A NUMERICAL SIMULATION OF THE ONE-LOCUS, MULTIPLE-ALLELE FERTILITY MODEL

Andrew G. Clark ¹ and Marcus W. Feldman ²

¹ Department of Biology, 208 Mueller Laboratory, Pennsylvania State University, University Park, Pennsylvania 16802
² Department of Biological Sciences, Stanford University, Stanford, California 94305

Numerical simulations were performed to determine the equilibrium behavior of the one-locus fertility model in which fitness is considered as a property of a pair of mating diploids. A series of patterns of "fertility matrices" were considered for a single locus with two to six alleles. From these simulations, 19 different statistics were collected that characterize, at equilibrium, the heterozygosity, the mean fitness and the fate of populations begun at the allele-frequency centroid. For more than one-half of the trajectories produced by random fertility matrices, there was a decrease in the mean fitness at some time on the way to equilibrium. The mean number of alleles maintained at equilibrium increased only slightly with matrix dimension. Despite the potential for fertility models to display multiple stable equilibria, random fertility models maintain fewer distinct stable points than do random one-locus viability models. Pleiotropic models were also considered with fertility and viability selection operating sequentially within each generation. Most of the equilibrium statistics (with the exception of mean fertility) for the pleiotropic model were intermediate between the corresponding random viability and fertility models.

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