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Register a new userHow Levy flights triggered by presence of defectors affect evolution of cooperation in spatial games
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Cooperation among individuals has been key to sustaining societies. However, natural selection favors defection over cooperation. Cooperation can be favored when the mobility of individuals allows cooperators to form a cluster (or group). Mobility patterns of animals sometimes follow a Levy flight. A Levy flight is a kind of random walk but it is composed of many small movements with a few big movements. Here, we developed an agent-based model in a square lattice where agents perform Levy flights depending on the fraction of neighboring defectors. For comparison, we also tested normal-type movements implemented by a uniform distribution. We focus on how the sensitivity to defectors when performing Levy flights promotes the evolution of cooperation. Results of evolutionary simulations showed that Levy flights outperformed normal movements for cooperation in all sensitivities. In Levy flights, cooperation was most promoted when the sensitivity to defectors was moderate. Finally, as the population density became larger, higher sensitivity was more beneficial for cooperation to evolve.
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Cooperative behaviour constitutes a key aspect of both human society and non-human animal systems, but explaining how cooperation evolves represents a major scientific challenge. It is now well established that social network structure plays a central role for the viability of cooperation. However, not much is known about the importance of the positions of cooperators in the networks for the evolution of cooperation. Here, we investigate how cooperation is affected by correlations between cooperativeness and individual social connectedness. Using simulation models, we find that the effect of correlation between cooperativeness and connectedness (degree) depends on the social network structure, with positive effect in standard scale-free networks and no effect in standard Poisson networks. Furthermore, when degree assortativity is increased such that individuals cluster with others of similar social connectedness, we find that bridge areas between social clusters can act as barriers to the spread of defection, leading to strong enhancement of cooperation in particular in Poisson networks. But this effect is sensitive to the presence of Trojan horses (defectors placed within cooperator clusters). The study provides new knowledge about the conditions under which cooperation may evolve and persist, and the results are also relevant to consider in regard to human cooperation experiments.
Cooperators forgo their interest to benefit others. Thus cooperation should not be favored by natural selection. It challenges the evolutionists, since cooperation is widespread. As one of the resolutions, information spreading has been revealed to play a key role in the emergence of cooperation. Individuals, however, are typically assumed to be passive in the information spreading. Here we assume that individuals are active to spread the information via self-recommendation. Individuals with higher intensities of self-recommendation are likely to have more neighbors. We find that i) eloquent cooperators are necessary to promote cooperation; ii) individuals need to be open to the self-recommendation to enhance cooperation level; iii) the cost-to-benefit ratio should be smaller than one minus the ratio between self-recommendation intensities of defector and cooperator, which qualitatively measures the viscosity of the population. Our results highlight the importance of active information spreading on cooperation.
In the evolutionary Prisoners 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 neighbors, 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-neighbor interactions on the contact network and synchronized 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 neighborhoods 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.
Data from a long time evolution experiment with Escherichia Coli and from a large study on copy number variations in subjects with european ancestry are analyzed in order to argue that mutations can be described as Levy flights in the mutation space. These Levy flights have at least two components: random single-base substitutions and large DNA rearrangements. From the data, we get estimations for the time rates of both events and the size distribution function of large rearrangements.
Spatial structure is known to have an impact on the evolution of cooperation, and so it has been intensively studied during recent years. Previous work has shown the relevance of some features, such as the synchronicity of the updating, the clustering of the network or the influence of the update rule. This has been done, however, for concrete settings with particular games, networks and update rules, with the consequence that some contradictions have arisen and a general understanding of these topics is missing in the broader context of the space of 2x2 games. To address this issue, we have performed a systematic and exhaustive simulation in the different degrees of freedom of the problem. In some cases, we generalize previous knowledge to the broader context of our study and explain the apparent contradictions. In other cases, however, our conclusions refute what seems to be established opinions in the field, as for example the robustness of the effect of spatial structure against changes in the update rule, or offer new insights into the subject, e.g. the relation between the intensity of selection and the asymmetry between the effects on games with mixed equilibria.
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