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.