Evolution of sexual dimorphism and Rensch's rule in the beetle genus (Hydraenidae): is sexual selection opportunistic?

Sexual size dimorphism (SSD) is widespread among animals, with larger females usually attributed to an optimization of resources in reproduction and larger males to sexual selection. A general pattern in the evolution of SSD is Rensch's rule, which states that SSD increases with body size in species with larger males but decreases when females are larger. We studied the evolution of SSD in the genus (Coleoptera, Hydraenidae), measuring SSD and male genital size and complexity of ca. 80% of its 150 species and reconstructing its evolution in a molecular phylogeny with 71 species. We found strong support for a higher evolutionary lability of male body size, which had an overall positive allometry with respect to females and higher evolutionary rates measured over the individual branches of the phylogeny. Increases in SSD were associated to increases in body size, but there were some exceptions with an increase associated to changes in only one sex. Secondary sexual characters (SSC) in the external morphology of males appeared several times independently, generally on species that had already increased their size. There was an overall significant correlation between SSD, male body size and male genital size and complexity, although some lineages with complex genitalia had low SSD, and some small species with complex genitalia had no SSD. Our results suggest that the origin of the higher evolutionary variance of male body size may be due to lack of constraints rather than to sexual selection, that may start to act in species with already larger males due to random variation.