Summary
A new numerical method, based on the stochastic differential equations, has been applied to the problem of the fixation of null alleles at duplicated loci. The results reported here were obtained under the assumption that individuals carrying homozygous null genes at both of the duplicated loci are lethal, but all the other genotypes are normal. The mean and median time for null alleles to fix can vary from 2N to 100N or more, depending on the mutation rate and the population size, where N is the population size. Linkage has strong effects on the fate of null genes in the populations, if 2Nc is of the order of 100 or less (c = recombination value). When the linkage is loose the frequencies of null genes in the course of fixation stay in a region where the frequency of the null gene is very low at one of the two duplicated loci. If the two loci are tightly linked, the fate of null genes at duplicated loci is determined by the mutation pressure and the random genetic drift, and selection plays a minor role. In these cases, the fixation time is invariably reduced and the trajectories can cover the entire region where the sum of null allele frequencies does not exceed unity. This makes the prediction that there should be rapid evolution of linked silent genes and pseudo-genes, and that silent DNA might be found close to functional genes.
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Contribution No. 1333 from the National Institute of Genetics, Mishima, Shizouka-ken, 411 Japan.
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Maruyama, T., Takahata, N. Numerical studies of the frequency trajectories in the process of fixation of null genes at duplicated loci. Heredity 46, 49–57 (1981). https://doi.org/10.1038/hdy.1981.5
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DOI: https://doi.org/10.1038/hdy.1981.5
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