Stepwise expansion of recombination suppression on sex chromosomes and other supergenes through lower load advantage and deleterious mutation sheltering

Many organisms possess sex chromosomes with non-recombining regions that have expanded progressively. Yet, the causes of this stepwise expansion remain poorly understood. Here, using mathematical modeling and stochastic simulations, we show that the widespread presence of deleterious recessive mutations in genomes can generate several phenomena that can contribute to the evolution of recombination suppression on sex chromosomes. We demonstrate that a significant proportion of new chromosomal inversions, or any other recombination suppressor, are initially advantageous because they carry fewer mutations than average. However, these less-loaded inversions generally fail to fix on autosomes because, as their frequency increases, the recessive deleterious mutations they carry are more likely to occur in a homozygous state, leading to a selective disadvantage. In contrast, the permanent heterozygosity of Y-like sex chromosomes shelters their inversions from this disadvantage, facilitating their fixation and thereby the stepwise expansion of non-recombining regions. Due to this sheltering effect, we show that fixation probabilities are substantially higher on Y-like chromosomes than on autosomes across a wide range of parameters, particularly when segregating deleterious mutations are moderately to strongly recessive, and this is true even after controlling for differences in effective population sizes between those chromosomes. Then, once recombination is suppressed, deleterious mutations accumulate on inversions, which could select for recombination restoration. However, we show that the accumulation of overlapping genomic rearrangements following recombination suppression can prevent its restoration. Overall, our theoretical model proposes a testable framework that may contribute to explaining evolutionary strata on sex and mating-type chromosomes, and other supergenes.