Abstract
Local adaptation leads to differences between populations within a species. In many systems, similar environmental contrasts occur repeatedly, sometimes driving parallel phenotypic evolution. Understanding the genomic basis of local adaptation and parallel evolution is a major goal of evolutionary genomics. It is now known that by preventing the break-up of favourable combinations of alleles across multiple loci, genetic architectures that reduce recombination, like chromosomal inversions, can make an important contribution to local adaptation. However, little is known about whether inversions also contribute disproportionately to parallel evolution. Our aim here is to highlight this knowledge gap, to showcase existing studies, and to illustrate the differences between genomic architectures with and without inversions using simple models. We predict that by generating stronger effective selection, inversions can sometimes speed up the parallel adaptive process or enable parallel adaptation where it would be impossible otherwise, but this is highly dependent on the spatial setting. We highlight that further empirical work is needed, in particular to cover a broader taxonomic range and to understand the relative importance of inversions compared to genomic regions without inversions. This article is part of the theme issue 'Genomic architecture of supergenes: causes and evolutionary consequences'.