Genotype by random environmental interactions gives an advantage to non-favored minor alleles

Abstract

Fixation probability, the probability that the frequency of a newly arising mutation in a population will eventually reach unity, is a fundamental quantity in evolutionary genetics. Here we use a number of models (several versions of the Moran model and the haploid Wright-Fisher model) to examine fixation probabilities for a constant size population where the fitness is a random function of both allelic state and spatial position, despite neither allele being favored on average. The concept of fitness varying with respect to both genotype and environment is important in models of cancer initiation and progression, bacterial dynamics, and drug resistance. Under our model spatial heterogeneity redefines the notion of neutrality for a newly arising mutation, as such mutations fix at a higher rate than that predicted under neutrality. The increased fixation probability appears to be due to rare alleles having an advantage. The magnitude of this effect can be large, and is an increasing function of the spatial variance and skew in fitness. The effect is largest when the fitness values of the mutants and wild types are anti-correlated across environments. We discuss results for both a spatial ring geometry of cells (such as that of a colonic crypt), a 2D lattice and a mass-action (complete graph) arrangement.

The effect of spatial randomness on the average fixation time of mutants

“…These parameters are also chosen randomly from a distribution, they characterize the fitness of mutants at different locations, and remain constant in time. The wild type and mutant fitness probability distributions may in general be the same or different, and the choice of mutant and wild type fitness values could be uncorrelated or correlated to different degrees [ 22 ]. Here, for illustration purposes, we will consider a discrete symmetric bimodal fitness distributions, such that fitness parameters are randomly selected to be 1 + σ or 1 − σ , with 0 < σ < 1.…”

“…In a number of previous studies, the evolutionary properties of mutants have been investigated under the assumption that fitness values of different types were kept constant. It has been recently recognized, however, that fluctuating fitness values can have important effects on the fixation probability and time [ 22 , 23 ]. In [ 24 ], the authors considered two different types of heterogeneity, a heterogeneous voter model where each voter has an intrinsic rate to change state and a partisan voter model where each voter has an innate and fixed preference for one opinion state (0 or 1).…”

“…In [ 22 ], we used a number of models (several versions of the Moran model and the haploid Wright-Fisher model) to examine fixation probabilities for a constant size population, where the fitness was a random function of both allelic state and spatial position. Namely, it was assumed that the fitness values of wild type cells and mutant cells were drawn from probability distributions, and were fixed for each location.…”

Environmental spatial and temporal variability and its role in non-favoured mutant dynamics

“…In this paper, we are using a specific type of probability distribution, a two-valued, zero skewness distribution, where value 1 + σ occurs with probability 0.5 and value 1 − σ with probability 0.5 (here σ = σ r for division rates and σ = σ d for death rates). Other distributions were investigated in [34,53]; the results were found to be qualitatively similar. Results of numerical simulations are presented in figure 2.…”

“…An important question is whether any of these effects become negligible with growing system size, N. Interestingly, the amount of advantage enjoyed by a minority species increases in large populations, allowing this 'selection' force to overcome random drift [34]. One way to measure the size of the effect as N increases is to compare the probability of mutant fixation (P N ) multiplied by N with unity.…”