Diversification or collapse of self-incompatibility haplotypes as a rescue process

In angiosperm self-incompatibility systems, pollen with an allele matching
the pollen recipient at the self-incompatibility locus is rejected.
Extreme allelic polymorphism is maintained by frequency-dependent
selection favoring rare alleles. However, two challenges result in a
"chicken-egg"problem for the spread of a new allele (a tightly
linked haplotype in this case) under the widespread "collaborative
non-self recognition" mechanism. A novel pollen-function mutation
alone would merely grant compatibility with a nonexistent style-function
allele: a neutral change at best. A novel pistil-function mutation alone
could only be fertilized by pollen with a nonexistent pollen-function
allele: a deleterious change that would eliminate all seed set. However, a
pistil-function mutation complementary to a previously neutral pollen
mutation may spread if it restores self-incompatibility to a
self-compatible intermediate. We show that novel haplotypes can also drive
elimination of existing ones with fewer siring opportunities. We calculate
relative probabilities of increase and collapse in haplotype number given
the initial collection of incompatibility haplotypes and the population
gene conversion rate. Expansion in haplotype number is possible when
population gene conversion rate is large, but large contractions are
likely otherwise. A Markov chain model derived from these expansion and
collapse probabilities generates a stable haplotype number distribution in
the realistic range of 10--40 under plausible parameters. However, smaller
populations might lose many haplotypes beyond those lost by chance during
bottlenecks.