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

The amount of standing variation present within populations is a fundamental quantity of interest in population genetics, commonly represented by calculating the average number of differences between pairs of nucleotide sequences (nucleotide diversity, π). It is well understood that both background and positive selection can cause reductions in nucleotide diversity, but less clear how local adaptation affects it. Depending on the assumptions and parameters, some theoretical studies have emphasized how local adaptation can reduce nucleotide diversity, while others have shown that it can increase it. Here, we explore how local adaptation shapes genome-wide patterns in within-population nucleotide diversity, extending previous work to study the effects of polygenic adaptation, genotypic redundancy, and 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. At low migration, 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. Across spatially extended environmental gradients, 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 within-population nucleotide diversity, so it will not be broadly useful for explaining increased FST. However, given that neither background nor positive selection inflate diversity, when peaks are found they suggest local adaptation may be acting on a causal allele in the region.