Evolution of a semilinear parabolic system for migration and selection without dominance

摘要: The semilinear parabolic system that describes the evolution of gene frequencies in diffusion approximation for migration and selection at a multiallelic locus without dominance is investigated. population occupies finite habitat arbitrary dimensionality shape (i.e., bounded, open domain R d ). coefficients depend on position; drift may position. primary focus this paper dependence λ, strength relative to migration. It proved if sufficiently strong λ small) operator divergence form, then allele with greatest spatially averaged coefficient ultimately fixed. stability each vertex an equilibrium exactly one present) completely specified. edge two alleles fully described when either (i) weak large) or (ii) has just appeared as increases. existence unexpected, complex phenomena established: even there are only three homogeneous isotropic (corresponding Laplacian), increases, arbitrarily many changes equilibria corresponding appearance internal can occur conditions protection loss both nonmonotonically λ. Neither these diallelic case.