Balancing selection and the crossing of fitness valleys in structured populations: diversification in the gametophytic self-incompatibility system

The self-incompatibility locus (S-locus) of flowering plants displays a striking allelic diversity. How such a diversity has emerged remains unclear. In this paper, we performed numerical simulations in a finite island population genetics model to investigate how population subdivision affects the diversification process at a S-locus, given that the two-genes architecture typical of S-loci involves the crossing of a fitness valley. We show that population structure increases the number of self-incompatibility haplotypes (S-haplotypes) maintained in the whole metapopulation, but at the same time also slightly reduces the parameter range allowing for their diversification. This increase is partly due to a reinforcement of the diversification and replacement dynamics of S-haplotypes within and among demes. We also show that the two-genes architecture leads to a higher diversity compared with a simpler genetic architecture where new S-haplotypes appear in a single mutation step. We conclude that population structure helps explain the large allelic diversity at the self-incompatibility locus. Overall, our results suggest that population subdivision can act in two opposite directions: it makes easier S-haplotypes diversification but increases the risk that the SI system is lost.