A Theory of Limits in Artificial Selection with Many Linked Loci

Abstract

Though linkage has been clearly recognized to be an important factor in artificial selection, particularly by Mather and his colleagues, the absence of any predictive treatment of its effect has remained one of the most important gaps in selection theory. In the last decade, there have been several efforts to attack the problem when many loci are involved using computer simulation (Fraser, 1957; Cockerham and Martin, 1958; Gill, 1965; Qureshi and Kempthorne, 1968, and others). These have rather illustrated its importance than increased our fundamental understanding. The problem is certainly very complex. In this paper we deal initially with a rather simplified situation with a set of loci equally spaced along a chromosome, each with two alleles with the same initial allelic frequencies and effects on the character under selection. We further restrict the problem by assuming additive gene action and initial linkage equilibrium. Nevertheless seven parameters are needed to describe the initial state of the population and the selection process. The necessary parameters and the symbols for them are:

• (i) The effective population size in Wright’s sense of the word (N).

• (ii) The number of loci (n).

• (iii) The difference between the two homozygotes at a locus in the character selected for (a).

• (iv) The initial frequency of the desirable allele at each locus (q).

• (v) A measure of the intensity of selection (i).

• (vi) The phenotypic variance of the character in the initial population (σ²).

• (vii) The map distance between adjacent loci (c).