The study of multiallelic genetic systems by matrix methods

Abstract

A matrix notation is developed to facilitate study of natural selection in large populations. The processes of mating (taking into account differences between genotypes in fertility in both sexes), segregation, and differential viabilities are each expressed in matrix notation. Assortative mating and non-random segregation can also be described by the method. The separate processes can then be combined to give simple equations relating the genic and genotypic frequencies in one generation to those in the previous generation. This will facilitate computer treatment of natural selection processes. The method can also be used to study equilibria and the conditions of their stability by examining the latents roots of the matrix. Several special cases of selection at an autosomal locus are examined. The method can be extended to sex-linked loci and two special cases are discussed.