The establishment of locally adaptive inversions in structured populations
Inversions have been proposed to facilitate local adaptation, by linking together locally coadapted alleles at different loci. Classic prior work addressing this question theoretically has considered the spread of inversions in "continent-island" models in which there is a unidirectional flow of maladapted migrants into the island population. In this setting, inversions are most likely to establish when selection is weak, because stronger local selection more effectively purges maladaptive alleles, thus lessening the advantage of inversions. Here, we show this finding only holds under limited conditions. We study the establishment of inversions in a "two-deme" model, which explicitly considers the dynamics of allele frequencies in both populations linked by bidirectional migration. For symmetric selection and migration, we find that stronger local selection increases the flow of maladaptive alleles and favours inversions, the opposite of the pattern seen in the asymmetric continent-island model. Furthermore, we show that the strength and symmetry of selection also change the likelihood that an inversion captures an adaptive haplotype in the first place. Considering the combined process of invasion and capture shows that inversions are most likely to be found when locally adaptive loci experience strong selection. In addition, inversions that establish in one deme also protect adaptive allele combinations in the other, leading to differentiation between demes. Stronger selection in either deme once again makes differentiation between populations more likely. In contrast, differentiation is less likely when migration rates are high because adaptive haplotypes become less common. Overall, this analysis of evolutionary dynamics across a structured population shows that established inversions are most likely to have captured strongly selected local adaptation alleles.