Dear Jason,
Thank you for your interest in our paper. You raise a number of important points, and we’re glad to have the opportunity to respond. We have copied your questions below, followed by our response.

Best,
Herman Pontzer, Vivian Allen, and John Hutchinson


Question 1) In the paper, it mentions that only bipeds were used because: "issues of weight distribution between fore and hindlimbs make biomechanical analysis of extinct quadrupeds more difficult and speculative."

Why then, were iguanas and alligators used as examples of the predictive power of the model? Though these taxa are extant, there was never any justification given for why quadrupedal taxa like Iguana and Alligator were used.

Response:
The model calculates the amount of muscle activated to support bodyweight each step. Calculating this “active muscle volume” (Vmusc) requires detailed information about the morphology of the joints and limb posture in order to calculate the effective mechanical advantage (EMA) and average fascicle length (fasc) for each muscle group involved. For bipeds, the model basically works like this:

(Hind fasc /Hind EMA) x (Bodyweight/step length) = Vmusc

For quadrupeds, bodyweight is supported by both the fore- and hind-limbs, and so the model also requires the percentage of bodyweight that is supported by the fore- versus hind-limbs:

(Hind fasc/EMA)(%Hind Bodywt/step lng) + (Fore fasc/EMA)(%Fore Bodywt/step length) = Vmusc

Knowing the percentage of bodyweight borne by the fore- and hind limbs is especially important for species where the mechanical advantage or average fascicle lengths of the fore- and hind-limbs are very different (an example of this is quadrupedal chimpanzees; see Pontzer et al. 2009 J Human Evol). In species where the mechanical advantage and average fascicle lengths are similar in the fore and hind limb, the (fasc/EMA) terms are identical, and one can simply use the bipedal equation. Essentially, this approach treats the forelimbs and hind limbs as mechanically similar.

We used alligators and iguanas to show that the model works well for known ectotherms and is not limited to endotherms. We would have liked to model the fore- and hind limbs separately, but detailed models of the forelimb are not currently available for those taxa. The fit of the model predictions for alligator and iguana cost suggests one of three possibilities. The first is that the correlation is spurious, and that the model predicted actual cost by random chance. This is possible, but we consider it unlikely given the performance of the model (r2 > 0.90) in broader samples. The second possibility is that mechanical advantage and fascicle lengths are similar enough in the fore- and hind limbs of these species that using hind limb values for both the fore- and hind limbs is sufficient for predicting total (fore + hind) active muscle volumes. The third possibility is that the mechanical advantage and fascicle lengths in the forelimb are very different from the hindlimb, but that nearly all the ground force is produced by the hindlimbs, making the error induced by equating the fore- and hind limb anatomy negligible. Experimental and modeling data from quadrupedal reptile kinematics and kinetics are needed to resolve the issue. Anatomical data (Allen et al., in press) indicates that, in alligators, the forelimb fasc values are shorter than the hind limb fasc values, approximately corresponding to the ~30% shorter fore- vs. hind limbs. Their mechanical advantage remains unknown, and complicated by the rather different kinematics (e.g. sprawling/more upright posture) and presumably kinetics of the fore- vs. hind limbs. The third possibility thus remains plausible, but the second possibility cannot be excluded either.

As for including quadrupedal dinosaurs, we did not feel it was appropriate for this study because we do not know what percentage of weight was borne by the forelimbs, and we lack the detailed anatomical models to calculate fore- and hind limb mechanical advantage and fascicle length. These unknowns make the endeavor of predicting metabolic costs more speculative than we felt was prudent.

References cited:
Allen, V., Ellsey, R., Jones, N., Wright, J., Hutchinson, J.R. In press. Functional specialization and ontogenetic scaling of limb anatomy in Alligator mississippiensis. Journal of Anatomy.

Pontzer, H., Raichlen, D.A., Sockol, M.D. (2009) The metabolic cost of walking in humans, chimpanzees, and early hominins. Journal of Human Evolution. 56, 43-54.


Question 1a) Also in regards to that question, it was mentioned a little further on that: "predicting total muscle volumes solely from hindlimb data for the extant quadrupeds simply assumes that the fore and hindlimbs are acting with similar mechanical advantage, activating similar volumes of muscle to produce one Newton of GRF. This assumption is supported by force-plate studies in other quadrupeds (dogs and quadrupedal chimpanzees)"

While the data cited certainly appears true for mammals, I don't believe that it holds as true for reptiles. There is a pretty substantial difference between fore and hindlimb muscle mass in many extant reptiles; including the two quadrupedal taxa used in this study. Much of the propulsive power in many reptiles resides on the hind limbs and tail; making them - in effect - "rear wheel drive." (Hotton 1994). This would appear to have at least some effect on the results of the model for these taxa.

Response:
First, a clarification: the model predicts total active muscle volume, the volume of muscle that is “turned on” to support body weight each step. This is different than “muscle mass”, the total mass of muscle in the limbs. Only a fraction of total muscle mass is activated to support bodyweight in each step. The volume of active muscle is what the model estimates in order to predict cost. It is therefore irrelevant whether there is more muscle mass in the fore- or hind limb, since it is possible that the same volume of muscle is activated in both during a stride cycle.

However, your point that more weight is borne by the hind limbs in reptiles is very likely to be correct. As discussed above, this will tend to improve predictions of cost that use only the hind limbs, since the forelimbs will bear less weight and be mathematically less important (i.e., the %Fore Bodyweight term will approach zero). Further, if the mechanical advantage and fascicle lengths are similar between fore- and hind limbs (again, muscle mass is not important here), the percentage of weight borne by the hind limbs is mathematically less important, since the (Fore fasc/EMA) and (Hind fasc/EMA) terms will be similar.

Question 2) The issue of associating aerobic capacity with metabolically generated (automatic) endothermy. Though it is certainly the most often cited hypothesis for how automatic endothermy evolved, Bennett & Ruben's hypothesis is sorely lacking in empirical support. Despite broad (but weak) correlations among taxa, there has yet to be discovered, any physiological link between the heat generating viscera that are responsible for the elevated metabolisms of birds & mammals (intestines, liver etc), and their aerobic systems (heart, lungs, skeletal muscle). Further, there is an ever growing collection of evidence that seems to indicate that no such link exists. From facultative scopes that vary substantially from the initial 5-10x BMR originally proposed by Bennett & Ruben, to a lack in rising BMR with exercised induced increases in VO2 max (e.g. Bingham et al 1989, Schulz et al 1991), to molecular data showing decreases in ATP availability with the onset of automatic endothermy (Walter & Seebacher 2009).

Response:
While the link between maximum aerobic power (VO2max) and resting aerobic power (BMR) is certainly of interest, it is not the focus of our paper. We simply start with the observation that maximum aerobic power is an order of magnitude greater in endotherms than in ectotherms (as Bennett pointed out long ago). Locomotor costs for the dinosaurs in our sample place the required aerobic power for walking and slow running well above the limit observed in modern ectotherms. We draw the conclusion that these taxa were therefore not ectotherms, but were instead endotherms; this is the simplest explanation for the data. However, as we point out, other explanations are possible, including the possibility that dinosaur physiology was unlike anything seen today, or that their aerobic capabilities were well above what is possible for modern ectotherms. We are unaware of any solid evidence that supports this view of dinosaur physiology.

Question 3) In regards to the VO2 max data presented, the authors mentioned that the largest aerobic scope known in reptiles was only 14.5x BMR. VO2max data for reptiles has found aerobic scopes to lie between 5-40x BMR; putting them well within the range of all but perhaps the largest taxa sampled. Some standout examples include Varanus caudolineatus with an aerobic scope of 35 (Thompson & Wither 1997), and Alligator mississippiensis which Colleen Farmer has recorded an aerobic scope of 40x BMR (Watanabe 2005).

Response:
Our figure of 14.5x BMR was based on our data, presented in the paper. This may underestimate true aerobic scope because we used a regression to estimate BMR when in fact the BMR of many ectotherms is considerably lower than predicted. While these lower BMR values will inflate the aerobic scope values considerably, it remains the case that the maximum aerobic power in ectotherms is limited to approximately 10% that of endotherms. That is, none of high aerobic scope values cited for ectotherms come about because VO2max values fall in the endothermic range, but rather because VO2max is marginally higher than usual and/or BMR values are lower (sometimes much lower) than expected. Therefore, suggesting that the dinosaurs in our sample were ectothermic but simply had extremely high aerobic scopes still requires an explanation for the high aerobic power demands, which exceed the limit seen in modern ectotherms.

Question 3a) Lastly the supplementary material for extant taxa VO2 max comparisons(Pontzer et al table S2) features a factorial scope for Heloderma suspectum that is only 7x RMR. Yet the supplement cites Beck et al 1995, which explicitly mentions the very high aerobic scope of this genus (30.4x
RMR). I suspect that the problem here lay with the regression equation used; which resulted in giving H.suspectum a higher RMR than actual.

Response:
Yes, you are correct that the difference in aerobic scope between that reported by Beck et al. (1995) and the data in our table is due to our use of a regression to estimate BMR.

Summary:
As we discuss in the paper, our model for predicting locomotor cost indicates that the aerobic power needed for walking and running in large bipedal dinosaurs substantially exceeded the limits of aerobic power seen in ectotherms today. There are really only four explanations for these results. First, our model may be highly flawed. While this is certainly possible, and all models are only approximations of reality and thus flawed in some sense, we find it unlikely given the excellent predictive power of the model over a wide range of living taxa. Second, the dinosaurs in our sample might have had an ectothermic physiology similar to that of living reptiles. This is possible, but unlikely, as it would severely limit the locomotor activity in these species below what most of us would consider plausible. Third, the dinosaurs in our sample may be ectothermic, but have physiologies unlike any reptile seen today, able to maintain aerobic power at levels seen only in endotherms today. This is possible, but extraordinary claims require extraordinary evidence. Finally, the dinosaurs in our sample may be endothermic. This is the simplest explanation that fits our data, and therefore the explanation we support. We are also aware that further work on the coupling of maximum aerobic power and resting aerobic power might someday show exactly why, physiologically, these two traits are related in living vertebrates, and might even demonstrate that these traits were uncoupled in dinosaurs. If so, we will have to rethink the data presented in our paper. But given what we know at this time, we feel that endothermy is the simplest, and therefore best, explanation for our data.