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.