A new model for measuring breeding genetic distance. II. Polygenic traits

The breeding genetic distance measure of a single locus (Carlson & Welch, 1977) is extended to polygenic traits. For two populations with means -x and approximately x, theta(-x, approximately x) is defined as the size of the largest subpopulation with mean approximately x which can be (artificially) selected from a population with mean -x. The distance is defined as 1--theta(-x, approximately x). It is shown that theta(-x, approximately x) can be calculated from truncation selection and formulas (two loci) and tables (three and four loci) are given. Values for theta(-x, approximately x) based on a normal approximation are seen to be adequate for most cases. The measure is applied to a data example (human skin colour) and to a discussion of the idea of 'genetic inertia'.