Positive allometry and the prehistory of sexual selection.

The function of the exaggerated structures that adorn many fossil vertebrates remains largely unresolved. One recurrent hypothesis is that these elaborated traits had a role in thermoregulation. This orthodoxy persists despite the observation that traits exaggerated to the point of impracticality in extant organisms are almost invariably sexually selected. We use allometric scaling to investigate the role of sexual selection and thermoregulation in the evolution of exaggerated traits of the crested pterosaur Pteranodon longiceps and the sail-backed eupelycosaurs Dimetrodon and Edaphosaurus. The extraordinarily steep positive allometry of the head crest of Pteranodon rules out all of the current hypotheses for this trait's main function other than sexual signaling. We also find interspecific patterns of allometry and sexual dimorphism in the sails of Dimetrodon and patterns of elaboration in Edaphosaurus consistent with a sexually selected function. Furthermore, small ancestral, sail-backed pelycosaurs would have been too small to need adaptations to thermoregulation. Our results question the popular view that the elaborated structures of these fossil species evolved as thermoregulatory organs and provide evidence in support of the hypothesis that Pteranodon crests and eupelycosaur sails are among the earliest and most extreme examples of elaborate sexual signals in the evolution of terrestrial vertebrates.