Probability of gene fixation in an expanding finite population.
A mathematical theory was developed, based on diffusion models, that enables us to compute the probability of a rare mutant allele eventually spreading through a population when the population size changes with time. In particular, we elaborated the case in which the mutant allele has a definite selective advantage and the population expands following the logistic law. In this case, the probability of ultimate fixation of a single mutant is given by u = 2s(Z/N), where s is the selective advantage and Z/N is a factor by which the probability of fixation is modified through population expansion. Analytical expression was obtained for Z/N, and the validity of the formula for u was checked by Monte Carlo experiments.
D000483:Alleles; D005787:Gene Frequency; D008954:Models, Biological; D009010:Monte Carlo Method; D009154:Mutation; D011158:Population Growth; D011338:Probability Theory; D012641:Selection, Genetic