Abstract
The Hill–Robertson effect describes how, in a finite panmictic diploid population, selection at one diallelic locus reduces the fixation probability of a selectively favoured allele at a second, linked diallelic locus. Here we investigate the influence of population structure on the Hill–Robertson effect in a population of size N. We model population structure as a network by assuming that individuals occupy nodes on a graph connected by edges that link members who can reproduce with each other. Three regular networks (fully connected, ring and torus), two forms of scale-free network and a star are examined. We find that (i) the effect of population structure on the probability of fixation of the favourable allele is invariant for regular structures, but on some scale-free networks and a star, this probability is greatly reduced; (ii) compared to a panmictic population, the mean time to fixation of the favoured allele is much greater on a ring, torus and linear scale-free network, but much less on power-2 scale-free and star networks; (iii) the likelihood with which each of the four possible haplotypes eventually fix is similar across regular networks, but scale-free populations and the star are consistently less likely and much faster to fix the optimal haplotype; (iv) increasing recombination increases the likelihood of fixing the favoured haplotype across all structures, whereas the time to fixation of that haplotype usually increased, and (v) star-like structures were overwhelmingly likely to fix the least fit haplotype and did so significantly more rapidly than other populations. Last, we find that small (N < 64) panmictic populations do not exhibit the scaling property expected from Hill & Robertson (1966 Genet. Res. 8, 269–294. (doi:10.1017/S0016672300010156)).
Highlights
Spatial structure is a defining characteristic of all biological systems
Given that population structure modelled as a network affects a single-locus diploid model of genetic drift [11], it is not surprising that we find similar consequences for two linked diploid loci subject to selection and drift
More than 50 years ago Hill & Robertson [18] explored the dynamical behaviour of variation at two linked diallelic loci in a finite randomly mating diploid population and found that selection acting at one locus interfered with the ability of selection at the second locus to fix a favourable allele. This classic result became known as the Hill–Robertson effect and suggested that recombination had an evolutionary advantage in allowing faster adaptation [19]
Summary
Gene flow within a finite structured population affects the trajectory of an evolving system, most notably the probability and time to fixation of an allele. Of note is early work by Maruyama [3,8] and Nagylaki [9] that showed under certain conditions fixation probability at a single locus subject to selection was invariant to the form of subdivision of an island-based population with migration.
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