A new model for measuring breeding genetic distance

A model is proposed for measuring the genetic 'distance' between two populations having gene frequencies p and p. The measure of distance is based on a hypothetical selection process as follows: From population P a subpopulation P can be selected having gene frequency p. Let Po be the largest subpopulation yielding gene frequency p, then the relative size of Po to p--denoted by thetao (p,p)--is a measure of the 'closeness' of populations having gene frequencies p and p, and 1-thetao (p,p) whould be a reasonable measure of genetic distance. We show that the calculation of thetao (p,p) is a special case of the linear programming problem and derive algebraic expressions for thetao (p,p) in the two-allele case. We discuse some of the implications of the use of this measure of distance and compare it to others which have been proposed. We use linear programming methods to calculate genetic distance for three alleles.