The effects of supergene evolution on the structure and stability of the G-matrix

The additive genetic variances and covariances of traits, collected in the G-matrix, summarise heritable variation within populations and are commonly used to predict the rate and direction of short-term multivariate evolution. These (co)variances are shaped by pleiotropy and genetic linkage, two features often associated with supergenes formed by chromosomal inversions. Yet how supergene evolution affects the structure and temporal stability of the G-matrix remains unclear. Here, we use mathematical analysis and individual-based simulations to investigate the evolution and genetic consequences of inversions capturing multiple pleiotropic loci underlying two traits subject to disruptive and correlational selection (selection favouring particular combinations of trait values). We show that inversions evolve under disruptive selection and are maintained by balancing selection because they preserve associations among alleles that together generate discrete phenotypic morphs. The genetic architecture reflects how selection acts on the traits: selection favouring diversification along a joint trait combination generally produces a single multi-trait supergene, whereas selection favouring independent diversification of each trait produces multiple independently segregating inversions. By suppressing recombination, these inversions increase additive genetic variance and narrow-sense heritability, and stabilise the overall amount of additive genetic variation through time. When dominance is allowed to evolve, dominance relationships become coordinated across linked loci within supergenes, although most genetic variance remains additive at the population level. Together, these results link the form of multivariate selection to the evolution of supergenes and to their consequences for the structure and temporal stability of the G-matrix.