群淘汰のおもちゃモデルにおける安定な平衡多型〔英文〕

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A basic model of group selection was formulated by Eshel (1972) and corrected for an "unnatural" assumption by Roughgarden (1979). The model assumes two counteracting selective forces, i.e, group selection and individual selection, in a deme-structured population; and was proposed in relation to the evolution of altruistic behavior. In this paper, I derive further properties of this model, concentrating on the special case of two haploid individuals per deme. Specifically, I prove the existence and stability of polymorphic equilibria in the extreme case of migration rate 1. The existence and stability of other equilibria are studied systematically by defining four regions in the (m, k)-parameter space for fixed s. Here, k is a measure of group selection, s is the selection coefficient against the individually deleterious type, and m is the migration rate. One region appears to correspond to stable polymorphic equilibria. The results are discussed in relation to the critical equality k=2Nms where N is the deme size (Aoki, 1982), and also in relation to polymorphic equilibria in the diffusion approximation when mutation is ignored (Kimura, 1983, 1984; Ogura and Shimakura, submitted).
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