allometry

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Testing for Size and Allometric Differences in Fossil Hominin Body Mass Estimation

  • by Natalie M. Uhl, Christopher W. Rainwater and Lyle W. Konigsberg

“Body size reconstructions of fossil hominins allow us to infer many things about their evolution and lifestyle, including diet, metabolic requirements, locomotion, and brain/body size relationships. The importance of these implications compels anthropologists to attempt body mass estimation from fragmentary fossil hominin specimens. Most calculations require a known “calibration” sample usually composed of modern humans or other extant apes. Caution must be taken in these analyses, as estimates are sensitive to overall size and allometric differences between the fossil hominin and the reference sample.

This research places body mass estimation into the framework of multivariate calibration. Estimators are extended to the calculation of prediction intervals for “new” cases as well as estimation of mean body mass and confidence intervals when a taxon provides more than one case for estimation. Models are evaluated through “leave one out” validation, simulations of extreme samples, and finally, application to two specific fossil hominin specimens, KNM-WT 15000 (Homo erectus) and LB1 (Homo floresiensis). The R and Rx statistics (Brown and Sundberg 1987), both of which are quadratic forms, result from calibration analyses and in this context quantify allometric and size departure of each of these hominins from the human reference material. Our results show that body mass estimation is possible for fossil hominins using a human reference sample because prediction intervals expand around individual estimates of body mass when the R statistic increases. The choice between Bayesian and maximum likelihood approaches can largely be based on the Rx statistic, as significant values for this statistic oblige us to argue against the Bayesian approach” (read more/not open access).

(Source: American Journal of Physical Anthropology, in press 2013; top image: johnhawks.net)

I first met S. J. Gould when he was a freshly minted Assistant Professor in Invertebrate Paleontology at Harvard and I a graduate student in evolutionary biology. Invertebrate Paleontology was well known then as a backwater in evolutionary biology, 80% devoted to the study of fossil foraminifera whose utility was that they predicted the presence of oil. In this environment, it was obvious that Gould would go far. New York City Jewish bright, verbiage pouring from his mouth at the slightest provocation, he would surely make a mark here.

This was not why I was visiting him. I had heard he was an expert in ‘allometry’—indeed had done his PhD thesis on the subject. Back then I wanted to know everything in biology, so I sought him out. Allometry refers to the way in which two variables are associated. It can be 1:1—the longer the fore-arm, the longer the total arm, or it can show deviations. For examples, the larger a mammal is, the more of its body consists of bone. Why? Because the strength of bone only goes up as the square of bone length whereas body weight goes up as the cube—thus larger bodies, weighing more, require relatively more bone. But what about antler size, I wanted to know, why is it that the larger the body size of the deer, the relatively larger his antlers? Why would natural selection favor that?

Gould leaned back in his chair. No, you have this all wrong, he said. This is an alternative to natural selection, not a cause of natural selection. My head spun. Natural selection was unable to change a simple allometric relationship regarding antler size that it had presumably created in the first place? Had it not already done so in adjusting bone size to body size? As I left his office, I said to myself, this fool thinks he is bigger than natural selection. Perhaps I should have said, bigger than Darwin, but I felt it as bigger than natural selection itself—surely Stephen was going for the gold!!

Many of us theoretical biologists who knew Stephen personally thought he was something of an intellectual fraud precisely because he had a talent for coining terms that promised more than they could deliver, while claiming exactly the opposite. One example was the notion of “punctuated equilibria”—which simply asserted that rates of (morphological) evolution were not constant, but varied over time, often with periods of long stasis interspersed with periods of rapid change. All of this was well known from the time of Darwin. The classic example were bats. They apparently evolved very quickly from small non-flying mammals (in perhaps less than 20 million years) but then stayed relatively unchanged once they reached the bat phenotype we are all familiar with today (about 50 million years ago). Nothing very surprising here, intermediate forms were apt to be neither very good classic mammals, nor good flying ones either, so natural selection pushed them rapidly through the relevant evolutionary space.

But Steve wanted to turn this into something grander, a justification for replacing natural selection (favoring individual reproductive success) with something called species selection. Since one could easily imagine that there was rapid turnover of species during periods of intense selection and morphological change, one might expect species selection to be more intense, while during the rest of the equilibrium stabilizing selection would rule throughout. But rate of species turnover has nothing to do with the traits within species—only with the relative frequency of species showing these traits. As would prove usual, Steve missed the larger interesting science by embracing a self-serving fantasy. Species selection today is a small but interesting topic in evolutionary theory, not some grand principle emerging from paleontological patterns.

Recently something brand new has emerged about Steve that is astonishing. In his own empirical work attacking others for biased data analysis in the service of political ideology—it is he who is guilty of the same bias in service of political ideology. What is worse—and more shocking—is that Steve’s errors are very extensive and the bias very serious. A careful reanalysis of one case shows that his target is unblemished while his own attack is biased in all the ways Gould attributes to his victim. His most celebrated book (The Mismeasure of Man) starts with a takedown of Samuel George Morton. Morton was a scientist in the early 19 th Century who devoted himself to measuring the human cranium, especially the volume of the inside, a rough estimate of the size of the enclosed brain. He did so meticulously by pouring first seeds and then ball bearings into skulls until they were full and then pouring them out and measuring their volume in a graduated cylinder. He was a pure empiricist. He knew brain size was an important variable but very little about the details (indeed, we do not know much more today). He thought his data would bear on whether we were one species or several, but in any case he was busy creating a vast trove of true and useful facts.

I love these people—they work for the future and gather data whose logic later generations will reveal. Precisely because they have no axes to grind or hypotheses to prove, their data are apt to be more reliable than the first wave after a new theory. I have benefitted from them in my own life, most memorably when I was shown a large and accurate literature on ratios of investment in 20 ant species, gathered long before anyone appreciated why these facts might be of some considerable interest, as indeed they were.

In any case, Morton grouped his data by population according to best estimates of gross relatedness, Amerindians with Amerindians, Africans with Africans, Nordic Europeans with Nordic, and so on. It is here, Gould alleged, that all sorts of errors were made that supported preconceived notions that among the smaller cranial capacity (and therefore stupider)) peoples would be Amerindians and Africans. For example, Gould claimed that Morton made more subgroups among Nordic people than tropical ones, thus permitting more of them to be above norm, but in fact, the opposite was true. Morton reported more Amerindian subsamples than European and routinely pointed out when particular Amerindian subsamples were as high or higher than the European mean, facts that Gould claimed Morton hid.

In other cases, Gould eliminates all samples with less than four individuals in order to reduce the number of sub-samples with only one sex—a statistically meaningless goal but one that happened to be biased in his favor and permitted him to make additional errors in his favor by arbitrarily eliminating some skulls while including others. If you are comparing group means, you may not wish to use means of less than four, but if you are adding up sub-samples to produce a larger sample, there is no reason not to aggregate all data. Morton is made to look careless and incorrect when it is really Steve who is arbitrarily biasing things in his own favor.

LOS ANGELES, CALIFORNIA—When Earth warms, mammals shrink. That’s what researchers found when they looked back 56 million years, during a time when global temperatures increased about 6° for a period of 20,000 years. Early horses, for example the now-extinct Hyracotherium (shown on the right next to a modern horse on the left), shrunk by about 30%, presumably to increase the ratio of skin area to body volume, and thus lose heat more easily. Now, scientists have found that this wasn’t a one-off event. At last week’s meeting here of the Society of Vertebrate Paleontology, another team of U.S.-based researchers looked at a slightly later but somewhat less severe warming period, which happened about 53 million years ago. Using molar size as a proxy for body size, the researchers looked at mammals in sediments from the fossil-rich Bighorn Basin of Wyoming. They found that the same thing happened: Mammals, including deer and small primates that resembled today’s lemurs, got small again, with horses like Hyracotherium downsizing by about 22% this time. In both cases, the animals rebounded to their previous sizes when the warming episode was over. Both this and the earlier warming episode were preceded by big increases in atmospheric carbon dioxide, similar to what we are seeing today. Time to get small, everyone?

Danielle Byerly/University of Florida

Ducks and Horses:

In an online Q&A session back in August, President Obama was asked, “Would you rather fight 100 duck-sized horses or one horse-sized duck?”

This question as answered by someone who actually knows the answer:

I feel it’s rather a shame Obama staffers neglected to consult me, as that question was, in essence, my PhD topic; I could have given the President better advice, and explained why his intuition—that a single giant duck would be an easier fight—is wrong, wrong, wrong.

It’s all about the allometry …

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Of mice, rats and men: Trabecular bone architecture in mammals scales to body mass with negative allometry

  • by Meir Max Barak, Daniel E. Lieberman and Jean-Jacques Hublin 

“Body mass (BM) in mammal species spans over six orders of magnitude. Although trabecular bone con- tributes to the mechanical properties of bones, we know much less about how trabecular bone scales with BM than about how cortical bone scales with BM. We therefore conducted a meta-analysis of the existing literature to test in rodents, humans and other mammals, predicted scaling properties between BM and several trabecular parameters: bone volume fraction (BV/TV), trabecular number (Tb.N), trabecular thickness (Tb.Th), trabecular separation (Tb.Sp), connectivity density (ConnD) and degree of anisotropy (DA). Our results show that BV/TV and DA are independent of BM and that Tb.N, Tb.Th and Tb.Sp scale with negative allometry relative to BM. Rodents appear to have relatively thicker and fewer trabeculae than humans, and we propose it that is due to a minimum thickness threshold ‘‘imposed’’ on mechanically functional trabeculae. Consequently, rodents (mice and rats) and humans demonstrate two distinct mechanisms to achieve variations in BV/TV. Although Tb.Th variation is the main contributing factor for differences in BV/TV in humans, Tb.N variation is the main contributing factor for differences in BV/TV in rodents. Our results also demonstrate no correlation between Tb.N and Tb.Th within each taxon (mice, rats and humans). Since rodents are a common animal model for research on bone bio- mechanics, the evidence that trabecular bone parameters scale and correlate differently in rodents than in humans suggests that care should be applied when extrapolating bone biomechanical results from small animals to large-bodied humans” (read more/open access).

(Open access source: Journal of Structural Biology 183:123-131, 2013 via Academia.edu; top image: Medical Pictures Info; middle image: Lawrence Livermore National Laboratory)

In an online Q&A session back in August, President Obama was asked, “Would you rather fight 100 duck-sized horses or one horse-sized duck?” The Atlantic wrote a cheerful article about Obama’s choice (horse-sized duck), but the biologists they hastily recruited as fact-checkers were obviously operating outside their specialty. I feel it’s rather a shame Obama staffers neglected to consult me, as that question was, in essence, my PhD topic; I could have given the President better advice, and explained why his intuition—that a single giant duck would be an easier fight—is wrong, wrong, wrong.

Some exploratory scatterplots showing the relationship of tree height measurements with tree diameter measurements.  These data were collected in plots at ICESat-GLAS LiDAR footprints in sparse Siberian larch forests.

Tree heights are derived through either a trigonometric technique, a laser rangefinder, an empirical model, or a direct estimate from an observer.  Scatterplots are faceted according to year of field collection and LiDAR campaign.

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Effects of allometry, productivity and lifestyle on rates and limits of body size evolution

  • by Jordan G. Okie, Alison G. Boyer, James H. Brown, Daniel P. Costa, S. K. Morgan Ernest, Alistair R. Evans, Mikael Fortelius, John L. Gittleman, Marcus J. Hamilton, Larisa E. Harding, Kari Lintulaakso, S. Kathleen Lyons, Juha J. Saarinen, Felisa A. Smith, Patrick R. Stephens, Jessica Theodor, Mark D. Uhen and Richard M. Sibly

“Body size affects nearly all aspects of organismal biology, so it is important to understand the constraints and dynamics of body size evolution. Despite empirical work on the macroevolution and macroecology of minimum and maximum size, there is little general quantitative theory on rates and limits of body size evolution. We present a general theory that integrates individual productivity, the lifestyle component of the slow– fast life-history continuum, and the allometric scaling of generation time to predict a clade’s evolutionary rate and asymptotic maximum body size, and the shape of macroevolutionary trajectories during diversifying phases of size evolution. We evaluate this theory using data on the evolution of clade maximum body sizes in mammals during the Cenozoic. As predicted, clade evolutionary rates and asymptotic maximum sizes are larger in more productive clades (e.g. baleen whales), which represent the fast end of the slow– fast lifestyle continuum, and smaller in less productive clades (e.g. primates). The allometric scaling exponent for generation time fundamentally alters the shape of evolutionary trajectories, so allometric effects should be accounted for in models of phenotypic evolution and interpretations of macroevolutionary body size patterns. This work highlights the intimate interplay between the macroecological and macroevolutionary dynamics underlying the generation and maintenance of morphological diversity” (read more/open access).

(Open access source: Proceedings of the Royal Society B 280(1764), 2013: 20131007; top images: Shingleton, A. 2010. "Allometry: The Study of Biological Scaling,“ Nature Education Knowledge 3(10):2)