Establishment process of a magic trait allele subject to both divergent selection and assortative mating

Multi-dimensional diffusion process of allele frequencies in population genetics

One of the ultimate goals of population genetics is to theoretically describe the behavior of allele frequency. Diffusion theory has been commonly used for this purpose mainly in one-locus one-population models, although it is not easy to handle diffusion theory in models with multiple loci or with multiple populations. This review introduces several successful cases, where multi-dimensional diffusion equations contributed to addressing evolutionary questions, thereby demonstrating its strong potential in population genetics.