The relationship between sexual dimorphism and intersex correlation: do models support intuition?
That a high genetic correlation between the sexes (rfm) constrains the evolution of sexual dimorphism and that they should negatively correlate with one another, are assumptions commonly made in the field of sex-specific adaptation. While some empirical observations support a general negative relationship, the mechanisms underlying this pattern and the conditions under which it arises are poorly understood. Concretely, two primary hypotheses are often invoked: first, that traits with ancestrally low rfm are less constrained in their ability to respond to sex-specific selection and thus evolve to be more dimorphic; second, that sex-specific selection acts to reduce rfm. However, no model to date has formalized these hypotheses and tested the conditions in which they hold. Here, we develop models of sex-specific stabilizing selection, mutation and drift to explore various scenarios potentially generating a negative correlation between intersex correlation and sexual dimorphism, with a focus on testing the common hypotheses. We recover the classical result that, with an infinite population size, rfm and sexual dimorphism are independent at equilibrium. Further, we show that this independence is maintained with a finite population; and this is in spite of the fact that, as we demonstrate, genetic drift generates nonzero sexual dimorphism even when selection between the two sexes is identical. Moreover, we demonstrate that the two common hypotheses only imply a negative association if additional assumptions are made. Specifically, that 1) some traits are sex-specifically adapting under directional selection, and 2) this sex-specific adaptation favours increased dimorphism more often than decreased dimorphism. These results provide, to our knowledge, the first mechanistic framework for understanding the conditions under which a negative correlation between intersex correlation and sexual dimorphism may arise. They also offer a compelling explanation for the inconsistent empirical evidence observed in nature, highlighting the importance of context-specific factors in shaping this relationship.