Chromosome-specific drift under stabilizing selection generates polygenic barriers to sex chromosome turnover

While sex chromosome systems show frequent evolutionary transitions in some clades, in many others they show long-term stability. Previous explanations of this stasis rely on evolutionary dynamics peculiar to sex chromosomes, such as the accumulation of deleterious mutations on the sex-specific chromosome or sexually antagonistic mutations on either sex chromosome. Here, I show that stabilizing selection on quantitative traits promotes stability of sex chromosome systems. The reason is that stabilizing selection, while keeping the value of the trait near its optimum, allows individual chromosomes' contributions to the trait to drift, and this chromosome-specific drift reduces the fitness of the novel sex-determining genotypes necessarily produced during sex chromosome turnover. Given the ubiquity of stabilizing selection on quantitative traits, chromosome-specific drift could play a pivotal role in preventing the turnover of sex chromosome systems across multiple stages of their evolution. The theory generates several testable predictions for the evolution of sex chromosome systems that align well with observed phylogenetic patterns. For example, although chromosome-specific drift acts as a global impediment to sex chromosome turnover, those turnovers that do occur should be more likely to maintain the system of heterogamety than to change it. The theory further predicts a higher rate of transitions from environmental to genetic sex determination, versus the reverse. Finally, the theory shows that the evolution of sexual dimorphism in complex traits can drive long-term sex chromosome stability.