Rate of Gene Silencing at Duplicate Loci: a Theoretical Study and Interpretation of Data from Tetraploid Fishes

A large-scale simulation has been conducted on the rate of gene loss at duplicate loci under irreversible mutation. It is found that tight linkage does not provide a strong sheltering effect, as thought by previous authors; indeed, the mean loss time for the case of tight linkage is of the same order of magnitude as that for no linkage, as long as Nu is nt much larger than 1, where N is the effective population size and u the mutation rate. When Nu is 0.01 or less, the two loci behave almost as neutral loci, regardless of linkage, and the mean loss time is about only half the mean extinction time for a neutral allele under irreversible mutation. However, the former becomes two or more times larger than the latter when Nu greater than or equal to 1.----In the simulation, the sojourn times in the frequency intervals (0, 0.01) and 0.99, 1) and the time for the frequency of the null allele to reach 0.99 at one of the two loci have also been recorded. The results show that the population is monomorphic for the normal allele most of the time if Nu less than or equal to 0.01, but polymorphic for the null and the normal alleles most of the time if Nu greater than or equal to 0.1.----The distribution of the frequency of the null allele in an equilibrium tetraploid population has been studied analytically. The present results have been applied to interpret data from some fish groups that are of tetraploid origin, and a model for explaining the slow rate of gene loss in these fishes is proposed.