The wave of gene advance under diverse systems of mating.

Mating systems will influence gene spread across the natural distribution of a plant species. Existing theories have not fully explored the role of mating systems on the wave of advance of an advantageous gene. Here, we develop a theory to account for the rate of spread of both advantageous and neutral genes under different mating systems, based on migration-selection processes. We show that a complex relationship exists between selfing rate and the speed of gene spread. The interaction of selfing with gametophytic selection shapes the traveling wave of the advantageous gene. Selfing can impede (or enhance) the spread of an advantageous gene in the presence (or absence) of gametophytic selection. The interaction of selfing with recombination shapes the spread of a neutral gene. Linkage disequilibrium, mainly generated by selfing, enhances the traveling wave of the neutral gene that is tightly linked with the selective gene. Recombination gradually breaks down the genetic hitchhiking effects along the direction of advantageous gene spread, yielding decreasing waves of advance of neutral genes. The stochastic process does not alter the pattern of selfing effects except for increasing the uncertainty of the waves of advance of both advantageous and neutral genes. This theory helps us to explain how mating systems act as a barrier to spread of adaptive and neutral genes, and to interpret species cohesion maintained by a low level of adaptive gene flow.