Body mass, temperature, and depth shape the maximum intrinsic rate of population increase in sharks and rays.

An important challenge in ecology is to understand variation in species' maximum intrinsic rate of population increase, r max , not least because r max underpins our understanding of the limits of fishing, recovery potential, and ultimately extinction risk. Across many vertebrate species, terrestrial and aquatic, body mass and environmental temperature are important correlates of r max . In sharks and rays, specifically, r max is known to be lower in larger species, but also in deep sea ones. We use an information-theoretic approach that accounts for phylogenetic relatedness to evaluate the relative importance of body mass, temperature, and depth on r max . We show that both temperature and depth have separate effects on shark and ray r max estimates, such that species living in deeper waters have lower r max . Furthermore, temperature also correlates with changes in the mass scaling coefficient, suggesting that as body size increases, decreases in r max are much steeper for species in warmer waters. These findings suggest that there are (as-yet understood) depth-related processes that limit the maximum rate at which populations can grow in deep-sea sharks and rays. While the deep ocean is associated with colder temperatures, other factors that are independent of temperature, such as food availability and physiological constraints, may influence the low r max observed in deep-sea sharks and rays. Our study lays the foundation for predicting the intrinsic limit of fishing, recovery potential, and extinction risk species based on easily accessible environmental information such as temperature and depth, particularly for data-poor species.