THE PROBABILITY OF FIXATION IN POPULATIONS OF CHANGING SIZE

The rate of adaptive evolution of a population ultimately depends on t he rate of incorporation of beneficial mutations. Even beneficial muta tions may, however, be lost from a population since mutant individuals may, by chance, fail to reproduce. In this paper, we calculate the pr obability of fixation of beneficial mutations that occur in population s of changing size. We examine a number of demographic models, includi ng a population whose size changes once, a population experiencing exp onential growth or decline, one that is experiencing logistic growth o r decline, and a population that fluctuates in size. The results are b ased on a branching process model but are shown to be approximate solu tions to the diffusion equation describing changes in the probability of fixation over time. Using the diffusion equation, the probability o f fixation of deleterious alleles can also be determined for populatio ns that are changing in size. The results developed in this paper can be used to estimate the fixation flux, defined as the rate at which be neficial alleles fix within a population. The fixation flux measures t he rate of adaptive evolution of a population and, as we shall see, de pends strongly on changes that occur in population size.