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 slightly reduces the parameter range allowing for the diversification of self-incompatibility haplotypes (S-haplotypes), but at the same time also increases the number of these haplotypes maintained in the whole metapopulation. This increase is partly due to a higher rate of diversification and replacement of S-haplotypes within and among demes. We also show that the two-genes architecture leads to a higher diversity in structured populations compared with a simpler genetic architecture where new S-haplotypes appear in a single mutation step. Overall, our results suggest that population subdivision can act in two opposite directions: it renders S-haplotypes diversification easier, although it also increases the risk that the self-incompatibility system is lost.