Counterintuitive properties of fixation probability and fixation time in population structures with spatially periodic resource distribution

TL;DR

This study investigates how spatially periodic resource distribution in structured populations affects fixation probabilities and times, revealing counterintuitive effects and conditions under which mutants become beneficial or coexistence occurs.

Contribution

It introduces a model analyzing fixation dynamics in spatially heterogeneous environments with periodic resource patterns, highlighting unexpected behaviors in evolutionary outcomes.

Findings

Heterogeneity can turn deleterious mutants beneficial.

Both types can have higher than neutral fixation probabilities simultaneously.

Fixation times exponentially increase with population size under certain conditions.

Abstract

Resource are often not uniformly distributed within a population. Spatial variations of concentration of a resource, change the fitness of competing strategies locally. The notion of fitness varying with respect to both genotype and environment is important in modeling cancer initiation, microbial evolution and evolution of drug resistance. Environmental interactions can be asymmetric, that is, they affect the fitness of one type more than the other. The question is how local environmental variations in network population structures change the selection dynamics in a finite population setting. We consider one-dimensional lattice population structures with spatial fitness distributions with a periodic pattern. Heterogeneity is determined by standard deviation of fitnesses and period. The model covers biologically relevant limits of two-habitat subdivided populations and randomly-distributed resources in high- and low-periods. We numerically calculate fixation probability and fixation times for a constant population birth-death process as fitness heterogeneity and period vary. We identify levels of heterogeneity for which a previously deleterious mutant, in a uniform environment, becomes beneficial. In other regimes of the problem we observe unexpected behavior where the fixation probability of both types are larger than their neutral value at the same time. This coincides with an exponential increase in time to fixation as a function of population size, which points to significant slow-down in selection process and the potential for coexistence between types in realistic time scales. We also discuss `fitness shift' model where the fitness function of one type is identical to the other up to a constant spatial shift. This leads to significant increase (or decrease) in the fixation probability of the mutant depending the value of the shift.