QUANTITATIVE STUDIES ON MATING SYSTEMS. III. METHODS FOR THE ESTIMATION OF MALE GAMETOPHYTIC SELECTIVE VALUES AND DIFFERENTIAL OUTCROSSING RATES.

Evidence was presented in the first paper of this series (Harding and Tucker, 19!64) that outcrossing rates of different genotypes are subject to genetic control. Significantly different outcrossing rates, were observed for genotypes from several populations of Phaseolus lunatus L. In Population 2 mean outcrossing rates for genotypes varied from as low as 3.2% to as high as 24.2%. In addition to the genotypic differences in propensity for cross-fertilization there was considerable environmental variation. In the estimation of outcrossing rates the assumption was made that different genotypes contributed equally to the male gametophytic population, i.e., there was no male gametophytic selection. Thus, male gametophytic selection is defined as the change in gene frequency which occurs between the parental sporophytic population and the population of gametes at fertilization. Any selective advantage indicated by the male gametophytic selective value may result from sporophytic pollen fecundity or pollinator attraction as well as from gametophytic fitness. One of the most common assumptions in population genetics is the equation q = R + 1/2 H where the gene frequency of reproduction is calculated from the frequencies of recessive (R) and heterozygous (H) diploid parents. But many studies indicate that gamete frequencies cannot be accurately estimated from sporophytic frequencies. Differences in pollen production have been reported in Vicia faba (Drayner, 1959) and Oenothera (Hoff, 1962). Pollinator preference has been reported in Medicago sativa where bumble bees were shown to prefer genotypes with higher sugar levels in the nectar (Pedersen and Bohart, 1953). Variation in fragrance (e.g. Jodon, 1944), as well as variation in flower color, can result in pollinator preference. Gametophytic competition has been reported in Zeac mays (Jones, 1920), Primula sinensis (Beale, 1939), Sorghum bicolor (Riccelli-Mattei, 1968), Gossypium hirsutum (Afzal and Khan, 1950) and Cheiranthus cheiri (Bateman, 1956). Vasek (1964) has presented a method which circumvents the assumption of equal gene frequency in the sporophytic and male gametophytic generations. By progeny testing heterozygotes as well as recessives, he estimated simultaneously the outcrossing rate and the gene frequency among male gametes of Clarkia exilis. However, the outcrossing rates of the recessive and the heterozygote were assumed to be equal. The analytical problem is that two progeny tests, yielding one degree of freedom each, provide only two degrees of freedom. Therefore, the choice is between assuming no male gametophytic selection and estimating an outcrossing rate for each genotype, or assuming no differential outcrossing and estimating one outcrossing parameter and the gene frequency among male gametes. The purpose of the present investigation is to develop statistical models and experimental methods which make possible the simultaneous estimation of differential outcrossing rates and male gametophytic selective values. These methods will be applied to data from three populations of Phaseolus lunatus and one population of Zea mays.