Size, shape, and microcephaly

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, [2 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 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 (ShapiroWilk W test, P >0.05), and the variances and covariances were homogeneous across groups (Box M test, P

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.


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