# Re: Resources, energetics and dinosaur maximal size

Oh no. There is plenty of math in the paper (much more so than the
```"typical"
paleo paper).<<<

Sort of.  So lets look at where McNab does and doesn't use math:

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First of all he postulates qualatatively that "The maximal size of vertebrates is limited principally by the abundance and quality of the resources used to sustain their activities."
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Of course at the margins of size this must be true, but as noted by Mike Habib the inclusion of the word "principally" makes this a radical statement, as it implies that behavior, morphology, and population density either play no important role (and are thus overwhelmed by the importance of resource quality and distribution) or else they are so plastic that the most optimized solution is always arrived at, both of which are almost certainly false. Starting off your math section with such a blatantly wrong grasp of evolutionary theory is not promising, but perhaps it is addressed later in the paper...
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He then follows this by claiming that herbivores are larger than carnivores because their food is more abundant, which is a shockingly radical notion that he support only with a single citation, despite other factors like the cost of resource acquisition, the cost of resource utilization (e.g. meat passes rapidly and cheaply through the gut while plant matter benefits from long stays), and external factors like safety (how large do you have to be to sufficiently acquire live prey/not get caught by predators) are all thought to play roles withing specific ecosystems.
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But never mind that, on to the math! Basically McNab is postulating that the daily energy expenditure budget (what he refers to as FEE, or field energy expenditure) can be reduced to a mass-independent equation a m^b, where a is the rate at which energy is spent, m is mass, and b is the scaling power related to mass (bascially that part that makes the equation mass-independent, and is based on many studies of how physiological processes scale with mass).
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Now this certainly is math (yay algebra...), but it's only as good as the data supporting it, and immediately I am concerned about the quantity "a". Why? Well, FEE is established empirically (good), as is mass (good) and the scaling power of physiological reactions (b) is also supported by a wide range data. But "a" is left hanging there; McNab invokes it to say that if FEE is held constant (e.g. animals of similar energy expenditure) that of course "a" and "m" must have an inverse relationship, but doesn't explain, for example, whether "a" should also have a scaling power. After all, "a" being rate of energy expenditure (not merely basal metabolism but rate of expenditure during a normal day) it must include locomotion, but as we all (hopefully) know, locomotion gets cheaper per unit mass as you get larger (within a similar body plan). Also, some mass-independent morphological variation in locomotion alters how much energy is used per unit distance. These are not things that can just be assumed for the sake of convenience. Worse, McNab himself points out that there are other non-mass specific factors that could decouple "a" from mass: "a tradeoff occurs between a and m; if a increases, m must decrease, and as a decreases, m may, or may not, increase, depending on the circumstances in the environment and the characteristics of the species, including its food habits."
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Think about that; sure, if FEE truly = a m^b, then holding FEE constant does indeed mean that as "a" goes up then "m" must come down (i.e. as energy use goes up mass must come back down). But wait! Even he points out that as "m" comes down that "a" may or may not come down depending on local circumstances. So...clearly FEE does NOT necessarily = a m^b for any organisms with...you know...an evolutionary history. Even if all species at one time started out with this hypothetically optimized FEE = a m^b relationship, times when "a" and mass varied independantly would accumulate in their lineages to the point that there is no a priori reason to assume any actual animal is at this point of optimization.
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McNab continues on to calculate the FEE for elephants and Paraceratherium (which he calculates at 11 tons, even though mass estimates get almost double that and McNab himself postulates an 11-15 ton mass range). At that point he concludes that "These values may indicate the maximal expenditures of herbivorous vertebrates in a terrestrial environment, reflecting the abundance and quality of the available resources, and the ability of these species to move from 1 area to another to satisfy their nutritional requirements."
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I guess maybe it's possible that Paraceratherium represents the pinnacle of all evolution in terms of terrestrial herbivore energy expenditure, but how does one test this? Just like above, Paraceratherium had its own evolutionary history, so how do we know that the relationship between "a" and "m" is maximized? Here's a simple thought experiment: why aren't there any indricothere-sized terrestrial mammals today? Were food resources really that much better in the Oligocene? It seems doubtful since indricotheres are often thought to have lived in semi-arid areas. Clearly extant mammals do not represent a maximized relationship between local resources, energy consumption and energy expenditure. And if there are (self-evidently) factors other than just resource abundance at work today...how do we know they weren't at work in the Oligocene? In fact, why on Earth would we assume otherwise?
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But wait! Aside from just attempts to correlate the equation with cherry-picked localities in the fossil record, McNab does offer one explanation for why large herbivorous mammals should be view as setting the standard against which other herbivores should be judged; the rate of acquiring food. This of course has been trotted out for several decades now and has usually been rejected (as noted by some other posts), but I want to point out that this is actually the entirety of the relevant data in the paper in my opinion. There is no empirical case made that the equation FEE = a m^b actually holds significant predictive power, and in fact if you applied it to a wider array of Cenozoic and Mesozoic terrestrial faunas it breaks down (why are large tyrannosaurs present in a habitat that contains no truly colossal herbivores, contra the idea that predator mass is linked to herbivore mass, etc.??). He dabbles in discussions about geographic restriction (based on very selective citations), discusses local resource abundance (noting that recent studies suggest roughly equal amounts of calories available from plants but then concluding anyways that resources "may have been lower" because of the lack of grasses...) and amazingly enough concluding that high metabolic rates may not be needed for fast growth by noting that altricial birds grow very fast with a lower metabolic rate than adults (never mind that both body temperature and all food gathering is supplied by the high metabolic adults) and a bit more selective citation to make the growth issue seem more muddled than the majority of the literature actually suggests.
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So aside from all that bait and switch, we are back to assuming that big terrestrial mammals are as big as terrestrial endotherms can get because their rate of energy acquisition and utilization is as high as terrestrial herbivores get (same argument that Leahy has been making in recent papers as well). McNab points out that a 3 tonne African elephant spends 16 hours a day eating. One is left having to imagine how a 15-20 ton indricothere managed to find 26 hours a day to eat, but regardless, we all know that while sauropods did use oral processing in acquiring their food, they did not spend as much time per unit mass consumed with mastication. It's even been pointed out that dinosaurian herbivores that appear better adapted to mastication (e.g. hadrosaurs) do not approach the larger sauropods in size, although this could of course be do to other factors.
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As Jason has pointed out, McNab does address this, claiming: "However, the rapid swallowing of coarse food is unlikely to increase Kh, because the limiting factor on food consumption then would be the rate of fermentation in the gut, which is reduced by swallowing unmasticated fibrous food, the time required for fermentation increasing with food intake and body mass. Thus, the huge abdominal masses of sauropods were undoubtedly large fermentation vats that may not have completely compensated for the absence of buccal processing of food."
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This would have been a fabulous time for some math related to digestive efficiency (horribly in elephants), the correlation between size and time of retention of food in the digestive track, etc. One problem that is assuaged has to do with time spent eating. Clearly an animal can't spend much more than 20 hours a day eating, and in reality 16-18 hours is a much better place to be. But of course you can be digesting food all the time...and in fact it's hard not to as an herbivore. So an increase in how much food can be processed per unit time internally, as well as increases in efficiency (what percentage of calories are extracted per unit mass over time) are clearly the places that would allow endotherms to get around the consumption constraints that McNab postulates, and as discussed above there is no reason to think that purely energetic constraints are what has driven maximum adult size (certainly they aren't today, and it's not clear what evidence there is for this ever having been true). It's not surprising that mammals retain fibrous plant material in their UI tracts for shorter periods of time than well-masticated food...what with mammals be specialized masticators and all. Is it true of dinosaurian herbivores (e.g. living birds that can't really masticate their food either)?
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Let me be the first to say that falsifying McNab's hypothesis about the relationship of size and energy budget does not prove that sauropods or other dinosaurs were mammal-level endotherms. Heck, we are still stuck with the problem that "mammal-level endotherm" covers a far broader swath of metabolic regimes than people seem to realize. But regardless, in my estimation McNab's paper completely fails to make the case that FEE found in extant organisms can make predictive generalizations about extinct ecosystems, so it ultimately fails to bring new data to the table in the discussion and instead relies on arguments about rates of food consumption that many workers find unconvincing.
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YMMV.

Scott Hartman
Science Director
Wyoming Dinosaur Center
110 Carter Ranch Rd.
Thermopolis, WY 82443
(800) 455-3466 ext. 230
Cell: (307) 921-8333

www.skeletaldrawing.com

-----Original Message-----
From: Jura <pristichampsus@yahoo.com>
To: DML <dinosaur@usc.edu>
Sent: Mon, Jul 27, 2009 10:06 am
Subject: Re: Resources, energetics and dinosaur maximal size

--- On Mon, 7/27/09, David Marjanovic <david.marjanovic@gmx.at> wrote:

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```So he's trying to do science without math? (What do
"large", "may", "not completely", "unlikely", "appreciably
higher" and so on really mean?)

If so, I'm unfortunately still right, even though (thanks
for correcting me) for the wrong reasons.

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++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

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Oh no. There is plenty of math in the paper (much more so than the "typical"
```paleo paper).

I can send you a copy if you'd like.

Jason

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