The population genetics of the self-incompatibility polymorphism in Papaver rhoeas .11. The effects of limited pollen and seed dispersal, overlapping generations and variation in plant size on the variance of S-allele frequencies in populations at equilibrium

The effects of limited pollen and seed dispersal, of overlap between generations and of variation in plant size on the steady-state variance of S-allele frequencies have been investigated in a simulated population of size 3840 containing 16 S-alleles whose initial frequencies were exactly equal. Simulations were run with each of the 16 possible combinations of these four factors to investigate their effects on the time for the population to reach steady state and on the average variance of S-allele frequencies in steady state. The time to steady state appeared to be relatively unaffected by any of the factors and was about 50 generations. However, the steady-state variance was markedly affected, with variation in plant size increasing this variance by an average of 228 per cent and overlapping generations decreasing the variance by an average of 30 per cent. The effects of limited pollen and seed dispersal were individually small, although their combined effect was to increase the steady-state variance by an average of 12 per cent. Limited seed and pollen dispersal, when combined with variation in plant size, caused the alleles to cluster. The four factors together caused a large increase in the average steady-state variance. Furthermore, even when a population is in steady state, the variance for a particular generation can be considerably greater than this average value. Consequently the frequencies of the S-alleles of a population in steady state can be very different. It is possible, therefore, that the large variation in S-allele frequencies found in samples taken from Papaver rhoeas populations is consistent with their being in steady state.