THE MAXIMUM LIKELIHOOD ESTIMATION OF THE NUMBER OF SELF-STERILITY ALLELES IN A POPULATION

Abstract

PREVIOUS estimates of the number of alleles, n, at a self-sterility locus have been based on a method of DOBZHANSKY and WRIGHT (1941 ) . These authors showed that the probability of two things being of the same kind, when taken at random from a population composed of n different kinds, is (1Jn) f nup2, where p is the proportion of any one kind. This was adapted to the case of the incompatibility locus by BATEMAN (1947), taking into account the working of the system, whereby the two alleles of every diploid individual must be different. In practice, estimates have been made from data which gave no evidence that the alleles differed in frequency. This is the situation expected in a population at equilibrium provided that there are no selective effects correlated with particular alleles. The value of p may then be assumed equal to l/n for all alleles, making the variance of p (upz) zero, and the last term of WRIGHT'S formula disappears. The estimate then depends on the proportion of pairs of individuals in the sample that carry identical alleles. In common with BATEMAN (1947) and RAPER, KRONGELB and BAXTER (1958), it is assumed that the alleles going to make up an individual are associ