Win-stay-lose-learn promotes cooperation in the spatial prisoner's dilemma game

Holding on to one's strategy is natural and common if the later warrants success and satisfaction. This goes against widespread simulation practices of evolutionary games, where players frequently consider changing their strategy even though their payoffs may be marginally different than those of the other players. Inspired by this observation, we introduce an aspiration-based win-stay-lose-learn strategy updating rule into the spatial prisoner's dilemma game. The rule is simple and intuitive, foreseeing strategy changes only by dissatisfied players, who then attempt to adopt the strategy of one of their nearest neighbors, while the strategies of satisfied players are not subject to change. We find that the proposed win-stay-lose-learn rule promotes the evolution of cooperation, and it does so very robustly and independently of the initial conditions. In fact, we show that even a minute initial fraction of cooperators may be sufficient to eventually secure a highly cooperative final state. In addition to extensive simulation results that support our conclusions, we also present results obtained by means of the pair approximation of the studied game. Our findings continue the success story of related win-stay strategy updating rules, and by doing so reveal new ways of resolving the prisoner's dilemma.     

Heterogeneous aspirations promote cooperation in the prisoner's dilemma game

To be the fittest is central to proliferation in evolutionary games. Individuals thus adopt the strategies of better performing players in the hope of successful reproduction. In structured populations the array of those that are eligible to act as strategy sources is bounded to the immediate neighbors of each individual. But which one of these strategy sources should potentially be copied? Previous research dealt with this question either by selecting the fittest or by selecting one player uniformly at random. Here we introduce a parameter that interpolates between these two extreme options. Setting equal to zero returns the random selection of the opponent, while positive favor the fitter players. In addition, we divide the population into two groups. Players from group select their opponents as dictated by the parameter , while players from group do so randomly irrespective of . We denote the fraction of players contained in groups and by and , respectively. The two parameters and allow us to analyze in detail how aspirations in the context of the prisoner''s dilemma game influence the evolution of cooperation. We find that for sufficiently positive values of there exist a robust intermediate for which cooperation thrives best. The robustness of this observation is tested against different levels of uncertainty in the strategy adoption process and for different interaction networks. We also provide complete phase diagrams depicting the dependence of the impact of and for different values of , and contrast the validity of our conclusions by means of an alternative model where individual aspiration levels are subject to evolution as well. Our study indicates that heterogeneity in aspirations may be key for the sustainability of cooperation in structured populations.     

Reputation-based partner choice is an effective alternative to indirect reciprocity in solving social dilemmas

When group interests clash with individual ones, maintaining cooperation poses a problem. However, cooperation can be facilitated by introducing reputational incentives. Through indirect reciprocity, people who cooperate in a social dilemma are more likely to receive cooperative acts from others. Another mechanism that enhances group cooperation is reputation-based partner choice, or competitive altruism. According to this framework, cooperators benefit via increased access to cooperative partners. Our study compared the effectiveness of indirect reciprocity and competitive altruism in re-establishing cooperation after the typical decline found during repeated public goods games. Twenty groups of four participants first played a series of public goods games, which confirmed the expected decline. Subsequently, public goods games were alternated with either indirect reciprocity games (in which participants had an opportunity to give to another individual from whom they would never receive a direct return) or competitive altruism games (in which they could choose partners for directly reciprocal interactions). We found that public goods game contributions increased when interspersed with competitive altruism games; they were also higher than in public goods games interspersed with indirect reciprocity games. Investing in reputation by increasing contributions to public goods was a profitable strategy in that it increased returns in subsequent competitive altruism and indirect reciprocity games. There was also some evidence that these returns were greater under competitive altruism than indirect reciprocity. Our findings indicate that strategic reputation building through competitive altruism provides an effective alternative to indirect reciprocity as a means for restoring cooperation in social dilemmas.     

Evolving learning rules and emergence of cooperation in spatial prisoner's dilemma

In the evolutionary Prisoner's dilemma (PD) game, agents play with each other and update their strategies in every generation according to some microscopic dynamical rule. In its spatial version, agents do not play with every other but, instead, interact only with their neighbours, thus mimicking the existing of a social or contact network that defines who interacts with whom. In this work, we explore evolutionary, spatial PD systems consisting of two types of agents, each with a certain update (reproduction, learning) rule. We investigate two different scenarios: in the first case, update rules remain fixed for the entire evolution of the system; in the second case, agents update both strategy and update rule in every generation. We show that in a well-mixed population the evolutionary outcome is always full defection. We subsequently focus on two-strategy competition with nearest-neighbour interactions on the contact network and synchronised update of strategies. Our results show that, for an important range of the parameters of the game, the final state of the system is largely different from that arising from the usual setup of a single, fixed dynamical rule. Furthermore, the results are also very different if update rules are fixed or evolve with the strategies. In these respect, we have studied representative update rules, finding that some of them may become extinct while others prevail. We describe the new and rich variety of final outcomes that arise from this co-evolutionary dynamics. We include examples of other neighbourhoods and asynchronous updating that confirm the robustness of our conclusions. Our results pave the way to an evolutionary rationale for modelling social interactions through game theory with a preferred set of update rules.     

Evolution of interactions and cooperation in the spatial prisoner's dilemma game

We study the evolution of cooperation in the spatial prisoner's dilemma game where players are allowed to establish new interactions with others. By employing a simple coevolutionary rule entailing only two crucial parameters, we find that different selection criteria for the new interaction partners as well as their number vitally affect the outcome of the game. The resolution of the social dilemma is most probable if the selection favors more successful players and if their maximally attainable number is restricted. While the preferential selection of the best players promotes cooperation irrespective of game parametrization, the optimal number of new interactions depends somewhat on the temptation to defect. Our findings reveal that the "making of new friends" may be an important activity for the successful evolution of cooperation, but also that partners must be selected carefully and their number limited.     

Eco-evolutionary feedback and the invasion of cooperation in prisoner's dilemma games

Unveiling the origin and forms of cooperation in nature poses profound challenges in evolutionary ecology. The prisoner's dilemma game is an important metaphor for studying the evolution of cooperation. We here classified potential mechanisms for cooperation evolution into schemes of frequency- and density-dependent selection, and focused on the density-dependent selection in the ecological prisoner's dilemma games. We found that, although assortative encounter is still the necessary condition in ecological games for cooperation evolution, a harsh environment, indicated by a high mortality, can foster the invasion of cooperation. The Hamilton rule provides a fundamental condition for the evolution of cooperation by ensuring an enhanced relatedness between players in low-density populations. Incorporating ecological dynamics into evolutionary games opens up a much wider window for the evolution of cooperation, and exhibits a variety of complex behaviors of dynamics, such as limit and heteroclinic cycles. An alternative evolutionary, or rather succession, sequence was proposed that cooperation first appears in harsh environments, followed by the invasion of defection, which leads to a common catastrophe. The rise of cooperation (and altruism), thus, could be much easier in the density-dependent ecological games than in the classic frequency-dependent evolutionary games.     

Synergy and discounting of cooperation in social dilemmas

The emergence and maintenance of cooperation by natural selection is an enduring conundrum in evolutionary biology, which has been studied using a variety of game theoretical models inspired by different biological situations. The most widely studied games are the Prisoner's Dilemma, the Snowdrift game and by-product mutualism for pairwise interactions, as well as Public Goods games in larger groups of interacting individuals. Here, we present a general framework for cooperation in social dilemmas in which all the traditional scenarios can be recovered as special cases. In social dilemmas, cooperators provide a benefit to the group at some cost, while defectors exploit the group by reaping the benefits without bearing the costs of cooperation. Using the concepts of discounting and synergy for describing how benefits accumulate when more than one cooperator is present in a group of interacting individuals, we recover the four basic scenarios of evolutionary dynamics given by (i) dominating defection, (ii) coexistence of defectors and cooperators, (iii) dominating cooperation and (iv) bi-stability, in which cooperators and defectors cannot invade each other. Generically, for groups of three or more interacting individuals further, more complex, dynamics can occur. Our framework provides the first unifying approach to model cooperation in different kinds of social dilemmas.     

Moving away from nasty encounters enhances cooperation in ecological prisoner's dilemma game

We study the role of migration in the evolution of cooperation. Individuals spatially located on a square lattice play the prisoner's dilemma game. Dissatisfied players, who have been exploited by defectors, tend to terminate interaction with selfish partners by leaving the current habitats, and explore unknown physical niches available surrounding them. The time scale ratio of game interaction to natural selection governs how many game rounds occur before individuals experience strategy updating. Under local migration and strong selection, simulation results demonstrate that cooperation can be stabilized for a wide range of model parameters, and the slower the natural selection, the more favorable for the emergence of cooperation. Besides, how the selection intensity affects cooperators' evolutionary fate is also investigated. We find that increasing it weakens cooperators' viability at different speeds for different time scale ratios. However, cooperation is greatly improved provided that individuals are offered with enough chance to agglomerate, while cooperation can always establish under weak selection but vanishes under very strong selection whenever individuals have less odds to migrate. Whenever the migration range restriction is removed, the parameter area responsible for the emergence of cooperation is, albeit somewhat compressed, still remarkable, validating the effectiveness of collectively migrating in promoting cooperation.     

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.     

The evolution of function-valued traits for conditional cooperation

In this paper we study the evolution of function-valued traits for cooperation in environments that display varying degrees of population viscosity. Traits measure an individual's intrinsic propensity to cooperate in a standard bilateral Prisoner's dilemma and can be increasing, decreasing or constant functions of the probability to interact with individuals of ones own genotype. We first analyse adaptation to homogenous environments (with constant degree of viscosity). Comparing environments characterized by different degrees of viscosity, we find that the relation between viscosity and the equilibrium type distribution is not monotone. In fact, it is possible that in fluid populations (no viscosity) there is more cooperation in equilibrium than in populations with intermediate degrees of viscosity. In a second step we analyse heterogenous environments (with varying degrees of viscosity). We find that under very weak assumptions on the distribution of the viscosity parameter strictly increasing functions are always selected and under some parameter constellations they are uniquely so.     

Beyond the prisoner's dilemma: Toward models to discriminate among mechanisms of cooperation in nature

The iterated prisoner's dilemma game, or IPD, has now established itself as the orthodox paradigm for theoretical investigations of the evolution of cooperation; but its scope is restricted to reciprocity, which is only one of three categories of cooperation among unrelated individuals. Even within that category, a cooperative encounter has in general three phases, and the IPD has nothing to say about two of them. To distinguish among mechanisms of cooperation in nature, future theoretical work on the evolution of cooperation must distance itself from economics and develop games as a refinement of ethology's comparative approach.     

Subtle social cues, explicit incentives and cooperation in social dilemmas

Subtle contextual social cues and the explicit incentive structure of social dilemmas are two important, but fundamentally different classes of determinants of cooperative behavior. The former provides subjective social information regarding the likelihood of attaining mutual cooperation by shaping one's expectations of the cooperative behavior of the interacting party. The latter provides objective, ecological information about the strategic opportunities offered by the situation. In prior research, both classes have generally been studied in isolation, hampering insight into how social judgments and ecological opportunities interact in shaping cooperation. To fill in this gap we set up a repeated mixed-motive game in which we manipulate subtle social cues and the incentive structure of the game simultaneously. We develop the hypothesis that social information is less important in shaping mutual cooperation of two team members when the incentive structure is such that it contains natural synergies. In contrast, when the incentive structure offers no synergy, “rational contracting” is hampered and social cues are essential for mutual cooperation to develop. The evidence we present in this paper is consistent with this hypothesis.     

Self-deception as a mediator of cooperation and defection in varying social contexts described in the iterated prisoner's dilemma

Deception and self-deception may be two related psychological capacities serving to enhance an individual's inclusive fitness. Self-deception has been defined as any psychological act in which one thought or belief is held at the expense of another. This study was designed to test the notion that we may deceive ourselves about our own intentions or the intentions of others in order to facilitate cooperation, if the cooperative behavior has the potential to improve fitness. We may also deceive ourselves in situations where we may need to compete with others, if not competing might represent a loss of fitness. The Self-Deceptio Questionnaire was administered to 80 women and 70 men to determine their levels of self-deception. A series of vignettes, conforming to the Prisoner's Dilemma game format, were administered in questionnaire material to measure participant's predispositions to cooperate or defect in three different contexts (family, mating, and neutral). Men predicted they would be less cooperative than women over all conditions, and participants anticipated cooperating more with kin than with non-kin. Moreover, participants who were high self-deceivers chose more cooperative responses in both family and mating contexts than those with low self-deception scores. Finally, the three-way interaction among sex, context, and level of self-deception suggested that the role of selfdeception in cooperation may vary according to the sex of the individual and the context.     

Social eavesdropping and the evolution of conditional cooperation and cheating strategies

The response of bystanders to information available in their social environment can have a potent influence on the evolution of cooperation and signalling systems. In the presence of bystanders, individuals might be able to increase their payoff by exaggerating signals beyond their means (cheating) or investing to help others despite considerable costs. In doing so, animals can accrue immediate benefits by manipulating (or helping) individuals with whom they are currently interacting and delayed benefits by convincing bystanders that they are more fit or cooperative than perhaps is warranted. In this paper, I provide some illustrative examples of how bystanders could apply added positive selection pressure on both cooperative behaviour and dishonest signalling during courtship or conflict. I also discuss how the presence of bystanders might select for greater flexibility in behavioural strategies (e.g. conditional or condition dependence), which could maintain dishonesty at evolutionarily stable frequencies under some ecological conditions. By recognizing bystanders as a significant selection pressure, we might gain a more realistic approximation of what drives signalling and/or interaction dynamics in social animals.     

The face of another: anonymity and facial symmetry influence cooperation in social dilemmas

In the present paper, we study how the morphological features related to developmental physiology of other participants influence the decision to cooperate in a social dilemma. To that end, we let a large sample of men play a prisoner's dilemma game, both anonymously and against a series of counterparts whose photographs were shown. We focus on three characteristics already linked to cooperative behavior and with described effects on the adult facial shape: facial fluctuating asymmetry, a frequently employed but debated proxy for developmental instability; the degree of facial dimorphism, related to levels of testosterone during puberty; and the second to fourth digit ratio, related to relative prenatal testosterone exposure. We find significantly higher cooperation rates in anonymous interactions than in the non-anonymous round. We also find that individuals are more likely to cooperate with more asymmetric counterparts, and that more asymmetric participants were less likely to believe that their counterpart would cooperate. Variables related to exposure to testosterone during development do not display any effect. We conclude by discussing how out-of-the-game rewards can explain our results.     

Human cooperation in social dilemmas: comparing the Snowdrift game with the Prisoner's Dilemma

Explaining the evolution of cooperation among non-relatives is one of the major challenges for evolutionary biology. In this study, we experimentally examined human cooperation in the iterated Snowdrift game (ISD), which has received little attention so far, and compared it with human cooperation in the iterated Prisoner's Dilemma (IPD), which has become the paradigm for the evolution of cooperation. We show that iteration in the ISD leads to consistently higher levels of cooperation than in the IPD. We further demonstrate that the most successful strategies known for the IPD (generous Tit-for-Tat and Pavlov) were also successfully used in the ISD. Interestingly, we found that female players cooperated significantly more often than male players in the IPD but not in the ISD. Moreover, female players in the IPD applied Tit-for-Tat-like or Pavlovian strategies significantly more often than male players, thereby achieving significantly higher pay-offs than male players did. These data demonstrate that the willingness to cooperate does not only depend on the type of the social dilemma, but also on the class of individuals involved. Altogether, our study shows that the ISD can potentially explain high levels of cooperation among non-relatives in humans. In addition, the ISD seems to reflect the social dilemma more realistically than the IPD because individuals obtain immediate direct benefits from the cooperative acts they perform and costs of cooperation are shared between cooperators.     

Protein-protein interaction site prediction based on conditional random fields

MOTIVATION: We are motivated by the fast-growing number of protein structures in the Protein Data Bank with necessary information for prediction of protein-protein interaction sites to develop methods for identification of residues participating in protein-protein interactions. We would like to compare conditional random fields (CRFs)-based method with conventional classification-based methods that omit the relation between two labels of neighboring residues to show the advantages of CRFs-based method in predicting protein-protein interaction sites. RESULTS: The prediction of protein-protein interaction sites is solved as a sequential labeling problem by applying CRFs with features including protein sequence profile and residue accessible surface area. The CRFs-based method can achieve a comparable performance with state-of-the-art methods, when 1276 nonredundant hetero-complex protein chains are used as training and test set. Experimental result shows that CRFs-based method is a powerful and robust protein-protein interaction site prediction method and can be used to guide biologists to make specific experiments on proteins. AVAILABILITY: http://www.insun.hit.edu.cn/~mhli/site_CRFs/index.html. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.     

The interaction of components controlling net phytoplankton photosynthesis in a well-mixed lake (Lough Neagh, Northern Ireland)

The homogeneous distribution of the phytoplankton in a shallow (mean depth 8·6 m) unstratified lake, L. Neagh, Northern Ireland, facilitated the study of the interaction of components controlling gross photosynthesis per unit area. These included the photosynthetic capacity, the phytoplankton content of the euphotic zone, and a logarithmic function describing the effective radiation input. These factors were analysed for two sites, the open lake and Kinnego Bay, which respectively had standing crops of up to 90 and 300 mg chlorophyll a m^?3 and maximum daily rates of gross integral photosynthesis of 11·7 and 15·6 g O₂ m^?2 day^?1. Values are reduced by the high contribution to light attenuation by non-algal sources, which increases at low standing crops particularly in winter, when values of integral photosynthesis decrease to 0·5 g O₂ m^?2 day^?1. This relative change is the result of self-shading behaviour of the phytoplankton altering the crop content of the euphotic zone at different population densities. Changes in the irradiance function, incorporating day length, are largely responsible for the changes in daily rates of integral gross photosynthesis; as daily irradiance is also a determinant of water temperature, it exerts further influence through the photosynthetic capacity which was strongly correlated with temperature. Much of the gain in gross photosynthesis resulting from higher photosynthetic capacity may not be reflected in a higher net column photosynthesis, because of the greater proportional rise in respiration with temperature. The balance in the water column between respiration losses and photosynthetic input may frequently alter since the ratio of illuminated to dark zones is between 1/4 to 1/5 in the open lake, and small shifts in any of the controlling features may result in conditions unfavourable for growth. This is analysed especially for the increase of diatoms in spring, when small modifications of the underwater light field can delay growth.     

Separation of hexokinase activity using different hydrophobic interaction supports

Hydrophobic interaction chromatography (HIC) has been used extensively for the separation of proteins and peptides by elution using a descending salt gradient, with and without the use of detergents or denaturing agents. In this paper we compare different hydrophobic interaction chromatographic media for the separation of multiple forms of hexokinase from rabbit reticulocytes. Among the different hydrophobic chromatographic media tested (Toyopearl Phenyl 650S, Ether 650S and Butyl 650S) Toyopearl Phenyl 650S offered the best separation of multiple forms of hexokinase, probably due to its intermediate hydrophobicity. In order to establish the optimal experimental conditions, we evaluated the effects of different salts, and the results obtained demonstrated that among the antichaotropic salts, ammonium sulphate is the most suitable for the separation of hexokinase sub-types. The sample loading capacity of the three Toyopearl supports was investigated and the recovery of enzymatic activity obtained ranged from 60% to 90%, depending on the different salts and hydrophobic media used. The chromatographic profiles of hexokinase activity from various mammalian and fungal tissues also demonstrate that Toyopearl Phenyl 650S can be successfully employed for the separation of multiple forms of enzymes from different biological sources.