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Is there an intrinsic body size constraint in mammalian carnivory? – reaction to Carbone et al. (2007) ‘The costs of carnivory’, part 1

Posted by pbio on 07 May 2009 at 22:24 GMT

Author: Marcus Clauss
Position: Senior Research Associate
Institution: Vetsuisse Faculty, University of Zurich
Submitted Date: May 08, 2008
Published Date: June 10, 2008
This comment was originally posted as a “Reader Response” on the publication date indicated above. All Reader Responses are now available as comments.

In a recent publication, Carbone et al. (2007) present a model that predicts the upper possible body size for carnivores (based on data from mammalian carnivores) of approximately 1 metric ton. The fact that both extant and extinct terrestrial mammalian carnivores approach but hardly surpass this threshold gives the model a posteriori plausibility. The authors base their model on an energy balance. Due to differences in the chosen allometric scaling factors – with daily energy expenditure (DEE, kJ/d) components scaling to body mass (BM) to the power of 0.75 and 0.68-0.70, but with daily energy intake (DEI, kJ/d) scaling to BM0.60 only, there must be a BM threshold above which DEE exceeds DEI. Here, both qualitative and - in part 2 - quantitative reservations against the model are presented.

Qualitative concerns
In their publication, Carbone et al. find that empirical DEI data does not scale to the common metabolic exponent of 0.75, but to BM0.60 within each group of carnivores – those relying on small and those relying on large prey. The authors interpret this as an indication that at larger body sizes, “carnivores adopt behavioral and ecological strategies to minimize costs”. This is an appealing interpretation. However, this automatically means that when estimating not only DEI but also DEE (the costs), one must not apply the 0.75 scaling in either case. In the quantitative model, the authors allow costs to scale to BM0.75 and BM0.70 although they state themselves that larger carnivores will adopt strategies to minimize these costs. This is not consistent.
In other words, the authors use two different functions to estimate the daily energy need (derived from different sets of empirical and/or theoretical data), and find these two functions in discrepancy. This evidently means that only one (or none) of these functions can be correct, and that one cannot use them both to calculate a threshold where they both intersect.
The question is, is there a concept that could set a body size limit to carnivory? The fact that the largest extant mammals, the cetaceans, are carnivores, could indicate that either terrestrial locomotion or prey availability, or both, are limiting factors. Seals, dolphins and baleen whales indicate that smaller prey may be feasible at higher body masses, most likely due to the prey’s much higher abundance or at least spatial density. Transferred to terrestrial predators, this could mean that prey density, not some intrinsic physiological constraint, determines the limits of carnivore body sizes and dietary preferences. In this sense, a higher prey density and availability in dinosaur times (Burness et al. 2001) could have led to a high diversity of large-sized theropod predators with a mammal-like metabolism. Note that the energy gains of hunting must, by necessity, be a function of current prey density and accessibility. Any model assessing an intrinsic constraint of carnivory must therefore allow for variability in these extrinsic factors; otherwise, it is just relevant for the particular ecological setting from which its empirical input variables were derived.

Quantitative considerations
In detail, the authors calculate net gain G (called “net assimilated gain” in their Fig. 2) (unit: kJ/d) as G = DEI – DEE
DEI is calculated as DEI = 0.66 I Th
with 0.66 being an energy conversion factor taken from the literature (to transform gross energy ingested into metabolizable energy), Th being the time spent hunting per day (in h), and I the intake rate of gross energy per unit hunting time (kJ/h). This rate is given for large carnivores as Imaximum = 3132 kJ/h BM(0.60).
Because Th was set to 3.5 h (per day), it results that
DEImaximum = 0.66 * 3.5 * 3132 BM(0.60) kJ/d = 7234.9 BM(0.60) kJ/d.

DEE is calculated as DEE = ErTr + EhTh
with Er and Eh being energy expenditure (kJ/h) at rest and during hunting, respectively, and Tr and Th being time (h) spent resting and hunting per day. It was assumed that Th = 3.5 h/d and therefore Tr = 20.5 h/d.
Er was defined as 5.5 BM(0.75) W = 5.5 BM(0.75) J/s = 19.8 BM(0.75) kJ/h; therefore, ErTr = 405.9 BM(0.75) kJ/d.
Eh was defined as 10.7 * v * BM(0.684) + 6.03 BM(0.697) (unit: W = J/s), with v being the average hunting speed, set at 7.4 m/s. If we assume that both exponents are equal, setting them to 0.70, this results in Eh = (10.7 * 7.4 + 6.03) BM(0.70) J/s = 306.8 BM(0.70) kJ/h. Note that by increasing the exponent, we estimate DEE even higher (and hence more constraining) than Carbone et al. (2007). As Th = 3.5 h, EhTh = 1073.6 BM(0.70) kJ/d.

This results in
G = 7234.9 BM(0.60) kJ/d – (405.9 BM(0.75) kJ/d + 1073.6 BM(0.70) kJ/d).
The carnivore body size threshold is defined as the BM at which G = 0. Assuming the same exponent of 0.75 for the bracketed term (again, increasing the constraining effect of DEE above the value used by Carbone et al. 2007), we can calculate the threshold as
7234.9 BM(0.60) kJ/d = 1479.5 BM(0.75) kJ/d.
Using log transformation, this yields
log(7234.9) + 0.6 log(BM) = log(1479.5) + 0.75 log(BM) or 4.60 = log(BM) or
BM = 10(4.6)

In other words, given the specific conditions of the assumed scaling of DEI and DEE from Carbone et al. (2007) and the maximum intake rate, a carnivore would appear unfeasible at a body size of app. 40 tons, not 1 ton. Using the above equations, for a continuously hunting carnivore (note that the model does not set a limit to daily hunting time), a limit would be reached when
DEImaximum = Eh

with DEImaximum = 0.66 * 3132 BM(0.60) kJ/hhunting time = 2067.1 BM(0.60) kJ/hhunting time
and Eh = 306.8 BM(0.70) kJ/hhunting time

2067.1 BM(0.60) kJ/hhunting time= 306.8 BM(0.70) kJ/hhunting time or
log(2067.1) + 0.6 log(BM) = log(306.8) + 0.7 log(BM) or
BM = 10(8.3)

In other words, among the model parameters used by Carbone et al. (2007), the energetic gains of hunting outweigh the costs of hunting so drastically that any potential energy deficit (due to the difference in scaling exponent) can be balanced by an increase in hunting time. Using this model, there is no realistic constraint in body mass for mammalian carnivores. The model, therefore, does not support the claim that terrestrial carnivores are intrinsically limited to a body size of approximately 1 ton, and that theropod (dinosaur) carnivores would have had to be ectotherms. In contrast, if the model was realistic, it could be used to demonstrate that carnivores with a mammal-like metabolism could function at any body size ever observed or estimated in a terrestrial carnivorous vertebrate.

In summary, the model presented by Carbone et al. (2007) does not allow the conclusion that there are intrinsic constraints in carnivory that limit the body size of carnivores in general. It is built on two quantitatively different predictions of energetic requirements (only one of which can be true, at best).

No competing interests declared.