Gene and allelic genealogies at a gametophytic self-incompatibility locus.

The properties of gene and allelic genealogies at a gametophytic self-incompatibility locus in plants have been investigated analytically and checked against extensive numerical simulations. It is found that, as with overdominant loci, there are two genealogical processes with markedly different time scales. First, functionally distinct allelic lines diverge on an extremely long time scale which is inversely related to the mutation rate to new alleles. These alleles show a genealogical structure which is similar, after an appropriate rescaling of time, to that described by the coalescent process for genes at a neutral locus. Second, gene copies sampled within the same functional allelic line show genealogical relationships similar to neutral gene genealogies but on a much shorter time scale, which is on the same order of magnitude as the harmonic mean of the number of gene copies within an allelic line. These results are discussed in relation to data showing trans-specific polymorphisms for alleles at the gametophytic self-incompatibility locus in the Solanaceae. It is shown that population sizes on the order of 4 x 10(5) and a mutation rate per locus per generation as high as 10(-6) could account for estimated allelic divergence times in this family.