No Arabic abstract
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.
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.
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.
The n-person Prisoners Dilemma is a widely used model for populations where individuals interact in groups. The evolutionary stability of populations has been analysed in the literature for the case where mutations in the population may be considered as isolated events. For this case, and assuming simple trigger strategies and many iterations per game, we analyse the rate of convergence to the evolutionarily stable populations. We find that for some values of the payoff parameters of the Prisoners Dilemma this rate is so low that the assumption, that mutations in the population are infrequent on that timescale, is unreasonable. Furthermore, the problem is compounded as the group size is increased. In order to address this issue, we derive a deterministic approximation of the evolutionary dynamics with explicit, stochastic mutation processes, valid when the population size is large. We then analyse how the evolutionary dynamics depends on the following factors: mutation rate, group size, the value of the payoff parameters, and the structure of the initial population. In order to carry out the simulations for groups of more than just a few individuals, we derive an efficient way of calculating the fitness values. We find that when the mutation rate per individual and generation is very low, the dynamics is characterised by populations which are evolutionarily stable. As the mutation rate is increased, other fixed points with a higher degree of cooperation become stable. For some values of the payoff parameters, the system is characterised by (apparently) stable limit cycles dominated by cooperative behaviour. The parameter regions corresponding to high degree of cooperation grow in size with the mutation rate, and in number with the group size.
Cooperation is prevalent in nature, not only in the context of social interactions within the animal kingdom, but also on the cellular level. In cancer for example, tumour cells can cooperate by producing growth factors. The evolution of cooperation has traditionally been studied for well-mixed populations under the framework of evolutionary game theory, and more recently for structured populations using evolutionary graph theory. The population structures arising due to cellular arrangement in tissues however are dynamic and thus cannot be accurately represented by either of these frameworks. In this work we compare the conditions for cooperative success in an epithelium modelled using evolutionary graph theory, to those in a mechanical model of an epithelium =- the Voronoi tessellation model. Crucially, in this latter model cells are able to move, and birth and death are not spatially coupled. We calculate fixation probabilities in the Voronoi tessellation model through simulation and an approximate analytic technique and show that this leads to stronger promotion of cooperation in comparison with the evolutionary graph theory model.
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.