Monday, April 5, 2010

Human Brain Evolution - a clear kink

Jerry Coyne has discussed human brain size evolution a couple of times recently, the latest one here.

Anyway, I grabbed the data from Lee and Wolpoff (2003) ("The pattern of evolution in Pleistocene human brain size", Paleobiology, 29(2), 2003, pp. 186–196), read it into R and looked at log brain size (since linear trend on the log scale corresponds to constant percentage growth). If there was a sudden jump in growth rate, it should show as a kink.

I then used the lowess function (which is a form of locally-linear regression) in R to smooth the data, to hopefully identify any such kinks and see where they fell. I used the default value of the smoothing parameter (f = 2/3). I then tried a range of other f-values, and all values between roughly 0.5 and 0.8 (a fairly wide range, so the conclusion is robust to the smoothing parameter) give very similar-looking fits, and a clear kink at the same x-value:

The smooth shown in green here is for f = 0.8

(Click the image for a larger version)

With this analysis, the kink plainly appears at 300 thousand years ago (but the ages of the observations are approximate and subsequently rounded).

There does seem to have been a substantial acceleration in growth in brain volume approximately 300 thousand years ago.

Edit: Here's a link to a somewhat related article at Panda's Thumb from some years ago, based on a different paper. Much of the data is the same, but contains additional information.


Cujo359 said...

It's an interesting idea that something happened roughly 250kya that changed us. That Nova special did a bit of speculating on something about then. I'll have to look at it again.

OTOH, there are few data points per time period on the left side of the 300kya line. Could it be sampling error?

Efrique said...

That there's a kink at all, no.

That is to say, the chance that a process whose underlying population mean (of log-brain-volume) growing at essentially a constant rate over time would produce the appearance of such a dramatic kink (given the sample sizes and ages of the fossils involved) is extremely small.

I could demonstrate this in a variety of ways.

However, if you're asking if there could be sampling error in the estimate of the location of the kink we get from a local linear fit, then absolutely. Indeed, even by a cursory visual examination, I can identify a few points that will have some influence on the location of the kink - move them each up or down a bit (which you can imagine as corresponding to the scenario "we simply found a different fossil in that time period") and the location of the kink might shift left or right as much as to the adjacent age (if I do some algebra I can actually calculate the senistivity of the kink to the point locations).

Add to that, I have treated the ages as all known. In fact the dating methods all carry a small error, so there's uncertainty there, which impacts things in a host of ways and which I have conveniently ignored.

So the location of the kink could easily be earlier or later - but unless there's some systematic bias in the data (which somehow deflates brain volume measurements at middling ages relative to early and late ages, for example), then I have little doubt there's a kink there.

Efrique said...

It occurs to me that that comments sounds like it contradicts my dicussion in the original post.

So let me clarify:

The location of the kink given the data values is not sensitive to how much smoothing we do.

However, the location of the kink given the amount of smoothing that was done will be somewhat sensitive to the particular data values; I haven't actually calculated it to the extent of being able to give some kind of error bars on the location of the kink (though I know ways to do that), but from looking at the data it seems as though it would be plausible for it to be something like 50K-100K years.

Given the relative sparsity at older ages, the potential error out the "old" side would probably be larger than the young side.