Time to fixation in changing environments

Although a large number of experimental and theoretical studies have been carried out in a constant environment, as natural environments vary in time, it is important to ask if and how these results are affected by a changing environment. Here, we study the properties of the conditional fixation time of a mutant in a finite, randomly mating diploid population which is evolving in a periodically changing environment. In a static environment, as the conditional mean fixation time of a co-dominant beneficial mutant is equal to that of a deleterious mutant with the same magnitude of selection coefficient, similar patterns for beneficial and deleterious sweeps may result. We find that this symmetry breaks even when the environment is changing slowly. Furthermore, for intermediate dominance, the conditional mean fixation time of a beneficial mutant in a slowly changing environment depends weakly on the dominance coefficient and is close to the corresponding results in the static environment; however, the fixation time for a deleterious mutant under moderate selection with a slowly varying selection coefficient differs substantially from that in the constant environment when the mutant is recessive. Our results thus suggest that the variability patterns and levels for beneficial sweeps are mildly affected by temporally varying environment but changing environment is likely to strongly impact those due to recessive deleterious sweeps.