Gene duplication in tetraploid fish: model for gene silencing at unlinked duplicated loci

Several groups of fishes, including salmonids and catastomids, appear to have originated through genome duplication events. However, these two groups retain approximately 50% of the loci examined as functioning duplicates, despite the passage of 50 million years or more of mutation and selection. Although other effects are not excluded, this apparently slow rate of duplicate silencing can be explained in terms of the effects of selection against defective double homozygotes to unlinked duplicates. We have derived a computer simulation of genetic drift that affords direct evaluation of the effects of population size (N), mutation rate (micron), initial allele frequencies, back mutation, fitness, and time on the probability of fixation for null alleles at unlinked duplicate loci. The results show that this probability is approximately linearly related to population size for N greater than or equal to 10(3). Specifically, for naive populations, the time for 50% probability of gene silencing is approximately equal to 15N + micron-3/4 generations. The retention of 50% of the loci as functional duplicates may therefore result from the large effective size of salmonid and catastomid populations. The results also show that, under most conditions for populations of 2000--3000 or larger, unlinked duplicate loci will be sustained in the functional state longer than tandem (linked) duplicates and hence are available for evolution of new functions for a longer time.