The interplay of local adaptation and gene flow may lead to the formation of supergenes.

Supergenes are genetic architectures resulting in the segregation of alternative combinations of alleles underlying complex phenotypes. The co-segregation of alleles at linked loci is often facilitated by polymorphic chromosomal rearrangements suppressing recombination locally. Supergenes are involved in many complex polymorphisms, including sexual, colour or behavioural polymorphisms in numerous plants, fungi, mammals, fish, and insects. Despite a long history of empirical and theoretical research, the formation of supergenes remains poorly understood. Here, using a two-island population genetic model, we explore how gene flow and the evolution of overdominant chromosomal inversions may jointly lead to the formation of supergenes. We show that the evolution of inversions in differentiated populations, both under disruptive selection, leads to an increase in frequency of poorly adapted, immigrant haplotypes. Indeed, rare allelic combinations, such as immigrant haplotypes, are more frequently reshuffled by recombination than common allelic combinations, and therefore benefit from the recombination suppression generated by inversions. When an inversion capturing a locally adapted haplotype spreads but is associated with a fitness cost hampering its fixation (e.g. a recessive mutation load), the maintenance of a non-inverted haplotype in the population is enhanced; under certain conditions, the immigrant haplotype persists alongside the inverted local haplotype, while the standard local haplotype disappears. This establishes a stable, local polymorphism with two non-recombining haplotypes encoding alternative adaptive strategies, that is, a supergene. These results bring new light to the importance of local adaptation, overdominance, and gene flow in the formation of supergenes and inversion polymorphisms in general.