A continuous migration model with stable demography

Publisher Website
Google Scholar
Abstract
A probability model of a population undergoing migration, mutation, and mating in a geographic continuum R is constructed, and an integrodifferential equation is derived for the probability of genetic identity. The equation is solved in one case, and asymptotic analysis done in others. Individuals at x, y ε R in the model mate with probability V(x, y) dt in any time interval (t, t + dt). In two dimensions, if V(x,y) = V(x−y) where V(x) ≈ V(x/β)/β 2 approaches a delta function, the equilibrium probability of identity vanishes as β → 0. The asymptotic rate at which this occurs is discussed for mutation rates u ≡ u o > 0 and for β ≈ Cu α, α > 0, and u → 0.

This publication has 14 references indexed in Scilit: