Self-incompatibility systems in angiosperms are exemplars of extreme allelic polymorphism maintained by long-term balancing selection. Pollen that shares an allele with the pollen recipient at the self-incompatibility locus is rejected, and this rejection favors rare alleles as well as preventing self-fertilization. Advances in molecular genetics reveal that an ancient, deeply conserved, and well-studied incompatibility system functions through multiple tightly linked genes encoding separate pollen-expressed F-box proteins and pistil-expressed ribonucleases. We show that certain recombinant haplotypes at the incompatibility locus can drive collapse in the number of incompatibility types. We use a modified evolutionary rescue model to calculate the relative probabilities of increase and collapse in number of incompatibility types given the initial collection of incompatibility haplotypes and the population rate of gene conversion. We find that expansion in haplotype number is possible when population size or the rate of gene conversion is large, but large contractions are likely otherwise. By iterating a Markov chain model derived from these expansion and collapse probabilities, we find that a stable haplotype number distribution in the realistic range of 10--40 is possible under plausible parameters. However, small or moderate-sized populations should be susceptible to substantial additional loss of haplotypes beyond those lost by chance during bottlenecks. The same processes that can generate many incompatibility haplotypes in large populations may therefore be crushing haplotype diversity in smaller populations.
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