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Evolving gene frequencies in a population with three possible alleles at a locus. (English) Zbl 1134.92027

Summary: A number of models involving reaction-diffusion equations have been developed by different authors to describe the changes in the frequency of alleles in a population. Each of these models describes the case in which there are only two possible alleles at the locus in question. We are interested in the more realistic possibility of three alternative alleles. A system of reaction-diffusion equations can be developed to describe this situation. After transforming to the traveling wave coordinates, we introduce a nonlinear transformation which allows us to find exact solutions under certain conditions imposed on two of the parameters.

MSC:

92D10 Genetics and epigenetics
35K57 Reaction-diffusion equations
35Q92 PDEs in connection with biology, chemistry and other natural sciences
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