Avoid the Noid… I mean Noise

As alluded to yesterday, my dissertation compares growth in an extinct animal with growth in living humans; this study is necessarily cross-sectional, meaning that it examines individuals at a single point in time. Alternatively, longitudinal data sample individuals from several points in time. So for instance if I constructed a growth curve by measuring the stature of a bunch of people of different ages in just a day, that would be cross-sectional. But if I had the time and wherewithal to measure some people’s heights once a year from birth to adulthood, well that’d be longitudinal. Cross-sectional data lack the resolution of longitudinal data, whereas longitudinal data can be prohibitively difficult to collect (such as in long-lived, slow-maturing animals like humans, or in extinct animals like Australopithecus robustus).

Some researchers abhor cross-sectional data, pointing out that the intricacies of individuals’ longitudinal growth will not be adequately captured in with cross-sectionally. American anthropology founder Franz Boas himself discussed this in a paper nearly 82 years ago. Anyway, I was reminded of this dichotomy today when perusing a paper that examined longitudinal brain activity in a cohort of adolescent kids (right, from Campbell et al. in press). The mess of jagged lines are individuals’ measurements from age 9-18, and the smoothed blue and red curves are the cross-sectionalized curves calculated from these kids. Oy, look at all that variation and caprice that gets left out in the cross-sectionalized curves!

Of course, this doesn’t mean that we should never use cross-sectional data to study growth – like I’d mentioned above, the fossil record necessitates a cross-sectional approach to the study of growth. As always, you have to understand and acknowledge the limits of your data.

ResearchBlogging.orgRead on
Boas, F. (1930). OBSERVATIONS ON THE GROWTH OF CHILDREN Science, 72 (1854), 44-48 DOI: 10.1126/science.72.1854.44

Campbell, I., Grimm, K., de Bie, E., & Feinberg, I. (2012). Sex, puberty, and the timing of sleep EEG measured adolescent brain maturation Proceedings of the National Academy of Sciences DOI: 10.1073/pnas.1120860109


Updated note on jaw growth in Australopithecus robustus

A few weeks ago I posted some early observations I’ve made about mandible growth in Australopithecus robustus compared with humans. My dissertation tests the null hypothesis that overall mandible growth is identical in the two species. This is complicated by the fact that there are many aspects of jaw growth (i.e. lots of variables) and not all fossils preserve the same parts. In these early preparatory stages I’m looking only at the height and width of the jaw at the second baby molar (in kids) and the second permanent premolar that replaces this baby tooth in older individuals, since this is something most of the fossils have. This work will get me ready for the hard comparisons, where the fossils aren’t so kind.

One concern I had in the earlier post was that my human sample was (and still is) fairly small, making comparisons rather tentative. Since then, I have about doubled my human sample (but I still have lots of work to do), so it’s timely to see if my earlier observations have held up. AND THEY DO!

To the right is a plot of jaw height at said tooth position across the growth period, humans being the black circles and A. robustus the thick red ones. Note that measures are standardized, taken relative to the smallest (not necessarily the youngest) individual in each sample. Before, I’d found that the two samples overlapped up to dental stage 4 (when the first permanent tooth comes in). After this point, the A. robustus jaw gets much larger through early adulthood, whereas in humans the height increase isn’t so drastic. With a larger sample, there is a bit more overlap in relative jaw height (especially early on), but the overall result is the same as I found earlier. Neat!

To the left is a similar plot, this time looking at width of the jaw across the growth period (these are also size-standardized as above, colors are the same). What’s remarkable is that the width of the human jaw is pretty much the same from infancy to adulthood. I remember thinking this when I first started looking at human jaws early last summer, but I’d never looked at how they compare with A. robustus, whose jaw continues to increase in absolute and relative width with age (and possibly even through adulthood; Lockwood et al. 2007). This plot is admittedly a bit confusing, as sizes are measured relative to the smallest and not youngest individuals, and the narrowest human jaw is in dental stage 4. The A. robustus sample also includes a very old adult (the highest point on the plot) while the human sample only goes to early adulthood. But the basic patterns are still pretty different: A. robustus jaws get wider up to dental stage 5 (you could think of it as pre- or early adolescence) then level out (not including our large older adult), but humans’ average jaw width is fairly constant throughout ontogeny. Of course, this is at only one position along the jaw, and others will probably different.

The fragmented jaws of the youngest A. robustus (i.e. SK 63 and SK 438) do not look too different from their human counterparts, but adults are very different. Here we can see part of the reason why. Bear in mind, though, that other aspects of mandible shape do differ between these species from birth. For example, humans have a bony chin from infancy, whereas A. robustus always lacks a true chin (SK 74 is an older, probably female adult A. robustus that does have a rather anomalous “chin” but it is not homologous to ours). Not all aspects of species-specific mandible shape arise during postnatal growth!

But there you go, an enlarged human sample produces a result consistent with my earlier observation. Note that these pictures do not represent statistical tests of my hypothesis! Yes, a visual inspection of the plotted numbers suggests the two species differ in how jaw height and width grows. But saying something statistical and “definitive” is difficult. In terms of height, growth does seem pretty much the same during childhood, but then divergent later on. Width growth in the two species seems totally different. To further complicate things, a “shape” ratio of jaw width divided by height (not shown) suggests parallel (but not identical) growth trajectories in the two species. What do these observed differences mean for the null hypothesis? Which and how many variables can differ before I can feel confident about whether to reject the hypothesis? Oy, I have my work cut out for me. Stay tuned!

That paper I referenced
Lockwood, C., Menter, C., Moggi-Cecchi, J., & Keyser, A. (2007). Extended Male Growth in a Fossil Hominin Species Science, 318 (5855), 1443-1446 DOI: 10.1126/science.1149211

Data, development and diets

As mentioned briefly but repeatedly on this blog, my dissertation is about growth of the lower jaw in Australopithecus robustus (right), comparing it with jaw growth in recent humans. This is important because we don’t really know exactly how skeletal-dental (especially skeletal) maturation of our fossil relatives compares with us today. From a developmental perspective, it is also important to know how and when adult form arises during growth, and how these processes vary within and between species.

It’s not easy to examine ontogeny in fossil samples. In a post a few weeks ago I included a drawing of some of the A. robustus juvenile jaws. At the time, I was pointing out variation in dental maturity (which is a nice thing when studying growth), but the picture also reveals a bigger bugbear – variable preservation of features (which is a terrible thing if you’re trying to study growth).

For example, the youngest individual in the fossil sample (right, viewed from above, front is at the top of the picture) includes only the second baby molar tooth, a bit of the bone surrounding the sides and back of the tooth, and a small portion of the ascending ramus. The oldest subadult in the sample (SKW 5), on the other hand, is almost entirely complete. In between these ages, jaws variously preserve different parts. Under these circumstances (i.e. lots of missing data), growth cannot be studied by traditional (namely, multivariate) methods (how I will deal with this is a topic for another day).

So while studying the fossils in South Africa, in order to maximize the number of comparisons I could possibly make, I measured just about every single linear dimension conceivable on these jaws. I thus have a spreadsheet with 300 columns of measurements I could take on each specimen. Most of the cells are empty : (

What’s a boy to do?! In order to compare A. robustus with humans, I need to take the same measurements on a growth series of human jaws, too. But life is short, and if I want to finish this project before I succumb to some sinister signature of senescence, I really can’t take hundreds of measurements on a human sample which is much larger than the fossils. Plus, a lot of the individual measurements are a bit redundant: some of the distances overlap, many of the variables can be taken on the right and the left sides, etc.

If I am to finish collecting data in a reasonable time frame, I need to cull my variables from 300 to however many (a) maximizes the comparisons I can make within the less-complete A. robustus sample, and (b) are not too repetitive. Boo. Plus I have to get these spreadsheets ready to be read and analyzed in the program R, which for whatever reason is always a pain in the ass.

Again, the statistics of the overall comparisons is a topic for another day, and I haven’t had the opportunity yet to write the analytical program(s). But I have looked at some individual traits in A. robustus compared with a subsample of humans. For example, at the left is a plot of changes in height of the jaw at the baby second molar or adult second premolar (which replaces the baby molar). Obviously my human sample is way to small at the moment to make any really meaningful statements about how growth compares between the two species. Note also that these are absolute measures and not size-corrected, and that these are stages of dental eruption rather than chronological ages. But from this preliminary view, the two species are very similar up to around when the first adult molar comes in (“stage 4” here). Thereafter, the A. robustus individuals dramatically increase in size rather fast, whereas humans only slowly increase in size.

Again, this is a very preliminary result, and only for a single measurement. But it is interesting in light of a recent study by Megan Holmes and Christopher Ruff (2011). These researchers compared jaw growth recent humans who differed in the consistency of their diets. They found that kids in the two populations were not too different, but the samples became more different with age to become fairly different as adults. Now, A. robustus seems to have eaten a diet with lots of hard objects (see recent review by Peter Ungar and Matt Spohneimer), but humans’ diet (and technology) really obviates the need for chewing as powerful as seen in A. robustus. So this dietary divergence may well be reflected in the growth difference suggested above, but it may not be the sole factor. PLUS I NEED TO INCREASE MY HUMAN SAMPLE.

Stay tuned for more analyses and results!

ResearchBlogging.orgReferences to make you smarter and stronger
Holmes, M., & Ruff, C. (2011). Dietary effects on development of the human mandibular corpus American Journal of Physical Anthropology, 145 (4), 615-628 DOI: 10.1002/ajpa.21554

Ungar, P., & Sponheimer, M. (2011) The Diets of Early Hominins. Science 334(6053), 190-193. DOI: 10.1126/science.1207701  


I’m going to do my best to keep up with the blog during by Big Summer Adventure, and one thing I’d like to do is “F-ing Fossil Friday!” in which I focus on fossils for a bit. We’ll see if I can make this pan out.
Today I got out the rest of the Australopithecus robustus mandibles at the Transvaal Museum (above), save for I think maybe 1. As you can see from the picture, taphonomy (what happens to an animal’s remains between death and our digging them up) creates a serious challenge for the study of variation in this species. I’m focusing on ontogenetic variation – differences associated with growth and development. In spite of its fragmentary nature, so far as I know this is the best ontogenetic series of any fossil hominid (I should probably look more into A. afarensis here, too). In the bottom left you’ll see SK 438, the youngest in the sample, whose baby teeth haven’t quite come in all the way. Poor little guy! At the top right corner is SK 12, probably the oldest individual and also a big bugger.
One thing that I’ve noticed so far, only a preliminary observation that I need to actually run some numbers on, is that as individuals get older, the length of their tooth row (molars and premolars) gets shorter. This is because of the tendency for teeth to move forward during growth – “mesial drift” – and for adjacent teeth to literally wear into one another, their ends becoming flatter and flatter. While I should have realized this, it was surprising at first to find some dimensions of the lower jaw actually decreasing during growth. Now, I still have to run some tests to see if this is a biologically significant phenomenon. But it’s always nice to learn something new, even after just 2 days back with my best extinct buddies.
Stay tuned to future eFfing fossil Fridays!

Good olde dentistrie

I’m reading up on mandibular rotation, which is the change in orientation of the mandibular corpus relative to the rest of the skull during growth (the corpus is the horizontal part of your jaw that holds up your teeth; check out the shape changes in the mandibles in the blog header). So far as I can tell, the original classic paper on the topic is by Bjork (1955). Growth was studied by implanting metal pins into the jaws, then seeing how they move across ontogeny via X-rays (which were once called “roentgenograms,” neat-o!) Here’s a picture of the procedure, from Bjork (1955):
HOLY GOD WHAT DID THAT KID DO TO DESERVE THIS?! And although there must be a third person there, it sorta looks like there’s a three-handed dentist wielding a hammer, a nail, and a kid’s face. No wonder so many people are afraid of the dentist.
BJORK A (1955). Facial growth in man, studied with the aid of metallic implants. Acta odontologica Scandinavica, 13 (1), 9-34 PMID: 14398173

Growing a Homo erectus kid, sort of

A paper, given at this year’s Physical Anthropology meetings, was just published online in the Journal of Human Evolution, with a re-evaluation of the height and possible growth pattern of a subadult skeleton of Homo erectus (KNM-WT 15000, aka “Nariokotome boy,” aka “Stripling youth”). When initially described, it was estimated that this young chap would gave grown to be around 6 feet tall. However, controversy around the skeleton’s age at death and probable growth pattern have made this quite a contentious topic. In the recent paper, Ronda Graves and colleagues used a South African human growth pattern and a pattern from “naturally-reared captive” chimpanzees to devise a series of intermediate growth patterns that might have characterized H. erectus. Using the pattern they felt most likely reflected the Nariokotome skeleton’s estimated life history parameters, the authors estimate the potential adult height of the youth to have been closer to about 5′ 4″.

All I’d like to say about this is that deciding how tall a subadult skeleton like this would have grown to be is inherently tricky. First, the individual’s height when he died has to be estimated, and this will always be an estimate, so there’s one level of error there. Next, in order to determine the duration of growth remaining had he lived, one must estimate the skeleton’s age at death. This has been debated for the Nariokotome skeleton, because the pattern of tooth eruption and tooth enamel formation seem to point toward an age of around 8-10 years; but the pattern of long-bone closure suggests an age closer to 13 or so years. If anything, this means we cannot assume a ‘human-like’ or ‘chimpanzee-like’ pattern of skeletal and dental development for H. erectus. But our final step in figuring out how tall this kid would’ve been is to use the previous 2 estimations to infer how much longer, and at what rate, he would have grown. Crap.
The authors tried to circumvent this issue by averaging/modifying the human and chimpanzee mathematical growth curves. The curves themselves come from averages of respective species samples, which then were combined (sort of like averaging) to create intermediate growth curves. They then also multiplied the intermediate curves by various constants, in attempt to model different life history patterns in the growth curves. Incidentally, one of these ‘altered life history’ models provided their preferred height estimate of 5′ 4″. I think this is a clever and interesting way to tackle the question of how to estimate height from fossils; but I think it’s important to bear in mind how far-removed from both their models they had to get to do this. How many assumptions and potential sources of error should be permissible? Are there any biological constraints that might actually render a human-chimp average growth pattern to be unrealistic? I dunno!
Anyway, an interesting paper, and with a pretty good literature review, too. As stated above, the model they preferred gave a much shorter height than traditionally accepted for this individual. The model (and so H. erectus) also lacks a modern human-like growth spurt, which this specimen would have ‘needed’ to attain a tall adult height like has been traditionally thought. Other researchers have used the cranial remains to argue that Nariokotome kid would have had a good amount of growth left to have a more characteristically H. erectus-like skull, though it is unclear if this necessarily means an adolescent growth spurt. So, this was a very interesting and thorough study, but I’m sure it’s not the last we’ll hear about growth and development in H. erectus.
The paper
Graves RR, Lupo AC, McCarthy RC, Wescott DJ, and Cunningham DL. Just how strapping was KNM-WT 15000? Journal of Human Evolution, in press.