Hamilton's rule in image scoring game derived by covariance analysis
06/05/16, 13:30 at Room 3631 (6th floor of building 3 of the Faculty of Sciences)
The evolution of altruistic behaviors has been analyzed mainly by three approaches: kin selection, group selection, and reciprocal altruism. Reciprocal altruism has been discussed actively in the context of the game theory. Image scoring game was proposed to demonstrate indirect reciprocal altruism (Nowak and Sigmund 1998a). Image score represents grades of a partner's cooperations through the past rounds. Without direct interactions, all players are informed about partners' behavior by their image score. Altruistic individuals cooperate indirectly each other using information about image score. In a simple two-score model, the condition for the evolution of altruism became a similar form of Hamilton's rule where relatedness in the original Hamilton's rule of kin selection was replaced by the probability of getting correct information (q>c/b). This Hamilton's rule in the two-score model was obtained using evolutionarily stable strategy (ESS) analysis (Nowak and Sigmund 1998b). They did not demonstrate clearly the evolutionary meaning of the probability of getting correct information in terms of kin and group selection. We applied the kin/group selection approach (i.e. covariance analysis) to the game theory. We derived the Hamilton's rule in the two-score model using covariance analysis instead of ESS analysis. We confirmed that the probability of getting correct information was proportional to the phenotypic relatedness. In addition, we derived Hamilton's rule of group selection in the two-score model. From two Hamilton's rules, we inferred that information about a partner's behavior and group structure can produce flexible pathways for the evolution of altruism. |
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