Abstract
In order to investigate under what conditions an altruistic trait evolves through group selection, the following diffusion model is formulated. Consider a species consisting of an infinite number of competing groups (demes) each having a constant number of reproducing members and in which mating is at random. Then consider a gene locus and assume a pair of alleles A and A', where A' is the "altruistic allele." Let x be the relative frequency of A' within a deme, and let φ = φ(x; t) be the density function of x at time t such that φ(x; t)Δx represents the fraction of demes whose frequency of A' lies in the range (x, x + Δx). Then, we have
where Mδx and Vδx stand for the mean and variance of the change in x per generation (due to mutation, migration, individual selection and random sampling of gametes) within demes, and c is a positive constant (called the coefficient of interdeme competition) and \(\bar x\) is the mean of x over the species, i.e. \(\bar x = \int_0^1 {x\phi } dx\). By studying the above diffusion equation at steady state (∂φ/∂t = 0), a condition is obtained for group selection to prevail over individual selection in the evolution of an altruistic trait.
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© 1986 Springer-Verlag
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Kimura, M. (1986). Diffusion model of population genetics incorporating group selection, with special reference to an altruistic trait. In: Itô, K., Hida, T. (eds) Stochastic Processes and Their Applications. Lecture Notes in Mathematics, vol 1203. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076876
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DOI: https://doi.org/10.1007/BFb0076876
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