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Asymptotic properties for Kimura's diffusion model with altruistic allele



Asymptotic properties for Kimura's diffusion model with altruistic allele



Stochastic methods in biology Proceedings of a workshop held in Nagoya, Japan, July 8-12, 1985: 53-70



The diffusion model was studied for a random-mating, diploid species, using an intergroup selection model recently proposed by Kimura. The stationary distributions for the relative gene frequencies of the altruistic allele are given, and their stability examined. According to the regions of the parameters, the model can be divided into 7 cases. In 3 of them, there are only 'trivial' stationary distributions, i.e. the relative gene frequency is equal to zero with probability 1, or equal to 1.

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