which are local attractors. It is also possible for periodic attractors to occur; such attractors comprise Red Queen dynamics with phenotype values that continue to change without ever settling down to constant values. From certain initial conditions, evolution leading to extinction of one of the species is also a likely outcome.     

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 evolution of fitness in life-history theory

Theory concerning the evolution of life history (the schedule of reproduction and survival) focuses on describing the life history which maximises fitness. Although there is an intuitive link between life history and fitness, there are in fact several measures of the 'black box' concept of fitness. There has been a debate in the bio-mathematical literature on the predictive difference between the two most commonly used measures; intrinsic rate of increase r and net reproductive ratio R0. Although both measures aim to describe fitness, models using one of the measures may predict the opposite of similar models using the other measure, which is clearly undesirable. Here, I review the evolution of these fitness measures over the last four decades, the predictive differences between these measures and the resulting shift of the fitness concept. I focus in particular on some recent developments, which have solved the dilemma of predictive differences between these fitness measures by explicitly acknowledging the game-theoretical nature of life-history evolution.     

ESS emergence pattern of male butterflies in stochastic environments

Summary The evolutionarily stable (or ESS) emergence schedule for males of univoltine butterflies is analysed in an environment in which the female emergence schedule fluctuates stochastically between years. The ESS emergence curve, computed using the mutant invadability criterion, is shown to be the one that maximizes mean logarithmic lifetime mating success in the population in which it dominates. If males have accurate information about the female emergence schedule within each year, their emergence curve would evolve to the one predicted by a deterministic game model. The male emergence curve would then shift between years, closely following year to year changes in the female emergence pattern. If, instead, males have uncertainty about the female emergence schedule, the ESS male emergence curve becomes broader than the one predicted by the deterministic game model and will not track the between-year fluctuation of female emergence well. In a special case, we show how the between-year variation of mean emergence date, the variance of emergence date, the sexual difference in mean emergence dates (protandry) and the between-year correlation of mean emergence dates of both sexes should change with the degree of accuracy of information available to males.     

Rewards and the evolution of cooperation in public good games

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

Asynchronous pupation of univoltine insects as evolutionarily stable phenology

Evolutionarily stable seasonal timing of larval feeding stages is studied theoretically for univoltine insects. In the evolutionarily stable (or ESS) population, each individual maximizes its own lifetime reproductive success by choosing the hatching and pupation dates, given the resource availability curve with a peak in the middle of a year, a higher daily mortality in the feeding stages, and the growth rate decreasing with the larval biomass in the population. If growth rate is proportional to the body size, the population at the ESS is composed of a mixture of phenotypes differing in hatching and pupation, but pupation interval over which some popation occur every day is much longer than hatching interval. If growth rate increases with the body size at a speed slower than linearly, large sized larvae should pupate earlier than small ones.     

The evolution of dispersal in a two-patch system: some consequences of differences between migrants and residents

We investigate how age-structure and differences in certain demographic traits between residents and immigrants of a single species act to determine the evolutionarily stable dispersal strategy in a two-patch environment that is heterogeneous in space but constant in time. These two factors have been neglected in previous models of the evolution of dispersal, which generally consider organisms with very simple life-cycles and assume that, whatever their origin, individuals in a given habitat have the same bio-demographic characteristics. However, there is increasing empirical evidence that dispersing individuals have different demographic properties from phylopatric ones. We develop a matrix model in which recruitment depends on local population densities. We assume that dispersal entails a proportional cost to immigrant fecundity, which can be compensated by differences in survival rates between immigrants and residents. The evolutionarily stable strategies (ESS) for dispersal are identified using a combination of analytical expressions and numerical simulations. Our results show that philopatry is selected (1) when dispersal rates do not vary in space, (2) when the metapopulation is a source-sink system and (3) when dispersal rates vary in space (asymmetric dispersal) and immigrants do not compensate for their reduced fecundity. We observe that non-zero asymmetric dispersal rates may be evolutionarily stable when (1) immigrants and residents are demographically alike and (2) immigrants compensate totally for their reduced fecundity through an increase in adult survival. Under these conditions, we find that the ESS occurs when the fitnesses at equilibrium in the two habitats, measured in our model by the realized reproductive rates, are each equal to unity. A comparison with previous studies suggests a unifying rule for the evolution of dispersal: the dispersal rates which permit the spatial homogenization of fitnesses are ESSs. This condition provides new insight into the evolutionary stability of source-sink systems. It also supports the hypothesis that immigrants have adapted demographic strategies, rather than the hypothesis that dispersal is costly and immigrants are at a disavantage compared with residents.     

Is it better to give information, receive it, or be ignorant in a two-player game?

The standard approach in a biological two-player game is toassume both players choose their actions independently of oneanother, having no information about their opponent's action(simultaneous game). However, this approach is not realisticin some circumstances. In many cases, one player chooses hisaction first and then the second player chooses her action withinformation about his action (Stackelberg game). We comparethese two games, which can be mathematically analyzed into twotypes, depending on the direction of the best response function(BRF) at the evolutionarily stable strategy in the simultaneousgame (ESS_sim). We subcategorize each type of game into two cases,depending on the change in payoff to one player, when both playersare at the ESS_sim, and the other player increases his action.Our results show that in cases where the BRF is decreasing atthe ESS_sim, the first player in the Stackelberg game receivesthe highest payoff, followed by both players in the simultaneousgame, followed by the second player in the Stackelberg game.In these cases, it is best to be the first Stackelberg player.In cases where the BRF is increasing at the ESS_sim, both Stackelbergplayers receive a higher payoff than players in a simultaneousgame. In these cases, it is better for both players to playa Stackelberg game rather than a simultaneous game. However,in some cases the first Stackelberg player receives a higherpayoff than the second Stackelberg player, and in some casesthe opposite is true.     

Evolution of kleptoparasitism as a war of attrition

Previous models of kleptoparasitism (resource stealing) assume that contests over resource items are of fixed duration. Here we suggest that such contests will often be well represented as a war of attrition, with the winner being the individual who is prepared to contest for the longer time. Given that time spent in contests cannot be used to search for other resource items, we provide an analytical expression for the evolutionarily stable distribution of contest times. This can be used to investigate the circumstances under which we would expect kleptoparasitism to evolve. In particular, we focus on situations where searching for conspecifics to kleptoparasitize can only be achieved at a cost of reduced resource discovery by other means; under such circumstances we show that kleptoparasitism is not evolutionarily stable.     

A new route to the evolution of cooperation

The Prisoner's Dilemma (PD) constitutes a widely used metaphor to investigate problems related to the evolution of cooperation. Whenever evolution takes place in well-mixed populations engaged in single rounds of the PD, cooperators cannot resist invasion by defectors, a feature, which is somewhat alleviated whenever populations are spatially distributed. In both cases the populations are characterized by a homogeneous pattern of connectivity, in which every individual is equivalent, sharing the same number of neighbours. Recently, compelling evidence has been accumulated on the strong heterogeneous nature of the network of contacts between individuals in populations. Here we describe the networks of contacts in terms of graphs and show that heterogeneity provides a new mechanism for cooperation to survive. Specifically, we show that cooperators are capable of exploring the heterogeneity of the population structure to become evolutionary competitive. As a result, cooperation becomes the dominating trait in scale-free networks of contacts in which the few highly connected individuals are directly inter-connected, in this way contributing to self-sustain cooperation.     

Evolutionarily stable kleptoparasitism: consequences of different prey types

We present two elaborations of the model of Broom and Ruxtonthat found evolutionarily stable kleptoparasitic strategiesfor foragers. These elaborations relax the assumption that thedistribution of times required to handle discovered food itemsis exponential. These changes increase the complexity of themodel but represent a significant improvement in biologicalrealism. In one elaboration, handling takes a fixed interval,t_h, at the end of which the whole value of the food item isobtained. We liken this to peeling then consuming a small orange.The other elaboration also assumes that handling takes a fixedinterval, t_h, but this time the reward from the food item isextracted continuously throughout the handling period. We likenthis to eating an apple. Both models predict that increasingfood density, the ease with which food items can be discovered,or the length of aggressive contests all act to make kleptoparasitismless common. The difference between the evolutionarily stablestrategy solutions of the apple and orange models provides aclear prediction of our theory. When prey items require handlingbefore yielding a lump sum at the end, then kleptoparasiticattacks will be focused on prey items near the end of theirhandling period. However, if prey items yield reward continuouslyduring handling, then attacks should be biased toward newlydiscovered food items. Another key difference between the modelpredictions is that kleptoparasitism increases with foragerdensity in the apple model, but decreases in the orange model.     

On several conjectures from evolution of dispersal

We address several conjectures raised in Cantrell et al. [Evolution of dispersal and ideal free distribution, Math. Biosci. Eng. 7 (2010), pp. 17–36 [9 Cantrell, R. S., Cosner, C. and Lou, Y. 2010. Evolution of dispersal and ideal free distribution. Math. Biosci. Eng., 7: 17–36. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]]] concerning the dynamics of a diffusion–advection–competition model for two competing species. A conditional dispersal strategy, which results in the ideal free distribution of a single population at equilibrium, was found in Cantrell et al. [9 Cantrell, R. S., Cosner, C. and Lou, Y. 2010. Evolution of dispersal and ideal free distribution. Math. Biosci. Eng., 7: 17–36. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]]. It was shown in [9 Cantrell, R. S., Cosner, C. and Lou, Y. 2010. Evolution of dispersal and ideal free distribution. Math. Biosci. Eng., 7: 17–36. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]] that this special dispersal strategy is a local evolutionarily stable strategy (ESS) when the random diffusion rates of the two species are equal, and here we show that it is a global ESS for arbitrary random diffusion rates. The conditions in [9 Cantrell, R. S., Cosner, C. and Lou, Y. 2010. Evolution of dispersal and ideal free distribution. Math. Biosci. Eng., 7: 17–36. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]] for the coexistence of two species are substantially improved. Finally, we show that this special dispersal strategy is not globally convergent stable for certain resource functions, in contrast with the result from [9 Cantrell, R. S., Cosner, C. and Lou, Y. 2010. Evolution of dispersal and ideal free distribution. Math. Biosci. Eng., 7: 17–36. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]], which roughly says that this dispersal strategy is globally convergent stable for any monotone resource function.     

Evolution of airborne infectious diseases according to changes in characteristics of the host population

The authors predicted evolutionary changes in airborne infectious diseases according to changes in the characteristics of the host population. The predictions were based upon a mathematical model of infectious diseases and the validity of the predictions was verified against the history of man and pathogens. The feature of this model is that it involves a density of pathogens in the environment as an additional variable which can be regarded as more suitable to airborne infectious diseases. In spite of this modification, this study reached a similar conclusion to the threshold density theory: that is, susceptible host density in the absence of the pathogen must be larger than that in the presence of the pathogen, for the pathogen to be persistent. Moreover the authors concluded that one type of pathogen cannot be replaced by another type of pathogen as long as the susceptible host density of the former type is the mininum one. The predictions were considered to be valid for a wide range of infectous diseases. Making use of these principles, the authors predicted that the variety of infectious diseases should increase as host density increases and that pathogens should evolve to be less virulent as the host life-span increases. The finalidea discussed is whether or nor the history of man and pathogen can be verified by the predictions.