Abstract
We analyse how migration from a large mainland influences genetic load and population numbers on an island, in a scenario where fitness-affecting variants are unconditionally deleterious, and where numbers decline with increasing load. Our analysis shows that migration can have qualitatively different effects, depending on the total mutation target and fitness effects of deleterious variants. In particular, we find that populations exhibit a genetic Allee effect across a wide range of parameter combinations, when variants are partially recessive, cycling between low-load (large-population) and high-load (sink) states. Increased migration reduces load in the sink state (by increasing heterozygosity) but further inflates load in the large-population state (by hindering purging). We identify various critical parameter thresholds at which one or other stable state collapses, and discuss how these thresholds are influenced by the genetic versus demographic effects of migration. Our analysis is based on a ‘semi-deterministic’ analysis, which accounts for genetic drift but neglects demographic stochasticity. We also compare against simulations which account for both demographic stochasticity and drift. Our results clarify the importance of gene flow as a key determinant of extinction risk in peripheral populations, even in the absence of ecological gradients.This article is part of the theme issue ‘Species’ ranges in the face of changing environments (part I)’.
Highlights
Most outcrossing populations carry a substantial masked mutation load owing to recessive variants, which can contribute significantly to inbreeding depression in peripheral isolates or after a bottleneck
The second equation describes the evolution of population size N: the first term describes changes in N under logistic growth, where the growth rate is reduced by a factor proportional to the log mean fitness; the second term captures the effect of migration; the third term corresponds to demographic fluctuations
A key parameter governing the fate of peripheral populations is 2LU = 2L(u/r0), the genome-wide deleterious mutation rate relative to the baseline rate of population growth: low-load states are possible only for 2LU & 1, provided selection against deleterious variants is sufficiently strong and/or migration high
Summary
Most outcrossing populations carry a substantial masked mutation load owing to recessive variants, which can contribute significantly to inbreeding depression in peripheral isolates or after a bottleneck. Environmental stochasticity—catastrophic events, as well as fluctuations in growth rates and carrying capacities, may dramatically lower extinction times [8] Both demographic and environmental fluctuations, in turn, reduce the effective size of a population, making it more prone to fix deleterious alleles; the consequent reduction in fitness further depresses size, pushing populations into an ‘extinction vortex’, which is often characterized by a complex interaction between the effects of genetic drift, demographic stochasticity and environmental fluctuations [9]. The consequences of asymmetric gene flow are typically simpler to analyse as we can focus on a single population, while taking the state of the rest 2 of the larger habitat as ‘fixed’ Such analyses are key to understanding more general scenarios where genotype frequencies and population sizes across different regions co-evolve. Modelling the polygenic nature of fitness variation is crucial, as changes in load (e.g. owing to migration) at any locus can affect all other loci by effecting changes in population size, which in turn influences the efficacy of selection across the genome
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