Polygenic local adaptation in metapopulations: A stochastic eco‐evolutionary model

Abstract

This article analyzes the conditions for local adaptation in a metapopulation with infinitely many islands under a model of hard selection, where population size depends on local fitness. Each island belongs to one of two distinct ecological niches or habitats. Fitness is influenced by an additive trait which is under habitat‐dependent directional selection. Our analysis is based on the diffusion approximation and accounts for both genetic drift and demographic stochasticity. By neglecting linkage disequilibria, it yields the joint distribution of allele frequencies and population size on each island. We find that under hard selection, the conditions for local adaptation in a rare habitat are more restrictive for more polygenic traits: even moderate migration load per locus at very many loci is sufficient for population sizes to decline. This further reduces the efficacy of selection at individual loci due to increased drift and because smaller populations are more prone to swamping due to migration, causing a positive feedback between increasing maladaptation and declining population sizes. Our analysis also highlights the importance of demographic stochasticity, which exacerbates the decline in numbers of maladapted populations, leading to population collapse in the rare habitat at significantly lower migration than predicted by deterministic arguments.

Genetic load and extinction in peripheral populations: the roles of migration, drift and demographic stochasticity

“…Since selection pressures are identical on the mainland and island, any systematic differences in allele frequencies or homozygosity between the two populations across multiple loci (which would generate LD and ID respectively) must arise solely due to differences in population size, which would translate into differences in the efficacy of selection between the mainland and island populations. In general, we expect LD and ID to be negligible when all ecological and evolutionary processes are slow relative to recombination [14]: this may not hold, however, when populations are small (and drift significant), making it necessary to evaluate how statistical associations between deleterious variants affect extinction thresholds. In the rest of the paper, we will only show results of the allele frequency simulations (assuming LE and zero inbreeding); we compare these with individual-based simulations and discuss how LD and ID affect population outcomes in Appendix B (SI).…”

“…We will refer to the analysis above as a 'semi-deterministic analysis' as it accounts for the stochastic effects of genetic drift on allele frequencies and load (via the expectation E[R g |N * ]) but neglects demographic stochasticity. In general, we expect the semi-deterministic analysis to become more accurate for larger ζ=r 0 K (see also Appendix B, SI), since 1/ζ governs the strength of demographic fluctuations [14].…”

“…With smaller r K, population sizes and load exhibit a weak dependence on migration even with Ks>Ks c , since demographic stochasticity may depress population sizes and inflate the effects of drift, especially at low numbers. Moreover, in this regime, populations are also prone to stochastic extinction for m 0 <1/2 [14], such that population size distributions are inherently bimodal. Thus, where demographic stochasticity is significant, a low level of migration may be needed for stable populations even with strong selection against additive alleles.…”

“…Moreover, when fitness has additional environmentdependent components, local adaptation must depend on alleles of intermediate effect and is hindered by high migration, especially for marginal habitats within the metapopulation. [14].…”

“…Migration also influences extinction risk via shifts in the frequencies of fitness-affecting variants: the resultant changes in fitness may decrease or increase population size, thus further boosting or depressing the relative contribution of migration to allele frequency changes within a population, setting in motion a positive feedback which may culminate in extinction (when gene flow is largely maladaptive; e.g., [13,14]) or population rescue (e.g., if gene flow supplies variation necessary for adaptation to local conditions, or reduces inbreeding load; e.g., [5,15,16]).…”