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

Abstract

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.

Keywords: chimaera; demography; elasmobranch; global change; life‐history theory; mortality; population growth rate.

FIGURE 1

Phylogeny, body mass, maximum intrinsic rate of population increase (r _max ), temperature, and median depth in sharks, rays, and chimeras. Phylogenetic tree is based on Stein et al. (2018), body mass estimates were sourced from FishBase (Froese & Pauly, 2016), r _max estimates from Pardo et al. (2016), median depth values from Dulvy, Fowler, et al. (2014), and mean annual temperature values (at median depth) were estimated based on species distribution maps from AquaMaps (Kaschner et al., 2015) and global temperature grids from the Argo database. Asterisks (*) denote temperature values corrected for mesothermy. Horizontal dotted lines indicate separate taxonomic orders.

FIGURE 2

Coefficient plots for the four models of log(r _max ) with lowest AICc values. Lighter colors indicate models with decreasing support based on ΔAICc. Error bars show the 95% confidence intervals, and effect sizes were considered significant when confidence intervals do not overlap zero. Shaded areas show the expected effect sizes for body mass (−0.33 to −0.25) and temperature (−1.0 to −0.6) based on metabolic scaling theory.

FIGURE 3

Relationship between maximum weight and maximum intrinsic rate of population increase r _max , in log space, for 63 chondrichthyan species. Median depth and temperature for each species are shown by the point size and color, respectively. Median temperatures are corrected for species, which have body temperatures that are higher than their surroundings. Fitted lines show predicted relationships based on the top‐ranked model. (a) Predicted allometric changes of r _max across median depths (10, 500, 1000 m) but constant median temperature (6°C), and (b) predicted allometric changes of r _max for three different median temperatures (6, 10, 20°C) but constant median depth (10 m).