Neutral behavior of shared polymorphism

Several cases have been described in the literature where genetic polymorphism appears to be shared between a pair of species. Here we examine the distribution of times to random loss of shared polymorphism in the context of the neutral Wright-Fisher model. Order statistics were used to obtain the distribution of times to loss of a shared polymorphism based on Kimura's solution to the diffusion approximation of the Wright-Fisher model. In a single species, the expected absorption time for a neutral allele having an initial allele frequency of 1/2 is 2.77 N generations. If two species initially share a polymorphism, that shared polymorphism is lost as soon as either of two species undergoes fixation. The loss of a shared polymorphism thus occurs sooner than loss of polymorphism in a single species and has an expected time of 1.7 N generations. Molecular sequences of genes with shared polymorphism may be characterized by the count of the number of sites that segregate in both species for the same nucleotides (or amino acids). The distribution of the expected numbers of these shared polymorphic sites also is obtained. Shared polymorphism appears to be more likely at genetic loci that have an unusually large number of segregating alleles, and the neutral coalescent proves to be very useful in determining the probability of shared allelic lineages expected by chance. These results are related to examples of shared polymorphism in the literature.