The relative strength of selection on modifiers of genetic architecture under migration load

Gene flow between populations adapting to differing local environmental conditions creates a "migration load" because individuals might disperse to habitats where their survival is low or because they might reproduce with locally maladapted individuals. The amount by which the mean relative population fitness is kept below one creates an opportunity for modifiers of the genetic architecture to spread due to selection. Prior work that separately considered modifiers changing dispersal or recombination rates, or altering dominance or epistasis, has typically focused on the direction of selection rather than its absolute magnitude. We here develop methods to determine the strength of selection on modifiers of the genetic architecture, including modifiers of the dispersal rate, after populations evolved local adaptation. We consider scenarios with up to five loci contributing to local adaptation and derive a matrix model for the deterministic spread of modifiers. We find that selection for modifiers of epistasis and dominance is stronger than selection for decreased recombination, and that selection for partial reductions in recombination are extremely weak, regardless of the number of loci contributing to local adaptation. The spread of modifiers for a reduction in dispersal depends on the number of loci, pre-existing epistasis and extent of migration load. We identify a novel effect, that modifiers of dominance are more strongly selected when they are unlinked to the locus that they modify. Overall, these results help explain population differentiation and reproductive isolation and provide a benchmark to compare selection on genetic architecture modifiers in finite population sizes and under demographic stochasticity.