Sexual selection explains Rensch's rule of allometry for sexual size dimorphism

In 1950, Rensch first described that in groups of related species, sexual size dimorphism is more pronounced in larger species. This widespread and fundamental allometric relationship is now commonly referred to as ‘Rensch’s rule’. However, despite numerous recent studies, we still do not have a general explanation for this allometry. Here we report that patterns of allometry in over 5300 bird species demonstrate that Rensch’s rule is driven by a correlated evolutionary change in females to directional sexual selection on males. First, in detailed multivariate analysis, the strength of sexual selection was, by far, the strongest predictor of allometry. This was found to be the case even after controlling for numerous potential confounding factors, such as overall size, degree of ornamentation, phylogenetic history and the range and degree of size dimorphism. Second, in groups where sexual selection is stronger in females, allometry consistently goes in the opposite direction to Rensch’s rule. Taken together, these results provide the first clear solution to the long-standing evolutionary problem of allometry for sexual size dimorphism: sexual selection causes size dimorphism to correlate with species size.