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Size, shape, and microcephaly

home :: fossils :: flores :: falk_2007_microcephaly_shape_flores

I've been taking quite a lot of notes while studying last week's paper by Dean Falk and colleagues.

The lede in all the articles about Falk and colleagues' paper is that they show that LB1's endocast is normal. But is it?

As Ralph Holloway and colleagues (2006) have noted, LB1 is not the same shape as an average-sized human endocast. It has strange protrusions in Brodmann's area 10 of the prefrontal cortex, it is very flat from top to bottom (platycephalic), it has an unusual proportion of cerebellum to neocortex, and it is quite asymmetrical. There seems to be no substantive disagreement about these features. These features do not show that LB1 had any of the spectrum of microcephaly disorders. But they do show that it's abnormal, at least in the context of modern humans.

In their supplementary material, Falk and colleagues show that the frontal lobes of microcephalics generally have a flattened orbital surface. In other words, they don't project downward into the space between the orbits so much. LB1 does not share this flattening -- it is like normal humans in this anatomy. I think this is an important observation, though it is not entirely clear how diagnostic it is for microcephalics.

But the main evidence in the paper relates to their use of a discriminant function to classify LB1:

As shown here, the frontal breadth relative to cerebellar width and lack of cerebellar protrusion of LB1's endocast classify it with 100% probability with normal H. sapiens rather than microcephalics (2516).

Them's strong words. Like most biological anthropologists, I have some experience with discriminant functions. It can be easy (although certainly not always!) to get highly significant statistical results, when the original samples are small as they are in this study. Small samples by chance exclude much of the variation that makes classification errors apparent.

So I looked carefully at the details of the discriminant analysis in this paper. I'm not so convinced they've shown the skull is "normal". I think that another way of looking at the same data makes the endocast look even more unusual.

Falk et al. (2007) do a great job of describing their methodology and include the StatSoft output for the discriminant function in their supplementary materials, as well as figures showing the distribution of each ratio in their samples. So we can make some progress interpreting exactly how the discriminant function came to its result.

The statistical analysis will require a bit of explanation for many readers. Here is the relevant text from the paper's methods section:

Discriminant and canonical analyses were used to study shape differences between virtual endocasts of microcephalic humans (n=9) and normal humans (n=10). For these analyses, we used the four ratios that we thought would discriminate between the two groups (2/1, [2Ð 4]/1, 6/5, and 8/6) (Fig. 2). Data were tested for normality with Shapiro-Wilk W tests, and the homogeneity of the variances and covariances was tested with a Box M test. Backward stepwise discriminant analysis was used to select the most powerful discriminators (SI Table 4). For the stepwise procedure, the F to enter was set at 4; F to leave was set at 3; and the tolerance was set at 0.01. Each discriminator plus the combination of the most powerful discriminators was used to classify each case into the group that it most closely resembled. In addition, LB1, the Basuto woman, and a human dwarf (which were not used to develop the discriminant and classification functions) were classified into the two groups. Posterior classification of cases was based on Mahalanobis distances, with a priori probabilities being proportional to group sample sizes. Data analyses were performed with JMP Statistical Software Release 5.0.1.2 and STATISTICA (data analysis software system, Version 7.1; StatSoft, Tulsa, OK). Scatter plots for the four variables that were analyzed are presented in SI Fig. 5. The data were normally distributed (ShapiroÐWilk W test, P >0.05), and the variances and covariances were homogeneous across groups (Box M test, P 0.05) (Falk et al. 2007:2517).

StatSoft has helpfully posted an online guide to their discriminant analysis procedures, which is really useful if you want an overview of the assumptions and methods.

Why these ratios?

Falk and colleagues chose to examine four ratios for their discriminant analysis, the ones they "thought would discriminate between the two groups."

To me, this is unclear. The difference between microcephalic and normal endocasts is entirely plain -- the two groups can be separated easily by their size. For various reasons, this highly discriminating variable has been considered unsatisfactory for classifying LB1. It is therefore of interest to see whether microcephalic endocasts share any other distinguishing characteristics besides their small size.

There is an obvious problem to overcome -- every linear measurement of the endocast is positively correlated with overall endocast volume. Any of these linear measurements individually would distinguish microcephalic from normal endocasts, because of the large size difference between the two samples. Like endocast volume, every one of these measurements would place LB1 with the microcephalics.

It is unlikely that a ratio would remove the correlation with size, since different brain regions and linear measures of them scale with different allometries. In particular, if we are searching for ratios that can distinguish microcephalic (i.e., small) and normal (i.e., big) skulls, such ratios will necessarily be correlated with size, by the sheer fact that the two groups are defined by their sizes.

Yikes!

There is no adequate resolution of this dilemma. The question about LB1 is whether it is a "normal shape" for an endocast of extremely small size. But normal-sized humans are not the appropriate sample for such a comparison, because no matter what shape we expect a "normal" endocast of LB1's size to be, it is probably not the shape of an average-sized human endocast.

So why did Falk and colleagues choose to report these four ratios? The paper doesn't give any clue. Each of the four gives a good discrimination between the two groups, as the scatterplot shows:

Supplementary figure 5 from Falk et al. 2007. These are scatterplots of the four ratios examined in the discriminant analysis. Notice that all the ratios are good separators for the microcephalic and normal human samples.

The reason why each ratio is a good discriminator is pretty obvious -- all of them are correlated with size! Apparently, cerebellum size scales with brain size at a negative exponent (as described below, cerebellar size is featured in all four ratios in one way or another) and frontal lobe size scales with a positive exponent (which features in plots B and D). Both these volumetric observations are true not only between normal and microcephalic humans, but also across different primate species.

So it seems pretty counterintuitive that a very small endocast like LB1 should look "normal" on these ratios. We should temper the "normal" a bit after looking at the scatterplots, though -- it seems that LB1 is really only "normal" on one of them, if "normal" means inside the range of the normal human sample and outside the range of the microcephalic sample.

The discriminant function attempts to find which of these ratios, combined together, best separate the normal and microcephalic groups. The analysis doesn't evaluate whether the measurements entered were the best for this purpose. Without the full dataset, we can't answer that question either.

But we can examine the four ratios used here, to see if they make biological sense for the purpose of classifying the groups. For a good discriminant function, we should try to choose variables that are as independent as possible -- because highly correlated variables give the same information again and again, and the analysis will reject them anyway. One way to get measurements that give more information is to employ measurements from different regions of the endocast. If we enter a broad range of different variables, the function will work for us to find the ones that best discriminate the groups. The analysis provides a significance test -- if it tells us that one region of the endocast is the crucial region for distinguishing two groups, then that is a really informative result.

Do these four ratios accomplish that goal? Let's take the ratios two at a time.

The relative frontal breadth problem

"Relative cerebellar width" is the breadth of the cerebellum divided by the maximum breadth of the endocast. "Relative frontal breadth" is the breadth of across the frontal lobes divided by the breadth of the cerebellum. Both ratios include the single measurement, cerebellar breadth, and so are likely to be strongly correlated with each other. A glance at the figure shows that the data scatter for each is basically an inverse of the other -- cerebellar breadth occurs as the numerator of one ratio, and the denominator of the other. In other words, the two ratios measure the same thing. It is therefore no surprise that one of them should quickly be eliminated from the stepwise discriminant.

What is a mystery to me is why the ratio of "relative frontal breadth" was defined relative to the cerebellar breadth instead of the maximum breadth. If it is true, as the scatterplot might suggest, that the microcephalics have disproportionately small frontal lobes, this should be evidenced relative to the rest of the neocortex. The ratio measured by Falk et al. confounds the breadth of the frontal lobes with the breadth of the cerebellum -- which we have other reasons to think might be large relative to brain size in microcephalics.

OK, so two of the ratios basically replicate the same observation -- relatively broad cerebella in microcephalics. That leaves us with three semi-independent ratios.

The relative length of the posterior base problem

The other two ratios present the same problem. Falk and colleagues (2007) define two parallel lines across the endocast: First is the line segment between the front-most (rostral) point of the endocast (frontal pole) and the backmost point on the occipital lobe (occipital pole). This is the cerebral length. The second is the line segment parallel to the cerebral length, passing through the backmost (caudal) point on the cerebellum (cerebellar pole). This is the cerebellar pole - projected frontal pole length. The intent is to show how much the cerebellum sticks out behind (or is tucked underneath) the neocortex.

The ratio (projected cerebellar pole length to cerebral length) is the "cerebellar protrusion" ratio. It is greater than one when the cerebellum "sticks out" behind the cerebrum; it is less than one when the cerebellum is tucked underneath the cerebrum. So this may measure the relative size of the cerebellum, if larger cerebella tend to protrude. It may also measure the angulation or "flexion" of the cranial base, if some endocasts are more tightly packed or bunched together than others.

UPDATE (2/7/2007): * I should point out that the LB1 endocast does not have a "cerebellar protrusion" of greater than one -- it's cerebellum doesn't actually protrude, nor do some of the microcephalics. The difference is that the ratio is higher in these than in normal humans. *

The "relative length of the posterior base" also uses these two measurements. Instead of simply dividing the projected cerebellar pole length by the cerebral length, it first subtracts the parallel length from the temporal pole (the most rostral point on the temporal lobe) to the frontal pole. This is not the same as the length of the frontal lobe, but it seems to mostly reflect the length of the frontal lobe. Shorter frontal lobes will generate a higher relative length of the posterior base.

If this sounds complicated, well, it is -- it's the sort of measurement you would never take unless you had a CT scan to compute all these parallel lines and projections. That's not a mark against it; it's just an explanation for why it takes so many words to describe it.

Now, the two ratios (cerebellar protrusion and relative length of the posterior base) are entirely identical except that the latter involves subtracting the frontal lobe length (or more correctly, a quantity strongly correlated with frontal lobe length). It is therefore obvious that they will be highly correlated.

OK, so we don't have three semi-independent ratios. We only have two.

Discriminating tastes

Every one of the four ratios is a good classifier. This is probably because each of them is correlated with endocast volume, just like any linear measurement would be. The use of ratios tends to reduce correlations with size, but doesn't eliminate them -- usually because the underlying linear measurements follow different allometries. Since the definition of microcephalic and normal groups is based on their size, it follows that any measure that can discriminate the groups must be correlated with size, at least within our sample.

The discriminant function reported in the paper is based on only two of the ratios. The analysis evaluates the correlations among the variables and eliminates those variables that do not contribute significantly to discrimination. In this case, one of each of the pairs of partly redundant variables was removed. That makes sense: almost all their information is already present in the other two ratios.

That means that if we chose the excluded variables instead of the ones the function included, we would do almost as well in distinguishing normal from microcephalic. The plots make that very clear -- choose relative cerebellar width and relative posterior base length for the function, and it will still assign the normal and microcephalic endocasts correctly. It just doesn't make very much difference. The reason why cerebellar protrusion and relative frontal breadth were included instead of the other two is that they explain a slightly greater amount of the between-group variance. In other words, they might make a difference if we tried to classify 200 skulls with the same means and variances instead of 20.

Nor does it make much difference to the classification of LB1. Both the relative cerebellar width and the relative frontal breadth (both partially redundant) would place LB1 with the normal group. In fact, it is beyond the normal group for relative cerebellar width, and beyond the normal mean for relative frontal breadth.

Wait a second. These two ratios are only different because frontal breadth is substituted for maximum endocast breadth. Yet the placement of LB1 relative to the normal group is highly extreme for one and less extreme for the other (frontal breadth). From this, we can infer (even if we can't see a scatterplot) that LB1 has a relatively narrow frontal lobe compared to its maximum breadth. Falk et al. (p. 2516) wrote as much, noting that the LB1 frontal breadth compared to its maximum breadth was similar to Homo erectus. But "similar to Homo erectus" also means "similar to microcephalics.

What we have here (judging from the ratios) is an endocast that looks like modern microcephalics. It's cerebellum protrudes posteriorly like a microcephalic. It has a narrow frontal lobe like a microcephalic. It has a relatively short frontal lobe like a microcephalic. There's only one exception: it has a narrow cerebellum.

What to call a abnormally normal abnormal skull

Let's review: it is very easy to discriminate microcephalic and normal skulls by size. Every measure or ratio that distinguishes microcephalic and normal skulls will necessarily be related to size, because size defines the groups. A small set of four ratios led to a discriminant function that could classify normal and microcephalic skulls. This discriminant classifies LB1 as "normal". All of the ratios involve the size of the cerebellum.

I think the observation here is that LB1 is abnormal for its size. Its cerebellum is relatively narrow (compared to brain width) but slightly elongated. This change in shape is what the ratios capture.

Why should the shape of the cerebellum be unusual in LB1? One explanation is that it isn't -- instead the shape of the neocortex is unusual. In particular, the neocortex is unusually flattened (Holloway et al. 2006). This means that for its small volume, the cerebral breadth is relatively broader, making the cerebellar breadth appear to be relatively short.

Another explanation is that the developmental alteration leading to small brain size in LB1 occurred in a pathway that affected cerebellar size more than is typical for microcephalics. It is not impossible that this alteration was favored by selection in a population of humans on Flores, but the current evidence cannot demonstrate this. We can just as easily propose that the developmental alteration was a distinctive form of microcephaly not fully captured by the present sample. However, the close similarity of LB1 to microcephalics in most measures hardly weighs against the hypothesis that its brain size was simply pathological.

In other words, LB1 is abnormally small, abnormally shaped, and abnormal in comparison with other human endocasts of comparably small size. Can this combination of measurements mean that the endocast really is normal after all? I don't think that a triple negative makes a positive.

Unfortunately, none of these considerations really address the core question, which is whether LB1 had a brain size representative of its population. In fact, I don't think there is any way to answer that question without finding more skulls, because LB1 does show clear evidence of pathology.

References:

Bush EC, Allman JM. 2004. The scaling of frontal cortex in primates and carnivores. Proc Nat Acad Sci USA 101:3962-3966. doi:0.1073/pnas.0305760101

Falk D, Hildebolt C, Smith K, Morwood MJ, Sutikna T, Jatmiko, Saptoro EW, Imhof H, Seidler H, Prior F. 2007. Brain shape in human microcephalics and Homo floresiensis. Proc Nat Acad Sci USA 104:2513-2518. doi:10.1073/pnas.0609185104

Holloway RL, Brown P, Schoenemann PT, Monge J. 2006. The brain endocast of Homo floresiensis: microcephaly and other issues. Am J Phys Anthropol 129 (supplement):105.

T. Jacob, E. Indriati, R. P. Soejono, K. Hsü, D. W. Frayer, R. B. Eckhardt, A. J. Kuperavage, A. Thorne, and M. Henneberg. 2006. Pygmoid Australomelanesian Homo sapiens skeletal remains from Liang Bua, Flores: Population affinities and pathological abnormalities. Proc Nat Acad Sci USA. PNAS published August 23, 2006, 10.1073/pnas.0605563103

Martin RD, MacLarnon AM, Phillips JL, Dobyns WB. 2006. Flores hominid: new species or microcephalic dwarf? Anat Rec 288A:1123-1145. doi:10.1002/ar.a.20389

Posted at 09:18 on 02/07/2007 | permanent link

Read other posts in /fossils/flores

John Hawks
Department of Anthropology
University of Wisconsin—Madison
Copyright © 2007 John Hawks