The ancestral graph and gene genealogy under frequency-dependent selection

Minority-advantage frequency-dependent selection has been proposed as the c ause for the high level of observed polymorphism in some self/nonself-recog nition systems. We present a mathematically rigorous derivation of the ance stral graph for a sample of genes that evolved according to a haploid infin ite-alleles model of minority-advantage frequency-dependent selection. In t he case of sufficiently weak selection, the gene genealogy can be extracted from the ancestral graph. We demonstrate that the gene genealogy under thi s model is identical to that obtained for a diploid model with heterozygote advantage. The case of strong selection is exemplified by a one-locus hapl oid self-incompatibility system; in this context, we investigate the number of alleles that can be maintained in a spatial versus a non-spatial habita t. Finally, we compare gametophytic self-incompatibility to the haploid sel f-incompatibility model. (C) 1999 Academic Press.