Zygotic Selection under Mixed Random Mating and Self-Fertilization: Theory and Problems of Estimation.

ECENT studies on experimental populations of barley and lima beans (JAIN and ALLARD 1960; ALLARD and WORKMAN 1963; HARDING, ALLARD and SMELTZER, in preparation) have provided estimates of the intensity of the selection maintaining genetic variation in these predominantly self-fertilized species. In each experiment, selective values were estimated from census data on genotypic frequencies in successive generations, by means of estimation formulas based upon the model of mixed random mating and selfing with selection described by HAYMAN (1953). It was assumed that all zygotic selection had occurred prior to the determination of the genotypic frequencies and consequently the estimated fitness values were considered to represent the so-called net Darwinian fitnesses defined in terms of the relative number of progeny left by different genotypes. However, PROUT (1965) has pointed out that if selection has not been completed at the time of the census, then the estimated viabilities may not represent the net fitness values. In addition, the selective differences can arise in many different ways (differential viability at one or more zygotic stages, differential fecundity of one or both sexes, gametic selection, etc.), and consequently appropriate estimators must depend both on the mode of selection and the stage at which the genotypic proporitons are determined (seed, seedling, or adult). For example, in the barley populations, a preliminary analysis of fitness components provided evidence for differential seedling emergence at locus b (lemma color), fertility differenccs at locus r (awn texture) and a combination of gametic and zygotic selection at the aleurone color loci bl, and bl, (JAIN 1961, and unpublished data). Analysis of multistage selection may also require the use of loci which can be scored at several different stages of the life cycle. In this paper we shall consider three different selection schemes appropriate for a population in which there is mixed random mating and self-fertilization. Their theoretical properties will be briefly examined and the formulas for the estimation of relative viabilities derived irom each model will be compared by an analysis of the barley and lima bean data and by application to data on multistage selection provided by computer simulation.