Survival of Mutant Genes

Abstract

The stochastic process leading to ultimate survival of mutation descendants has been formulated for random mating populations or organisms in which the pattern of family size distribution is approximated by a negative binomial distribution. The results for some cases of human populations indicate that the chances of ultimate survival for mutants possessing fitness advantages of heterozygotes over homozygotes are approximately two-thirds the chances computed under the assumption of Poisson series for family size distribution. The effect of fluctuations in population size is found to be very great at the early stages of the evolution of individual mutant genes. A mutant which occurs during the expansion phase of population fluctuation has far greater chances of survival than one which arises during the contraction, or even the stable phase. In other words, expansion of population size would serve to reduce the danger of random extinction of mutants. The reverse is true for mutations that occur during contraction phases. When descendants of a mutation survive through the early stages of the evolution, the fitness of the mutant heterozygote relative to the normal homozygotes becomes the dominant factor in determining the fate of the mutation. A possible transition from the strongly stochastic stage to the mainly deterministic stage of the evolution of the mutation is discussed in an attempt to connect the present work with the evolutionary dynamics of large populations.