^{*}

CC conceived and designed the study. CC and AT contributed data. CC and JMR analyzed data. CC wrote the paper.

The authors have declared that no competing interests exist.

Mammalian carnivores fall into two broad dietary groups: smaller carnivores (<20 kg) that feed on very small prey (invertebrates and small vertebrates) and larger carnivores (>20 kg) that specialize in feeding on large vertebrates. We develop a model that predicts the mass-related energy budgets and limits of carnivore size within these groups. We show that the transition from small to large prey can be predicted by the maximization of net energy gain; larger carnivores achieve a higher net gain rate by concentrating on large prey. However, because it requires more energy to pursue and subdue large prey, this leads to a 2-fold step increase in energy expenditure, as well as increased intake. Across all species, energy expenditure and intake both follow a three-fourths scaling with body mass. However, when each dietary group is considered individually they both display a shallower scaling. This suggests that carnivores at the upper limits of each group are constrained by intake and adopt energy conserving strategies to counter this. Given predictions of expenditure and estimates of intake, we predict a maximum carnivore mass of approximately a ton, consistent with the largest extinct species. Our approach provides a framework for understanding carnivore energetics, size, and extinction dynamics.

Predators face severe energetic constraints that affect many aspects of their ecology and evolution [

In order to estimate the scaling of carnivore energy budgets, we develop a simple model that incorporates both the scaling of costs associated with body mass and the differences in time and energy budgets associated with hunting strategy. In our model, predatory carnivores are divided into two basic hunting groups (following [_{r}T_{r}_{h}T_{h},_{h}_{r}_{h}_{r}_{r}^{0.75} and _{h}^{0.684} ^{0.697}, where

The model predictions for DEE (using parameter values in Materials and Methods) are compared against estimates of DEE for 14 species of free-ranging wild carnivores (

(A) Estimates of DEE (kJ) against carnivore mass (kilograms) for 14 species, together with the model prediction of DEE (red line) and the piecewise regression fit (black line) (

(B) Estimates of DEI (kJ) against carnivore mass (kilograms) for 32 species, together with the predicted DEI (red line) and piecewise regression fit (black line) (see text for details and

(C) The scaling of DEI in relation to predicted DEI based on the scaling of FMR [

Three Alternative Models Were Fitted to Both DEE and DEI Values

Net rate of assimilated energy gain (kilojoules/day) showing predicted upper limits for the two dietary groups: small-prey feeders, (based on small vertebrates) (tan line) and large-prey feeders based on average intake (light blue dashed line) and maximum intake (dark blue dashed line). The net assimilated energy gain is calculated as 0.66 × DEI (kilojoules/day) − DEE [

To provide a more robust test of the predicted increase in energy expenditure, we compared our model predictions against a surrogate for DEE, daily energy intake (DEI, kilojoules/day)—a measure that is more readily obtained in the field, and for which we found estimates for 32 species (see

Across all carnivores, the scaling exponents of DEE (0.74 ± 0.10, 95% confidence interval) and DEI (0.79 ± 0.09, 95% confidence interval) (

Within each dietary group, relatively small carnivores exhibit costly strategies (falling near the upper boundary); while relatively large carnivores exhibit energy conserving strategies (near the lower boundary). This suggests that within each dietary group, expenditure and intake rates impose increasing constraints as size within groups increases, leading to the shallower exponents within groups. The sigmoid curve fit of observed values of DEI intersects the upper and lower boundary of predicted DEI at masses near the size limits of the two dietary groups. At the upper size range of the large-vertebrate-prey feeders, the sigmoid curve intersects the lower boundary just above 1,100 kg, near the maximum mass estimated for some extinct carnivores (see below). At the lower end of the small-prey feeders, the sigmoid curve intersects at around 100 grams near the mass of the smallest carnivore species. The qualitative trend suggests that these upper and lower limits to DEE and DEI represent constraints on behavioral and metabolic adjustments, which then impose constraints on carnivore size.

In order to estimate net rate of gain (kilojoules/day) for these two dietary groups, the model predictions of DEE were combined with observed estimates of intake rate. Net gain _{h}_{r}T_{r}_{h}T_{h},^{0.6}, with an intercept of 1,010 kJ/h at 1 kg body mass based on the observed scaling of DEI (converted to an hourly rate,

Using the above calculations, we predict a maximum carnivore mass of 18 or 45 kg (for invertebrate and small-vertebrate-prey feeders, respectively,

Our model provides insights into dietary changes and the evolution of body size in mammalian carnivores. Using a simple energetic model, we predicted that hunting costs and resulting energy requirements would increase with an increase in prey size. We therefore expected to find a marked increase in DEE and DEI around the 14.5- to 21-kg size range, where carnivores are found to switch to hunting large-vertebrate prey [

In previous research [

Although the primary scaling of DEE and DEI corresponds with the expected three-fourths power scaling of metabolic rate [

Our model assumes that the costs of transport scale with body mass according to typical mammalian estimates [

In addition to the need to reduce expenditure, we predict some of the very largest extinct carnivores would consume about four times the intake estimated for lions [

Given these energetic constraints, we predict a maximum mass for a mammalian carnivore at 1,100 kg. Among extant species, the polar bear is the largest carnivore with the largest recorded individual weighing 1,002 kg [

Our analysis provides a broad perspective on energy and time budgets in mammalian terrestrial carnivores and provides insights into carnivore conservation and evolution, helping us to understand the vulnerability of large carnivores to historical and future extinctions. Among extant carnivores, the largest species are particularly vulnerable to human threat processes [

There were consistent differences in energy and time budgets for small- and large-prey-hunting carnivores. Our aim here was to broadly characterize these differences in the model. For carnivores hunting small prey (invertebrate and small vertebrates), there was no consistent differences in travel speeds or time budget across prey types or by predator sizes, so we used fixed average for travel speed of 1.19 km/h (_{h},_{h}

Our analysis of net gain uses a maximum estimate of intake rate of 746 kJ/h for invertebrate feeders [^{0.6}_{ave} = 1,010 kJ/h) and a maximum rate (_{max} = 3,132 kJ/h) for the same two species (the African wild dog and gray wolf), which have high estimated intake rates for their size.

Most average daily intake rates (data and sources are listed in

(113 KB DOC)

We thank John Gittleman, Sam Turvey, Georgina Mace, Jonathan Baillie, Nick Isaac, Peter Bennett, Valerie Olson, and Ben Collen for their comments during the development of this research. We also thank Johan du Toit, Stephen Wroe, and Ray Huey for their helpful comments on earlier drafts of the manuscript.

daily energy expenditure

daily energy intake

field metabolic rate