Polymorphism and loss of duplicate gene expression: a theoretical study with application of tetraploid fish.

We studied the fixation of null alleles at independent duplicate loci, assuming that wild-type active alleles mutate irreversibly to nonfunctional null alleles and that the population is finite and panmictic. Solving the two-dimensional Kolmogorov backward equation numerically, we obtained the rate at which one of the active genes is lost and the amount of heterozygosity at specified times. Previously harmful genes, including recessive lethals, can be fixed at one of the duplicate loci, which would not happen with a single locus. Examination of data from several fish families showed that the rate of fixation of null alleles is too slow and the amount of heterozygosity too small to be compatible with complete recessivity at all loci. Our conclusion differs in this regard from that of Bailey et al. [Bailey, G.S., Poulter, R. T. M. & Stockwell, P. A. (1978) Proc. Natl. Acad. Sci. USA 75, 5575--5579]. They also reported that the time taken for 50% of the loci to be fixed for null alleles is approximately 15N + v-3/4, in which N and v are the effective population sizgote is lethal. We found that the fixation rate depends not only on N, but also on Nv.