Mating system and the critical migration rate for swamping selection

Crow et al. (1990) and Barton (1992) have examined the critical migration rate for swamping selection in the nuclear system. Here, I use the same methodology to examine the critical migration rate in the cytonuclear system for hermaphrodite plants with a mixed mating system. Two selection schemes for a nuclear gene (heterozygote disadvantage and directional selection) and the directional selection scheme for organelle genes are considered. Results show that under random mating, the previous results are applicable to plant species by appropriate re-parameterization of the migration rate for nuclear and paternal organelle genes. A simple complementary relationship exists between seed and pollen flow in contributing to the critical migration rate. Under the mixed mating system, the critical migration rate of seeds and pollen for nuclear and paternal organelle genes can be changed due to the effects of selection and the cytonuclear linkage disequilibrium generated by migration and inbreeding. A negative but not complementary relationship exists between seed and pollen flow in contributing to the critical migration rate, varying with the mating system. Partial selfing can also adjust the critical seed flow for the maternal organelle gene, with a small critical migration rate for species of a high selfing rate. Both concordance and discordance among cytonuclear genes can occur under certain conditions during the process of swamping selection. This theory predicts the presence of various contributions of seed versus pollen flow to genetic swamping for plants with diverse mating systems.