Time to fixation in changing environments

Abstract

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.

Joint effect of changing selection and demography on the site frequency spectrum

“…5 for on-average neutral selection and various environmental scenarios suggest that in addition to demography, varying selective environment (about zero mean) is a potentially important factor for explaining the lower levels of neutral genetic diversity than predicted on the basis of constant neutral population assumption (for a recent overview, see B uffalo (2021)). In a recent study, we have shown that changing selective environment breaks the symmetry between the conditional fixation times for beneficial and deleterious mutations which leads to different levels of neutral heterozygosity at a linked site due to beneficial and deleterious sweeps, and that the neutral heterozygosity is strongly affected due to the deleterious sweeps even when the selection is changing slowly while the beneficial sweeps are not much impacted (K aushik and J ain , 2021). In this article, the fundamental quantity of interest is the mean absorption time and the key effect is that as a newborn mutant is more likely to be lost when selection is negative than when it is positive, and in a slowly changing environment, the contribution to polymorphism will come only from the part of the cycle when the selection is strongly positive, the time-averaged quantities will be quantitatively different from those due to positively selected mutants in constant environment.…”

“…For the model detailed in Section 2, these coefficients have been derived in our earlier work (K aushik and J ain , 2021), using which we find that The above equation is subject to the initial condition f ( x , 0), and boundary conditions, Lim x →0 xf ( x, t ) = 2 N ( t ) μ and f (1, t ) finite (E vans et al ., 2007). The first and second term on the RHS of (5) describe the effect of selection and random genetic drift, respectively, and the boundary condition at low allele frequency models the balance between the loss of polymorphism due to the absorption of the mutant allele by genetic drift alone and the gain by new mutations (for other modeling approaches, see Ž ivkoviĆ et al .…”

“…Furthermore, at each site, the homozygotes AA and aa have fitness 1 and 1+ s ( t ), respectively, and the fitness of the heterozygote aA is 1+ hs ( t ) where the dominance coefficient 0 < h < 1. The frequency x of the mutant allele a increases or decreases at rate r b or r d respectively, which are given by (D evi and J ain , 2020; K aushik and J ain , 2021) where w a ( t ) = (1 + s ( t )) x + (1 + hs ( t ))(1 − x ) and w A ( t ) = (1 − x ) + (1 + hs ( t )) x are the marginal fitness of allele a and A , respectively, and is the average fitness.…”

Effect of beneficial sweeps and background selection on genetic diversity in changing environments

“…In a recent study (K aushik and J ain , 2021), the effect of a continually changing environment on the genetic diversity in a randomly mating population was investigated using a two-locus model with one neutral and one selected locus. It was discovered that the Maruyama-Kimura symmetry (M aruyama , 1974; M aruyama and K imura , 1974) for conditional mean fixation time in static environment does not hold in a changing environment, and the deleterious sweeps are strongly affected due to varying selection.…”

“…It was discovered that the Maruyama-Kimura symmetry (M aruyama , 1974; M aruyama and K imura , 1974) for conditional mean fixation time in static environment does not hold in a changing environment, and the deleterious sweeps are strongly affected due to varying selection. The beneficial sweeps, on the other hand, are robust for slow or moderate changes in the selective environment (K aushik and J ain , 2021). Here, we extend these results for selective sweeps to a more general case of inbreeding population.…”