Covariances among Relatives in Populations under Mixed Self-Fertilization and Random Mating

S UMMARY The study deals with a population which is reproducing partly due to random mating and partly due to selfing. The effect of such a combination of mating systems in varying degrees, on the genetic variability in the population and also on the covariances of relatives, is considered. The covariances of relatives are determined in terms of the additive and dominance components of variance, and the amount of selfing. These covariances could be used for estimation of the two components of variance. The results are compared with the corresponding results for a random-mating population. Several research workers have considered the variance, and covariances of relatives, in a diploid population where the mating process is either random mating or some regular system of inbreeding such as selfing or full-sib mating. Fisher (1918) considered a random-mating population, obtained the variance of individuals and developed formulas for the correlation between various types of relatives for autosomal loci for the cases of no epistasis and dual epistasis. These results have been extended to cover more complex situations in random-mating populations. Kempthorne (1955) and Horner (1956) have studied covariances of relatives under certain regular systems of inbreeding. Cockerham (1963) has described several mating designs and their analyses for the estimation of genetic variances based on covariances of relatives. The aim of the present paper is to investigate similar properties when the progeny is produced partly by outcrossing and partly by selfing. Such a situation is of interest because there are crops such as wheat, rice, barley and lima beans, which are largely, but not wholly, selfed, and crops like cotton which are moderately self-fertilized. We shall assume that the population is large and that it reproduces in nonoverlapping generations with constant probabilities e of selfing and y ( = 1- ) of random mating. We shall discuss the nature of the variance and of covariances of relatives under such a mixture of mating systems.