Total number of individuals affected by deleterious mutant genes in a finite population

Abstract

The means and standard errors of the total numbers of heterozygotes and homozygotes affected by deleterious mutant genes and the extinction time are studied by using diffusion methods. For an overdominant mutation, the effects of an increase in population size on these quantitites are much more profound than that of an increase in initial number of mutant genes whereas for a partially recessive mutation the situation is reversed. For a completely recessive mutation, the expected total number of mutant homozygotes is independent of the population size and degree of inbreeding, though the expected total number of heterozygotes and the average extinction time are dependent on these factors, particularly the population size. The effect of inbreeding on these quantitites is very similar to that of reduction in effective population size and is usally small at the prevailing level of inbreeding, except for mutations with large degrees of overdominance in large populations. The standard errors of these quantities are large. The expected total number of sickle-cell mutant homozygotes in the U.S. population has been computed.