The relationship between separation time and genetic distance based on angular transformations of gene frequencies

Expressions are constructed for the theoretical expectation and the variance of the statistic chord2 used in connection with the genetic distances introduced by Cavalli-Sforza and Edwards. The gene frequency probability distribution is taken from Kimura's solution of the diffusion equation for pure random drift. The expression for the expectation is used for discussing whether distances are independent of original gene frequencies, and whether they are proportional to separation times. A modified method for estimating such separation times is proposed, and an example is given with cattle breeds. The accuracy of procedures based on genetic distances is evaluated using the variance of chord2.