ISOLATION BY DISTANCE

Abstract

important S line of attack on the evolutionary problem. While such differences can only rarely represent first steps toward speciation in the sense of the splitting of the species, they are important for the evolution of the species as a whole. They provide a possible basis for intergroup selection of genetic systems, a process that provides a more effective mechanism for adaptive advance of the species as a whole than does the mass selection which is all that can occur under panmixia. TUDY of statistical differences among local populations is RANDOM DIPPERENTIATION UNDER THE ISLAND MODEL Mathematical consideration requires the use of simple models of population structure. The simplest model is that in which the total population is assumed to be divided into subgroups, each breeding a t random within itself, except for a certain proportion of migrants drawn a t random from the whole. Since this situation is likely to be approximated in a group of islands, we shall refer to it as the island model. The gene frequency (4) of a subgroup tends to vary about a certain equilibrium point (q) in a distribution curve (+(q)) determined by the net systematic pressure (measured by Aq, the net rate of change of gene frequency per generation from recurrent mutation, immigration, and selection) in conjunction with the cumulative effects of accidents of sampling (random deviation aq, variance per generation U:,) (WRIGHT 1929, 1931, 1942). Let N be the effective size of the subgroup, m the effective proportion of its population replaced in each generation by migrants, and qt the gene frequency in the total population. The rate of change of gene frequency per generation in a subgroup, taking account only of immigration pressure, is Aq=-m(q-qt). In a random breeding population U&= q(1-q)/2N. Substitution in (I) g;ves the following, choosing C so that J&$(q)dq= I (WRIGHT 1931, 1942).