Asymptotic properties of the equilibrium probability of identity in a geographically structured population

Publisher Website
Google Scholar
Abstract
Let I(x, u) be the probability that two genes found a vector distance x apart are the same type in an infinite-allele selectively-neutral migration model with mutation rate u. The creatures involved inhabit an infinite of colonies, are diploid and are held at N per colony. Set in one dimension and in higher dimensions, where σ2 is the covariance matrix of the migration law (which is assumed to have finite fifth moments). Then in one dimension, in two dimensions, and in three dimensions uniformly for Here C 0 is a constant depending on the migration law, K0 (y) is the Bessel function of the second kind of order zero, and are the eigenvalues of σ2. For symmetric nearest-neighbor migrations, in one dimension and log m i in two. For is known in one dimension and C 0 does not appear. In two dimensions, These results extend and make more precise earlier work of Malécot, Weiss and Kimura and Nagylaki.

This publication has 7 references indexed in Scilit: