Aanlysis of some regular systems of inbreeding

A probabilistic method is used to calculate the asymptotic rate of loss of genetic variability for half-sib and first-cousin mating of an infinite number of individuals. For both systems of inbreeding, all probabilities of nonidentity by descent converge to zero at ultimate rate proportional to t-1/2, where t is the time in generations. The rate of decay is faster for half-sibs than for first cousins, the respective asymptotic allozygosities being 4(pit)-1/2 and 8(pi t)-1/2.