This post now includes an additional comparison of these authors' results at the 80% probability level, which is a much more generous statistical regime than the 99% that I originally proposed, which remains in the text. Together these calculations pretty much nail the coffin shut [provisionally] on the notion of big eyeballs and latitude. Here beginneth the original lesson.
Back out on the limb I go...
It isn't often that I seek to disparage the work of people I know and of whom I'm fond [not necessarily, but frequently, mutually exclusive subsets of humanity]. So, I won't do it today, either. But I do want to query the authors of two papers having to do with the Neanderthal eyeball, one of which was published yesterday. [Was it only yesterday? Seems like I've been thinking about these two for way longer than that. Ah, well. On we go.] Get out your slide rule ... erm ... graphing calculator. [By the way, did you know that the iPhone calculator is just like a regular number pad in portrait, but it switches to a scientific calculator when you turn the phone to landscape mode???? I think that's way kewl. What's that you say? "Small things amuse small minds." What's your point?] Grab your calculator, and hold on!
Yesterday's publication is
In the graph below you see that orbital volume varies between about 22 ml and 27 ml [roughly 27 cubic centimetres (cc)]. The samples were drawn from 12 populations at different distances from the equator. A scatter plot of orbital volume against latitude shows that the further away from the equator one lives, the larger one's eyeballs will be. Someone living at about 65 degrees north latitude has the largest eyeballs. Ahh. But there's more to this comparison than *cough* meets the eye, as I'll explain on the other side of this graph.
The authors attribute this variability to microevolutionary adjustments to varying levels of ambient light, which, they say, becomes dimmer and dimmer the further away you are from the equator. Therein lies my first question. Surely the average ambient light at 60 degrees and above---which amounts to nearly constant daylight for upwards of 6 months---would beat out the roughly 50/50 day--night split at the equator. I think the Inuit might have a different tale to tell, especially when you consider that what llight there is gets reflected and multiplied such that in the daylight in the winter, those wandering about outside the igloo had better have their sunglasses on or risk snow blindness and ultimately persistent blindness. And what about the rainforest dwellers who rarely see the sun? There should be plenty of variability, even holding latitude constant, dependent on average actual ambient light. So how do the authors arrive at such a compelling distribution of eyeball size and latitude? Follow me! ... Um. Better bring an umbrella---there might be fallout from the following. [Fallout from the following. That's practically poetry.]
The data for the above graph are given in the supplemental material. I reproduce it here to illustrate my point.
I compared mean orbital volumes for each of the 12 groups graphed above, taking into account sample size and sample variance [i.e. standard deviation]. As I suspected, at the 99% probability level one finds that those means between about 23 and 27 are not statistically different from one another. In other words, it's impossible to argue that those 8 or 9 samples weren't drawn at random from a single population having a mean somewhere between 23 and 27. The same can be said for those means between about 22 and about 26. Depending on where you cut, there might be two populations with statistically different means. Certainly nowhere near 12.
{Update 16:41 UTC March 15, 2013}
The 99% level is perhaps a little too stringent, even for my liking. So I went back to the group mean orbital volumes and discovered that, even at the 80% probability level [a really generous level, I might add] the following is true. Of the twelve group means...
None of the four group mean orbital volumes in the 26 ml range are statistically distinguishable from one another.
None of the four group mean orbital volumes in the 24 ml range are statistically distinguishable from one another.
None of the four group mean orbital volumes in the 21--23 ml range are statistically distinguishable from one another.
From these results the potential number of groups means falls from 12 to 3. This would mean that the graph shown above is, at best, tantalizing as to the hypothesized relationship between latitude and orbital size in modern humans. This is more like I would have expected given the potential for widely varying levels of ambient light at each latitude.
Continuing with the update. At the 80% probability level
None of the eight smallest group mean orbital volumes---i.e those between 21.83 and 24.46---are statistically distinguishable from one another.
Thus, within the 12 groups of orbital mean volumes one can reduce them to just two distinct groups: one group with a mean somewhere between 21.83 and 24.46 ml; another group comprising the four means of 26 ml and above.
I think I can probably stop the update here.}
All in all, the mean values of orbital volume vary so little from the equator to 60 degrees latitude, and the within-group variance is often so great that the authors' conclusions in this paper are severely undermined. To provide a more robust dataset they would need to sample more individuals at each latitude such that mean orbital volume was statistically different for each group in comparison to the others.
So much for my questions about Pearce and Dunbar 2012. Now it's on to yesterday's publication.
Pearce, Stringer and Dunbar (Yesterday) examine the orbital volumes and endocranial volume of 'Anatomically Modern Homo sapiens' (AMHs) and Neanderthals. They report significant differences in cranial capacity between AMHs and Neanderthals, and adduce the difference to different evolutionary pathways wherein the Neanderthals devoted more grey matter to ocular efficiency (in the form of larger eyeballs) in the face of latitude dependent reduced ambient light. On the other hand, those wicked AMHs said we're gonna get along fine without better eyesight as long as we can live in larger social groups. [I won't get into what I think about that conclusion.]
Here I'm reproducing Table 1 from Pearce et al. 2013, to illustrate a bit of arithmetic that might make me three new enemies of two and a half friends. [The half is for Pearce, whom I know not, but because Pearce works with Robin, it's like what? Two degrees of separation? Heck! We're practically family.]
The first bit that caught my eye is the orbital volumes of the two kinds of Homos. A whopping 34.15 ml (cc) for the Neanderthals. Moreover, by comparison with the earlier work by Pearce and Dunbar the AMHs in this study also have a whopping orbital volume---29.15 ml (cc). In their earlier paper the largest sample mean for the present-day AMHs was just shy of 27 ml (cc). That was for someone living above the Arctic Circle. My first question is: where did you find these AMHs? At the North Pole? So that's why Santa sees you when you're sleeping---he has way bigger eyeballs than you and I put together? Well, sort of. Actually. Maybe not. Okay. Call a spade a spade. No way.
Keeping in mind what I said earlier regarding the mean orbital volume in the Pearce and Dunbar paper, have a look at the means, standard deviations and sample sizes upon which Pearce et al. hang their conclusions about Neanderthals and AMHs. In the table above the mean orbital volume for the Neanderthals is given as 34.15 cc (s.d. 3.39; n=5). That of the AMHs is 29.51 cc (s.d. 2.07; n=4). Seems substantial. No? No. Do a difference of means test and whaddayaknow? They're statistically indistinguishable at the 99% level, and at the 95% level. I.O.W., statistically speaking, the two results cannot be distinguished from two separate samples drawn at random from a single population with mean of X and s.d of Y. So, what does that do to their thesis about eyeballs and brain size and evolution and stuff?
I'll let you break it to them.
All right. To use a quaint saying of British origin, I'm knackered. And I think it best if I lay low for a while.
So, fare ye well until we meet again!
Back out on the limb I go...
Yesterday's publication is
Eiluned Pearce, Chris Stringer and R. I. M. Dunbar,And the earlier one on which yesterday's is partly based is similar, but not so similar that even I'm compelled to ask questions. The preceding paper is
"New insights into differences in brain organization between Neanderthals and anatomically modern humans." Proceedings of the Royal Society B[iological Sciences], 280, 20130168, published 13 March 2013
Eiluned Pearce and Robin Dunbar, "Latitudinal variation in light levels drives human visual system size." Biology Letters 8, 90--93, 2012. doi: 10.1098/rsbl.2011.0570 first published online 27 July 2011Kayso in the oldest of the two articles the authors looked at some modern human skulls from different latitudes and arrived at the data presented below. In (a) you see the tight correlation between latitude and orbital volume [a proxy for eyeball size---a reasonable assumption]. Their sample comprised 55 healthy adult people like you and me ['cept these ones were dead---so, not that much like you and me (although, there have been days...) nor, under the circumstances could they be described as being very healthy. So, I'm sure the authors meant something else ;-) ]
In the graph below you see that orbital volume varies between about 22 ml and 27 ml [roughly 27 cubic centimetres (cc)]. The samples were drawn from 12 populations at different distances from the equator. A scatter plot of orbital volume against latitude shows that the further away from the equator one lives, the larger one's eyeballs will be. Someone living at about 65 degrees north latitude has the largest eyeballs. Ahh. But there's more to this comparison than *cough* meets the eye, as I'll explain on the other side of this graph.
 |
| From Pearce and Dunbar 2012. |
The data for the above graph are given in the supplemental material. I reproduce it here to illustrate my point.
 |
| From Pearce and Dunbar 2012. |
{Update 16:41 UTC March 15, 2013}
The 99% level is perhaps a little too stringent, even for my liking. So I went back to the group mean orbital volumes and discovered that, even at the 80% probability level [a really generous level, I might add] the following is true. Of the twelve group means...
None of the four group mean orbital volumes in the 26 ml range are statistically distinguishable from one another.
None of the four group mean orbital volumes in the 24 ml range are statistically distinguishable from one another.
None of the four group mean orbital volumes in the 21--23 ml range are statistically distinguishable from one another.
From these results the potential number of groups means falls from 12 to 3. This would mean that the graph shown above is, at best, tantalizing as to the hypothesized relationship between latitude and orbital size in modern humans. This is more like I would have expected given the potential for widely varying levels of ambient light at each latitude.
Continuing with the update. At the 80% probability level
None of the eight smallest group mean orbital volumes---i.e those between 21.83 and 24.46---are statistically distinguishable from one another.
Thus, within the 12 groups of orbital mean volumes one can reduce them to just two distinct groups: one group with a mean somewhere between 21.83 and 24.46 ml; another group comprising the four means of 26 ml and above.
I think I can probably stop the update here.}
All in all, the mean values of orbital volume vary so little from the equator to 60 degrees latitude, and the within-group variance is often so great that the authors' conclusions in this paper are severely undermined. To provide a more robust dataset they would need to sample more individuals at each latitude such that mean orbital volume was statistically different for each group in comparison to the others.
So much for my questions about Pearce and Dunbar 2012. Now it's on to yesterday's publication.
Pearce, Stringer and Dunbar (Yesterday) examine the orbital volumes and endocranial volume of 'Anatomically Modern Homo sapiens' (AMHs) and Neanderthals. They report significant differences in cranial capacity between AMHs and Neanderthals, and adduce the difference to different evolutionary pathways wherein the Neanderthals devoted more grey matter to ocular efficiency (in the form of larger eyeballs) in the face of latitude dependent reduced ambient light. On the other hand, those wicked AMHs said we're gonna get along fine without better eyesight as long as we can live in larger social groups. [I won't get into what I think about that conclusion.]
Here I'm reproducing Table 1 from Pearce et al. 2013, to illustrate a bit of arithmetic that might make me three new enemies of two and a half friends. [The half is for Pearce, whom I know not, but because Pearce works with Robin, it's like what? Two degrees of separation? Heck! We're practically family.]
 |
| From Pearce et al. 2013 |
The first bit that caught my eye is the orbital volumes of the two kinds of Homos. A whopping 34.15 ml (cc) for the Neanderthals. Moreover, by comparison with the earlier work by Pearce and Dunbar the AMHs in this study also have a whopping orbital volume---29.15 ml (cc). In their earlier paper the largest sample mean for the present-day AMHs was just shy of 27 ml (cc). That was for someone living above the Arctic Circle. My first question is: where did you find these AMHs? At the North Pole? So that's why Santa sees you when you're sleeping---he has way bigger eyeballs than you and I put together? Well, sort of. Actually. Maybe not. Okay. Call a spade a spade. No way.
Keeping in mind what I said earlier regarding the mean orbital volume in the Pearce and Dunbar paper, have a look at the means, standard deviations and sample sizes upon which Pearce et al. hang their conclusions about Neanderthals and AMHs. In the table above the mean orbital volume for the Neanderthals is given as 34.15 cc (s.d. 3.39; n=5). That of the AMHs is 29.51 cc (s.d. 2.07; n=4). Seems substantial. No? No. Do a difference of means test and whaddayaknow? They're statistically indistinguishable at the 99% level, and at the 95% level. I.O.W., statistically speaking, the two results cannot be distinguished from two separate samples drawn at random from a single population with mean of X and s.d of Y. So, what does that do to their thesis about eyeballs and brain size and evolution and stuff?
I'll let you break it to them.
All right. To use a quaint saying of British origin, I'm knackered. And I think it best if I lay low for a while.
So, fare ye well until we meet again!
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When they absolutely have to publish something, anything will do.
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