Local adaptation can cause both peaks and troughs in nucleotide diversity within populations

Local adaptation is expected to cause high FST at sites linked to a causal locus, however this pattern can also be driven by background or positive selection. Within-population nucleotide diversity could provide a means to differentiate these scenarios, as both background and positive selection deplete diversity, whereas some theoretical studies have shown that local adaptation increases it. However, it is unclear whether such theoretical predictions generalize to more complicated models. Here, we explore how local adaptation shapes genome-wide patterns in nucleotide diversity and FST, extending previous work to study the effect of variable degrees of polygenicity and genotypic redundancy in an adaptive trait, and different levels of population structure. We show that local adaptation produces two very different patterns depending on the relative strengths of migration and selection, either markedly decreasing or increasing within-population diversity at linked sites at equilibrium. When migration is low, regions of depleted diversity can extend large distances from the causal locus, with substantially more diversity eroded than expected with background selection. With higher migration, peaks occur over much smaller genomic distances but with much larger magnitude changes in diversity. In spatially extended clinal environments both patterns can be found within a single species, with increases in diversity at the center of the range and decreases towards the periphery. Our results demonstrate that there is no universal diagnostic signature of local adaptation based on nucleotide diversity, however, given that neither background nor positive selection inflate diversity, when peaks are found they strongly suggest local adaptation.