Evolution at a multiallelic locus under migration and uniform selection.
The semilinear parabolic system that describes the evolution of the gene frequencies in the diffusion approximation for migration and selection at a multiallelic locus is investigated. The population occupies a finite habitat of arbitrary dimensionality and shape. The drift and diffusion coefficients may depend on position, but the selection coefficients do not. It is established that if p is a uniform equilibrium point under pure selection, then p is a migration-selection equilibrium, and that generically the introduction of migration does not change the stability of p. It is also proved that if p is a uniform, globally asymptotically stable, internal equilibrium point under pure selection, then the gene frequencies converge to p when both migration and selection are present. Thus, in this case, after a sufficiently long time, there is no genetic indication of the spatial distribution of the population.
Nagylaki
Thomas
T
Department of Ecology and Evolution, The University of Chicago, 1101 East 57th Street, Chicago, IL 60637, USA. choman@uchicago.edu
Lou
Yuan
Y
D000483:Alleles; D004641:Emigration and Immigration; D019143:Evolution, Molecular; D005787:Gene Frequency; D008957:Models, Genetic; D012641:Selection, Genetic; D006801:Humans