Abstract
We consider the classical single locus two alleles selection model with diffusion where the fitnesses of the genotypes are density dependent. Using a theorem of Peter Brown, we show that in a bounded domain with homogeneous Neumann boundary conditions, the allele frequency and population density converge to a constant equilibrium lying on the zero population mean fitness curve. The results agree with the case without diffusion obtained by Selgrade and Namkoong. Frequency and density dependent selection is also considered.
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Research partially supported by NSF grant DMS-8601585
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Lui, R. Convergence to constant equilibrium for a density-dependent selection model with diffusion. J. Math. Biology 26, 583–592 (1988). https://doi.org/10.1007/BF00276061
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DOI: https://doi.org/10.1007/BF00276061