Deviations From Hardy’s Formulas Under Partial Isolation

Abstract

The profound mathematical studies by R. Fisher [1] and S. Wright [2] deal with the evolution of gene concentration in a population in which free crossing dominates. The purpose of this paper is to give a method for obtaining similar results for a population consisting of a large number of partial populations weakly connected with each other. Mathematical analysis was applied to the following scheme: a population with a constant number of individuals N consisting of s partial populations of n individuals each (N = sn) with free crossing in each partial population and in which in every generation on the average k “wandering” individuals are isolated from every population; regardless of their origin, wandering individuals randomly join any of the partial populations, where they take part in creating the next generation. This scheme was indicated as a possible one by N.P. Dubinin and D.D. Romashov. A number of other, not less interesting, schemes of restricted crossing do not yet succumb to mathematical treatment.

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Dokl. Akad. Nauk SSSR3 (1935), 129-132. Presented by S.N. Bernshtein.