Evolving gene frequencies in a population with three possible alleles at a locus

A number of models involving reaction–diffusion equations have been developed by different authors to describe the changes in 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. In the present paper, 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.