genetic drift

I'm redoing many of my lecture figures with Mathematica, which beats the heck out of my old Excel plots.

This isn't an advertisement. With some work, you can plot just as nicely with R or Gnuplot, both of which are free. Apple's Numbers also does some very attractive plots, although with fewer options. But I'm running through some things and thought the outcome might be of interest to some people. Feel free to use these figures if they're useful.

I have an excellent e-mail question about last week’s Neandertal mtDNA paper, which has provoked a lot of commentary.

Krause et al. (2007) list 15 Neandertal partial mtDNA sequences. Ten of these at that time presented relatively long portions, including the central Asian Okladnikov and Teshik Tash specimens, Mezmaiskaya, Feldhofer 1 and 2, Vindija 75 and 80, Scladina, Monte Lessini, and El Sidrón 1252. The same paper lists five additional specimens for which only a very short sequence had been recovered (just enough to diagnose as part of the Neandertal clade), including Vindija 77, El Sidrón 441, Engis 2, Rochers de Villeneuve, and La Chapelle-aux-Saints.

We do not know that every Neandertal belonged to the same mtDNA clade as those 15 sequences. Some of them may have looked different, possibly including the new clade otherwise present in later Upper Paleolithic and living people. But based on the 15 sequences we have, we can say that a large fraction of Neandertals must have carried the “Neandertal haplogroup.” Exactly how large a fraction depends on what we are willing to believe about contamination, preservation, and the randomness of our sample.

Now, let’s consider the question: Can we predict anything about Neandertal evolution and relationships based on this small, possibly unrepresentative sample of mtDNA?

The answer is that it doesn’t matter very much whether we have 5 sequences or 500. If 15 out of 15 specimens from different sites across Europe preserve a single mtDNA haplogroup, we can’t say it was universal, but we can say it was common. If 40 out of 50, or 400 out of 500 specimens had the same haplogroup, that would increase the precision, but not change the basic fact: Neandertals had at least one common haplogroup that is now so rare it has never been found in a sample of 100,000 or more people. We deserve some explanation.

The possible explanations are:

1. Random genetic drift
2. Accelerated genetic drift due to demographic turnover
3. Population extinction and replacement
4. Natural selection

Drift

Random genetic drift is fairly easy to refute, although it might not appear so at first. In favor of drift: There were few Neandertals, and the population size of the succeeding Upper Paleolithic, up through the Last Glacial Maximum, was also small—the best estimates are on the order of 2000 people for Western Europe and 5000 for continental Europe to the Urals (Bocquet-Appel et al., 2005). There would have been perhaps twice or more that number across the entire Neandertal range. The effective population size represented by this population would have been smaller; perhaps 3000–5000 for Neandertals and Aurignacian-era people, only half, or around 2000, females. Genetic drift in this small mtDNA population would have been much stronger than for autosomal genes, and very much stronger than in most recent human populations.

But when we plug these numbers into a model of random genetic drift, it starts to appear very unlikely that drift alone could explain the observations. Let’s assume (falsely) that our Neandertal genetic samples all dated to 40,000 years ago, and the female effective size was 2000 individuals between then and 15,000 years ago, and that the population of Neandertal country were a random mating pool. Following these assumptions, on averageall the mtDNA genomes at 15,000 years ago would descend from only 4 or 5 ancestral copies in the population 40,000 years ago. If these five ancestral copies were, by chance, a different haplogroup from the 15 copies we’ve already found, then drift could explain the data.

However, this still doesn’t appear very likely. So far, every one of the Neandertals shares a single haplogroup. The frequency of this haplogroup was apparently very high, making it very unlikely that all five ancestral copies would have belonged to some other haplogroups of which we have never found any trace.

Notice that this argument does not depend very much on the number of Neandertal mtDNA sequences that we have found. The fact that there are 15 helps to constrain the frequency of the haplogroup within the population 40,000 years ago, in our model. That frequency is unlikely to be less than around 85%, assuming random sampling. But suppose there were only five. We would still know that the Neandertal haplogroup was very common in its population, even if we thought it was only 50%. It would still be unlikely to draw four or five ancestral copies and have all of them be some other haplogroup that we haven’t found.

This gives us a considerable confidence margin against drift. We need it. After all, the Neandertals were not randomly sampled at a single time, and it is possible that some of them actually carried a human-like mtDNA sequence, which we now falsely interpret as contamination. But even with these shadows hanging over us, it would still be unlikely that none of the ancestors of today’s mtDNA variation were like the Neandertal haplogroup.

Also, the population was not a random-mating pool. When we add geographic structure to the story, which tends to reduce the importance of genetic drift, we find that the possibility that drift alone is almost zero, and it remains very unlikely that a single migration of modern humans interbreeding with Neandertals under random drift could explain the observations, either (Currat and Excoffier, 2004).

Extinction

It is at this point that most geneticists turn to the hypothesis of complete Neandertal extinction. They have a point. Genetic drift apparently cannot explain what we have observed, In their point of view, if genetic drift alone cannot explain the Neandertal mtDNA disappearance, then the only other random process at hand is extinction.

I think that hypothesis is false. It does not account for morphological similarities between Neandertals and later people, genetic evidence that suggests a strong ancient population structure with introgression, or with the apparent behavioral continuity in the Upper Paleolithic.

Happily, I don’t have a commitment to random processes. Instead, I think that the mtDNA evolution of Europe was driven by nonrandom processes of demographic turnover and selection.

Demographic turnover

Here we come to an important point. No one believes that later Europeans evolved from earlier Neandertals by a random process of genetic drift. Yet that is precisely the hypothesis that most studies have set up to refute. Without question it is valuable to set up boundary conditions under the hypothesis of random genetic drift. But the time has come to investigate more interesting models.

Personally, I am surprised that more complicated metapopulation dynamics have not gotten more attention as an explanation for the Neandertal mtDNA results. Population sources and sinks are a hot topic in biology, and you would think that anthropologists would have picked up on this. To my knowledge, the only time anyone has examined a population sink model was in 2001, when Milford Wolpoff and I worked with mathematician Per Enflo on such an idea for Neandertals (Enflo et al., 2001). This idea deserves a fuller treatment (I think I’ll suggest it as a project for one of my classes this year!).

In a nutshell, a population sink is a region where the average rate of reproduction is below replacement levels. This region can remain populated only if individuals migrate in from other places. The places that reproduce above replacement are called population sources. The continual migration from sources to sinks creates a genetic gradient. Individuals sampled at any given time in the population sink are overwhelmingly likely to have ancestors not in the sink but in one or more source populations.

Europe today is a population sink. The population of the continent does not produce enough children to replace itself, and immigration from other parts of the world is high. There are several reasons to suggest that Europe may have been a population sink in prehistory as well. In Neandertal and Upper Paleolithic times, climate fluctuations created unique challenges in Europe, where caloric expenditures were high and food harder to obtain than some other regions.

Continual migration into Europe would provide a simple explanation for why none of today’s mtDNA haplogroups derive from the European Neandertals. The mtDNA population of 15,000 years ago had a few ancestors 40,000 years ago, and none of these ancestors lived in the sink population—all came from the source population in Africa or West Asia. The Neandertal mtDNA variation would have been a short-lived phenomenon, continually being turned over from source populations. Some Neandertal genes would have survived in Europe for hundreds of thousands of years, but some would have come in with more recent migrants from the population source.

There are points that argue against this source-sink hypothesis. The Neandertal-human divergence time for mtDNA is not very different than that estimated for the autosomal genome. If a European population sink had made genetic drift more powerful, that should have affected mtDNA more than the autosomes, so we might expect a more recent mtDNA divergence. Still, there is nor reason why the source-sink dynamic need have been constant over Neandertal evolution, and there may have been multiple sources in the Pleistocene, not only Africa and West Asia. Investigating the boundary conditions of the source-sink model and its correspondence to autosomal genetic results would be helpful.

I should note that mtDNA is not special. Neandertals had lots of traits that are now very rare. The horizontal-oval, or “bridged” mandibular foramen is a prominent example. Out of the relatively small sample of Neandertal mandibles, half have this derived form. Fewer than one percent of recent European mandibles have this form. As for mtDNA, a once-common variant is now very rare. And as for mtDNA, we deserve some explanation. A source-sink model would appear consistent with the continued evolution of such traits during the Upper Paleolithic—a time when the extinction and replacement hypothesis predicts no change in these characters.

Natural selection

The other nonrandom hypothesis is natural selection, which would presumably have favored one or more modern human types while eliminating the original Neandertal haplogroup. I won’t say much about that hypothesis here, since I discussed it in my initial post about the whole-mtDNA-genome sequencing. Selection has a leg up over the other hypotheses now because it seems like there’s good evidence it happened.

Still, selection on mtDNA alone could not explain the total pattern of observations about Neandertals. Physical traits that were once frequent in Neandertals were much less common or absent in later Europeans, and some continued to reduce in frequencies over time. To explain these changes, we must invoke either selection on other traits, or continued demographic turnover in the post-Neandertal population (probably more immigration into Europe) or both.

So selection on mtDNA has never been a sufficient or necessary hypothesis, even if we assume that other genes carried by Neandertals still survive. But given the current evidence that suggests something distinctive about the mtDNA of recent humans, natural selection may receive renewed attention as a factor in the disappearance of the Neandertal mtDNA haplogroup.

References

OK, I'm clearly going to have to cut out the beer if I'm going to do anything about stories like this one:

New research led by UC Davis anthropologist Tim Weaver adds to the evidence that chance, rather than natural selection, best explains why the skulls of modern humans and ancient Neanderthals evolved differently. The findings may alter how anthropologists think about human evolution.

Weaver's study appears in the March 17 issue of the Proceedings of the National Academy of Sciences. It builds on findings from a study he and his colleagues published last year in the Journal of Human Evolution, in which the team compared cranial measurements of 2,524 modern human skulls and 20 Neanderthal specimens. The researchers concluded that random genetic change, or genetic drift, most likely account for the cranial differences.

In their new study, Weaver and his colleagues crunched their fossil data using sophisticated mathematical models -- and calculated that Neanderthals and modern humans split about 370,000 years ago. The estimate is very close to estimates derived by other researchers who have dated the split based on clues from ancient Neanderthal and modern-day human DNA sequences.

The close correlation of the two estimates -- one based on studying bones, one based on studying genes -- demonstrates that the fossil record and analyses of DNA sequences give a consistent picture of human evolution during this time period.

"A take-home message may be that we should reconsider the idea that all morphological (physical) changes are due to natural selection, and instead consider that some of them may be due to genetic drift," Weaver said. "This may have interesting implications for our understanding of human evolution."

If you've been reading for long, you might reasonably wonder what I think about this study. My work has shown rapid natural selection in recent humans, consistent with evidence from recent skeletal samples for rapid evolutionary change. So it might seem incongruous that a study could assume that there has been no natural selection on the skeletal traits of recent human populations, and come to any kind of sensible conclusion.

I am actively working on this particular problem, with a manuscript in preparation, so I don't want to comment too extensively. However, I can say a brief word about why I disagree with the analysis.

A model of phenotypic evolution by genetic drift requires an assumption about the effective size of the population (N_e). Weaver et al. (2008) assume a model of "mutation-drift equilibrium." This is an assumption that the effective population size has not changed over time in the populations under consideration -- in this case, the Neandertal and human populations back at least as far as their common ancestor.

In their analysis, Weaver et al. (2008:4647) assume that the effective sizes of the human and Neandertal lineages, throughout the last few hundred thousand years, were equal to 2700 individuals. They wrote this:

The second reference point is the effective population size, PN_e, under a mutation-drift-equilibrium model for sub-Saharan African human populations. Zhivotovsky and colleagues (ref. 17) estimated N_e from 271 microsatellites using an equation equivalent to our Eq. 7 as ≈ 2,700 individuals. Once again, we are just assuming that the morphological and microsatellite estimates should match up under the same model, not that this is the most realistic model to use to infer the actual effective population size.

This is an astounding assumption. It is important because a small effective size allows rapid evolution by genetic drift. But it is contradicted by other evidence.

For one thing, most other sets of genetic data indicate a long-term effective size of at least 10,000 for human populations -- four times larger than assumed in this study. All things being equal, this means that the rate of phenotypic evolution by genetic drift should be four times slower than assumed by Weaver et al. (2008). Some of this difference between real and assumed effective sizes may be washed out by their process of calibration -- their equations involve several unknowns that must be simultaneously estimated, and give a lot of wiggle-room to the results. But that points to another weakness of the analysis -- there's so much wiggle room that almost any level of phenotypic difference might look like "drift."

Moreover, the human population has vastly increased in numbers within the last 50,000 years. Weaver et al. (2008) use the phenotypic and genetic divergences of recent humans to calibrate their "clock" of phenotypic evolution. But the phenotypic divergences between recent human populations, with very large effective population sizes (N_e > 100,000) are simply not comparable to those between Middle Pleistocene humans and Neandertals -- at least, not without taking into account the vast difference in effective population sizes.

But please don't take my word for it. I am a clear partisan on the side of natural selection in recent human evolution. Weaver's quote in the press release above implies that we should accept a pluralistic model, in which genetic drift accounts for some changes. I agree entirely. But their analysis assumes that genetic drift accounts for all changes. I don't deny the role of genetic drift, but I do deny that it explains much about recent skeletal evolution in humans. Random chance cannot do much in a very large population in a few hundred generations.

I really don't understand why you would want to use a heuristic value for effective population size, when it is contradicted by genetic and archaeological evidence. I will be writing about effective population size over the next week, introducing some of the importance of the concept for these kinds of analyses. You're welcome to take a look at what I have to say, and take it or leave it.

Last year around this time, I noted that I happened to be reading Sewall Wright during a TV episode that mentioned Sewall Wright. It's not so unusual for me to be reading Wright, but in this instance I was directed to something I hadn't paid much attention to before.

I'm reminded of the article today because I talked about its basic theme during a lecture, and also because I'm writing up some stuff about effective population size, a concept attributed to Wright.

John Gillespie's 2000 article, "Genetic drift in an infinite population," introduced the concept of pseudohitchhiking, or "genetic draft." An important thing about pseudohitchhiking is that it behaves as a stochastic force very much like genetic drift. The formal difference between the two is that the stochasticity of a pseudohitchhiking locus depends on recombination and selection, while genetic drift depends on neither. Gillespie's paper considered to what extent pseudohitchhiking led to similar predictions for the change in allele frequency. This is a connection he made more explicit in his 2001 article, "Is the population size of a species relevant to its evolution?" by drawing out the first and second moments of neutral evolution under both drift and pseudohitchhiking. For drift, these are (Gillespie 2001:2161, eqs. 1 and 2):

The first equation means that the expected change in allele frequency under drift is zero. This is otherwise known as the deterministic component. Under selection, the expected change in allele frequency depends on the current frequency and the fitnesses of genotypes. Under drift all genotypes have equal fitnesses and the only possible changes are stochastic, therefore the expected change is zero irrespective of the current allele frequency.

The second equation describes the variance of the change in allele frequency. You might think this variance would be zero, since the expected amount of change is zero. But the variance represents the magnitude of possible changes from the expected value due to random sampling a finite number of individuals. This is the stochastic component of allele frequency evolution.

The magnitude of these stochastic changes is directly proportional to heterozygosity and inversely proportional to population size. Larger populations have smaller potential changes in allele frequency due to random sampling. Intermediate allele frequencies (near 50 percent) can change more due to random sampling than high or low frequencies. These relations are embodied by the second equation above -- and if you're keeping score, this second equation is used in defining the variance effective population size.

The two equations help to frame the discussion of effective population size. The size of a population is relevant to its evolution only under certain contexts. If the deterministic change in allele frequencies is the dominant pattern of evolution, then population size is irrelevant to the outcome. In contrast, if random sampling is the most important cause of allele frequency changes, then the outcome (fixation or loss) may be indeterminate, but the population size is very important to the rate of the process.

As Gillespie's article makes clear, genetic drift is not the only stochastic process affecting the evolution of allele frequencies. His mechanism of pseudohitchhiking is one. And there are many others -- all non-deterministic in that their outcomes cannot be predicted from the frequencies of alleles or their phenotypic effects. The rate of these processes depends on different things: some internal to the population and some external. Genetic drift depends on the size of the population and its allele frequencies; genetic draft depends on the rate of recombination, the rate of generation of new favorable mutations, and the relative fitnesses of these mutations. Environmental stochasticity depends on the demography of other species as well as physical factors such as water availability and the weather.

Sewall Wright tried to categorize these stochastic processes, as well as the deterministic ones, making a catalog of of the processes that can cause evolutionary changes. Those of us who teach intro classes are well accustomed to talking about the "forces of evolution" -- selection, drift, gene flow, and mutation. These are important because they constitute different patterns of change in allele frequencies. But Sewall Wright went beyond this four-fold categorization, linking different aspects of these patterns with their stochastic and deterministic effects.

First, he defines the problem in terms of allele frequencies:

As is now generally appreciated, the seemingly very diverse factors that must be taken into account in population genetics can best be brought under a common viewpoint by considering their effects on gene frequency (Wright 1955:17).

Then he provides a full breakdown of different patterns of evolutionary change, or "modes" of change of the gene frequencies in a population:

Modes of Change of Gene Frequency

I. Immediate
1. Directed processes (mean change in allele frequencies determinate in principle)
a. Recurrent mutation
b. Recurrent immigration and crossbreeding
c. Mass selection

2. Random processes (variance in change in allele frequencies determinate in principle)
a. Fluctuations in mutation
b. Fluctuations in immigration
c. Fluctuations in selection
d. Accidents of sampling

3. Unique events
a. Novel favorable mutation
b. Unique hybridization
c. Swamping by mass immigration
d. Unique selective incident
e. Unique reduction in numbers

II. Secular change in system of coefficients
1. From internal causes (control by new adaptive peak)
2. From changes in environment
a. In home territory
b. In colonized territory

This breakdown clearly separates the deterministic factors of evolution (here, category 1, "Directed processes") from the stochastic factors (everything else). I find a couple of things very interesting from this perspective:

1. Wright makes a distinction between recurrent mutation, whose effect is more or less deterministic on allele frequencies, and "novel favorable mutation", each of which is a random, unlikely event. Both are distinguished from "fluctuations in mutation," which might be described as an intermediate between the two -- although writing in 1955 it is plausible that Wright may actually have meant alterations in the propensity toward mutations due to variation in radiational or chemical processes. This is one indication of the difference between Wright and Fisher, who felt that novel mutations might become more or less predictable in large populations.

I also noticed how many of Wright's "unique events" have been marshalled by one or another researcher to explain human evolution.

Another point of interest, reflecting the several instances of interesting evolutionary trends under domestication that I've linked this week, is Wright's accommodation of artificial selection within this scheme:

It may be noted here that artificial selection also imposes a new system of peaks toward one of which mass selection may be expected to drive the population rapidly. Since the peak attained is not a natural one, progress is almost inevitably at the expense of fecundity and viability. On relaxation, the population may be expected to return toward the original peak, or to another, and usually lower one, if the artificial selection has driven it across what was naturally a valley (Wright 1955:17).

This should be amended, in that selection comes at the expense of fecundity and viability in the previous environment, not the new artificially selected one. But the prediction that artificial selection should decrease fitness in the species' natural environment comes straightforwardly considering the nature of selection as a deterministic force. If the species was initially well adapted to its natural environment, any changes resulting from artificial selection would likely make it worse, not better.

Wright's well-known idea was that the stochastic factors might play an important role allowing a population to explore the adaptive landscape. In his "shifting balance" formulation, the division of an abundant species into many small subpopulations tends to maximize the species' ability to evolve toward higher fitness peaks, because a small group might have a fortuitous combination of alleles allowing it to move to a higher fitness peak. This model has been controversial even up to the present day, because of our lack of knowledge about the characteristics of "fitness landscapes".

But it is worth pointing out Wright's definition of the stochastic factors here, each of which might operate in conjunction with genetic drift in the shifting balance model. It is clear from the list that the balance between these different factors might itself change over time -- for instance, in our acceleration idea, the incidence of novel mutations is greatly accelerated in a growing population, ultimately increasing the scope of the deterministic process.

References:

Gillespie JH. 2000. Genetic drift in an infinite population: the pseudohitchhiking model. Genetics 155:909-919.

Gillespie JH. 2001. Is the population size of a species relevant to its evolution? Evolution 55:2161-2169.

Wright S. 1955. Classification of the factors of evolution. Cold Spring Harbor Symp Quant Biol 20:16-24.

I'm just looking through the January/February 2008 Evolutionary Anthropology, which is all about modern human origins in Africa. The special issue resulted from a conference at Stony Brook, along with a few additions to round out the topic.

I'll have some things to say about these articles, but one thing struck me. I'll describe the problem:

Dan Lieberman's paper, "Speculations about the selective basis for modern human cranial form," discusses five categories of functional requirements that might have been involved in the evolution of the "modern" human cranial anatomy. Each of these imposes distinctive requirements on the form of the head -- not all of which are fully understood -- but all of which changed in ways that parallel the basic changes in cranial form of the Late Pleistocene.

But Tim Weaver and Charles Roseman's paper, "New developments in the genetic evidence for modern human origins," claims that the modern human cranial anatomy originated by genetic drift, without any substantial selection:

Evolutionary quantitative genetic analyses, in fact, show that Neandertal and modern human cranial differences can be explained by genetic drift, making it unlikely, at least for the cranium, that modern human anatomical features were spread by natural selection rather than a range expansion out of Africa. An important point is that these analyses do not simply compare the magnitude of the morphological differences between Neandertals and modern humans; they are multivariate tests of how the patterns of covariation across different cranial measurements compare to those expected for divergence by genetic drift. Natural selective hypotheses designed to account for Neandertal and modern human cranial differences would also need to show multivariate consistency with the observed patterns of variation. While it may be possible to imagine natural selective scenarios that mimic genetic drift for a single measurement, such as fluctuating directional natural selection, the scenarios become much less plausible for multivariate patterns of variation (Weaver and Roseman 2008:78).

Both these papers cannot be correct. A full text search of Lieberman's paper does not find the words "drift" or "random," and "neutral" only appears as part of "neutral horizontal axis." Yet Weaver and Roseman cite the neutrality of cranial form as the main evidence against Eswaran's model of an adaptive dispersal of cranial form. According to them, all of Lieberman's "speculations" must be wrong.

I thought maybe I could get some insight into this dilemma by reading Günter Bräuer's paper, "The origin of modern anatomy: by speciation or intraspecific evolution." That title sounds fairly clear -- if we're talking about a speciation of modern humans to explain their anatomy, that sounds like the kind of rapid change that ought to indicate selection of some kind.

Bräuer shows some skepticism toward Lieberman's ideas about cranial evolution:

In my view, Lieberman, McBratney, and Krovitz's interpretation that anatomical modernization can be boiled down to just a few autapomorphies or genetic changes will be difficult to accommodate within the current fossil evidence (Bräuer 2008:27-28).

OK, but does this disagreement mean that Bräuer is likewise skeptical of adaptive hypotheses to explain modern cranial form? Again, a full text search fails to find the words, "drift," "neutral," or "random." But neither does it find the word "selection." Bräuer is concerned with describing the pattern of evolution of the modern human cranial form, but is entirely noncommittal on the question of why it evolved. That would seem to be problematic in itself: wouldn't we expect a different pattern of evolution if natural selection caused the changes, than if genetic drift caused them? Wouldn't the two causes make different predictions about the role of speciation in the process?

I'll have more to write about Bräuer's interesting paper, but on this issue, I think that is all I can extract from it. Osbjorn Pearson's paper, "Statistical and biological definitions of 'anatomically modern' humans," has more to say on the issue. Pearson cites the work that suggests modern human cranial form evolved under random genetic drift, saying:

Ideally, one would like to partition morphological distance into differences due to genetic drift, adaptation, and environmental interactions with ontogeny. Recently, several promising studies have shed light on these issues, including the amount of morphological diversity in recent humans that likely reflects genetic drift and the effects of the toughness of foods on the cranial morphology and occlusion of nonhuman primates, retrognathic mammals (for example, hyraxes), and humans from different parts of the world. Nevertheless, much remains to be done before these relationships become completely clear (Pearson 2008:40-41).

He later suggests (p. 44) that "rapid morphological change due to drift during population bottlenecks" may be involved in the evolution of modern cranial form. On the other hand, Pearson also suggests that "selection for new, advantageous traits or genes, or some combination of the two [selection and drift]" may have occurred. That would seem fairly noncommittal.

However, Pearson's description of the series of events -- a stepwise, sequential series of anatomical changes ultimately in a worldwide context up to and including the Holocene -- seems pretty unlikely to result from genetic drift alone. Indeed, Pearson writes,

In common with many other parts of the world, [African] crania that have dimensions or suites of morphological traits that make them statistically indistinguishable from the living populations appear only during the Holocene (Pearson 2008:45).

If the evolution of modern cranial form is a process that continued into the Holocene, it is quite impossible to have been caused by drift alone, since the effective population sizes of human populations were too large, and drift could hardly have caused a "nearly universal pattern of gracilization" (ibid.). So Pearson's paper certainly heightens the contrast between the adaptive and drift scenarios. If the events are as Pearson describes them, the "genetic drift alone" hypothesis must be false.

Philip Rightmire's paper is about earlier events, and Chris Stringer and Nick Barton's paper is a conference review. That leaves only Ian Tattersall and Jeff Schwartz's paper, "The morphological distinctiveness of Homo sapiens and its recognition in the fossil record: clarifying the problem," to clarify the problem.

Tattersall and Schwartz direct their attention to the kinds of features that are suitable for identifying a species from the fossil record -- uniquely derived features, or "autapomorphies." In their view, species must be accurately diagnosed from sets of specimens ("alpha taxonomy") before any kind of evolutionary hypotheses can be tested.

Because of this, they don't talk very much about the kinds of evolutionary forces that might cause the patterns they see. The paper includes only one reference to "random" and "adaptive," both in a single sentence:

However, there are some materials of this period [the late Middle Pleistocene] that fall outside, but not far outside, the strictest definition of Homo sapiens as based on the living species. Most of these (for example, Border Cave 5, Boskop, Fish Hoek, Klasies River Mouth except for AP 6222, and maybe Cave of Hearths) form a generally poorly dated South African group in which cranial structure largely conforms to the modern Homo sapiens morphology except that, most notably, the bipartite brow and/or the inverted-T-shaped chin are lacking. Do such fossils represent distinctive and now extinct populations of Homo sapiens that lacked two or more of the most striking autapomorphies of the living species merely as a result of random (or even adaptive) population variation? Or did they belong in life to one or more distinctive reproductive entities whose histories did not impinge, at least biologically, on that of today's Homo sapiens? (Tattersall and Schwartz 2008:52, emphasis added)

The bolded sentence is important. Tattersall and Schwartz view adaptive and random variations as equivalent: small changes between populations that may occur even without the kind of significant isolation that would invite a taxonomic interpretation. They contrast these in the next sentence with "distinctive reproductive entities whose histories did not impinge." And they are correct; modern human populations have morphological differences as a result of both selection and drift, and their histories certainly have impinged on each other.

But it makes a difference whether selection or drift was the cause of changes, because selection is more powerful than drift. Weak selection can cause a level of morphological differentiation that would require long isolation by random drift alone. If selection were involved in African regional differentiation, there may be no reason to posit "distinctive reproductive entities whose histories did not impinge" -- in fact, their histories almost certainly would have impinged.

In other words, the relation of the pattern of features to the taxonomic status of the populations depends on the evolutionary forces that generated the pattern.

As Weaver and Roseman note, their hypothesis that modern human cranial form evolved neutrally depends on the pattern of evolution of different features, not the amount of evolution of any single feature. But the amount of evolution must still be explained; under their hypothesis, it must have occurred in small populations over a substantial period of time. In their hypothesis, the cranial differentiation of African late Middle/early Late Pleistocene fossils would have emerged during relatively long periods of parital or complete isolation. Under that hypothesis, Tattersall and Schwartz would be correct to place these fossils into different taxa, only one of which was ancestral to living people -- or at least principally ancestral, allowing for some small amount of hybridization and introgression.

In contrast, Lieberman's adaptive hypotheses are consistent with the evolution of modern human cranial morphology within a broader, larger population. Patterns of selection may explain the variation among the fossils. Today's humans may have emerged from a population with substantial cranial polymorphism. That scenario would seem to be consistent with the patterns described by Pearson -- in which modern human cranial variation does not standardize until very late, perhaps even Holocene times. Only selection could cause this kind of evolution within the large populations of the last 10,000 years, or even within the large populations of the last 70,000 years.

I picked this problem first, because it was the first to stand out to me in the papers. It does seem a fairly glaring contradiction. I don't expect the authors to have noticed the contradiction in advance; I think that they approach the question of human origins from fundamentally different viewpoints.

As you can tell, two of the papers are not concerned with the causes of evolution at all -- their aim is to map the pattern of morphological variation onto putative speciation events. But it seems to me that if we approach the fossil record with the idea that speciation is the major cause of such patterns, then we have already assumed how the evolution happened. It may not have escaped your notice that this is the major reason for disagreement about modern human origins: One group of authors wants to assume the conclusion, foreclosing further discussion.

I don't have any complaints about the papers that were chosen for the issue -- in fact, I'm interested in reading the current opinions of all these authors. So far, I would say that each paper is a well-written expression of its authors' ideas, and I appreciate having all that in one place.

But it does seem a little strange that a special issue devoted to modern human origins in Africa doesn't have more, um, diversity of opinion. Several of the papers discuss multiregional evolution. They apparently believe that it is an important enough viewpoint to include their reasons for disbelieving it. One of the papers (Weaver and Roseman) includes a section about genetic introgression, kindly citing my work. Another (Bräuer) claims that it is reasonable to include all Middle Pleistocene humans in Africa and Europe as part of "one polytypic species, Homo sapiens" (Bräuer 2008:32).

So the work of those of us who write about evolutionary mechanisms seems to be making an impact. Still, it's kind of like "dark matter" -- you only know about the ideas because of their effects on what you can read! In this case, you can read a lot of peoples' opinions about these ideas -- you just can't read them from the people who thought of them.

What boring meetings these must be, with everybody agreeing with each other all the time, and nobody to point out all these contradictions!

References:

Bräuer G. 2008. The origin of modern anatomy: by speciation or intraspecific evolution? Evol Anthropol 17:22-37. doi:10.1002/evan.20157

Lieberman DE. 2008. Speculations about the selective basis for modern human cranial form. Evol Anthropol 17:55-68. doi:10.1002/evan.20154

Pearson OM. 2008. Statistical and biological definitions of "anatomically modern" humans: Suggestions for a unified approach to modern morphology. Evol Anthropol 17:38-48. doi:10.1002/evan.20155

Tattersall I, Schwartz JH. 2008. The morphological distinctiveness of Homo sapiens and its recognition in the fossil record: Clarifying the problem. Evol Anthropol 17:49-54. doi:10.1002/evan.20153

Weaver TD, Roseman CC. 2008. New developments in the genetic evidence for modern human origins. Evol Anthropol 17:69-80. doi:10.1002/evan.20161

RPM at Evolgen has a post raising a concern I've been seeing a lot the last week or two:

If you add up all three classes of mutations -- deleterious, neutral, and beneficial -- and figure out how many have fixed over the time scale you're looking at, you get the amount of evolutionary change along the lineage in question. So, to say that there was increased evolution along the human lineage in recent history implies that there was an increase in the total number of genetic changes. However, an increase in the amount of adaptive evolution (or an increase in the number of mutations fixed by positive selection), means there was an increase in the number of beneficial changes along the human lineage in recent history.

Here's the point in a nutshell:

1. Our recent acceleration paper suggests that the rate of adaptive human evolution has vastly increased during the past 40,000 years.

2. Some people confuse the idea of adaptive evolution with the idea of neutral evolution.

3. We can't let this happen, because, well, choose one: (a) we're good acolytes of Stephen Jay Gould; (b) people might start suggesting that all the human phylogeography based on "neutral" loci is irrelevant or worse; (c) we have a deep concern with the pattern of evolution of gene variants that don't actually do anything interesting.

I tend to notice that the various critiques of acceleration don't include any mathematics. I don't really understand this, since the math is simple. It is a whole lot easier to look at this algebra than to write a four or five-paragraph blog post!

So, let's consider some of the mathematical relations describing neutral evolution and how they apply to the recent increase in human population numbers.

1. The expected change in frequency of a neutral allele each generation is zero. That is, after all, why we call them neutral.

2. But the variance in the change in frequency of a neutral allele is related to population size -- in fact it is p(1 - p)/2N_e, where N_e is the effective population size (actually the variance effective size).

3. Because of this relation, neutral alleles in large populations change more slowly in frequency than those in small populations. Once human populations reached an effective size on the order of 100,000 -- certainly by 40,000 years ago -- the change in allele frequency due to drift alone became extremely small (on the order of 10^-6 or less per generation).

4. So neutral evolution in the past 40,000 years should have vastly slowed compared to earlier phases of human evolution.

Except...

5. Changes in population size make absolutely no difference to the neutral substitution rate. The rate of generation of new neutral mutations is directly proportional to population size (2N_eu for an autosomal locus). But the rate of fixation is inversely proportional to population size (1/2N_e). So the neutral substitution rate is simply u: the neutral mutation rate, irrespective of population size. That's part of what makes the neutral substitution rate cool -- and of course, what underlies the molecular clock assumption.

6. From this, we might conclude that the rate of neutral evolution was absolutely unchanged in the last 40,000 years. Of course, now it is obvious that the problem is what we mean by "rate" -- do we mean the substitution rate or the per-generation rate of change in allele frequency?

Except...

7. It should be obvious that we don't mean "neutral substitution rate" because this is irrelevant to recent human evolution. The fixation time of a new neutral mutation is directly proportional to the effective size of the population (4N_e generations for an autosomal locus). It doesn't take much figuring to show that is a long, long time from now with today's population size. There is no chance that a new neutral mutation within the last 40,000 years could be near fixation today -- in fact, every neutral segregating allele 40,000 years ago ought to still be segregating today!

8. From that perspective, we might well conclude there has been no neutral evolution in the last 40,000 years -- because it is vanishingly unlikely that any neutral variation has been lost during that time.

Except...

9. Our study actually did find a large number of neutral areas of the genome that had recently approached fixation, and a much larger number of initially rare neutral variants that have reached substantial frequencies during the last 40,000 years. Empirically, neutral evolution has been very rapid during recent human history. This is entirely the result of ...

10. Hitchhiking. The fast rate of generation of new adaptive mutations means that the rate of neutral evolution by hitchhiking has vastly accelerated in the recent past. This is, after all, how we manage to find evidence of selection in the first place -- the hitchhiking effect on neutral markers!

Therefore, the rate of neutral evolution in humans really has accelerated, as a function of hitchhiking on new adaptive mutations. For every selected mutation, we are talking about hundreds of kilobases' worth of linked neutral variants that have been experiencing rapid changes in frequency due to hitchhiking. In the long run, this will have not a jot of effect on the neutral substitution rate, but it accounts for most of the neutral evolution of allele frequencies in human populations.

I expect that there will be people who don't like this idea. I expect many of them have been counting on various neutral markers being informative about population movements. I'm not saying that neutral markers aren't informative, but we really need to consider the effects of selection on these distributions of markers.

Another class of people who don't like this idea are those who propagate one of my pet peeves -- the idea that we need to "invoke" selection as some kind of extraordinary event. The use of this term is very clear: Its only purpose is to vilify folks who want to explain evolution in terms of Darwin's mechanism. It's precisely the same way that we vilify creationists -- they want to "invoke" supernatural forces to explain evolutionary changes.

It's time to get the message -- natural selection has been the major force driving recent human evolution. Humans are no exception to the natural order -- any species that has increased in numbers and changed in ecology to the extent of ours should undergo a rapid pulse of selection resulting in the appearance and proliferation of many more new adaptive mutations. In fact, it looks like domesticated species like maize have undergone a similar effect. There's no "invoking" here, and neutrality is not a hypothesis that can explain these observations.

The foregoing should make one thing very clear -- I have nothing against neutral evolution. I am not an "adaptationist", and have no stakes whatsoever in the "adaptationist-neutralist controversy". This is not a matter of preferences or verbal arguments -- it is simple algebra!

What's more, its pretty obvious that this account of recent neutral evolutionis an evolutionary scenario of which Stephen Jay Gould would have been proud: the most widespread source of change in human genes is chance linkage to a relatively small number of selected sites.

It's just that there are quite a few more of these selected sites than anybody probably expected to find.

Skeleton of an Irish elk (Megaloceros giganteus) at the Carnegie Museum of Natural History. Photo by Via Bulatao, available on Flickr. Creative Commons license

Rudbeckia flower, viewed in ultraviolet light. Dark, UV-absorbing nectar guides are not apparent in the visible spectrum. Photo by kds315, available on Flickr. Creative Commons license

Papilio caterpillar. Photo by scorius, available on Flickr. Creative Commons license

A bee orchid. Photo by Mr. Bov, available on Flickr. Creative Commons Attribution license

Razib has been working over genetic drift real good (concerning effective population size and population history, and founder effects). It deserves it.

This post is about genetic drift applied to phenotypic -- not molecular -- evolution. The two are distinct for two important reasons: first, phenotypes are widely genetically correlated with each other while unlinked DNA sequences are not; and second, because the theoretical reasons for some nucleotides to have no correlation with fitness are very strong, but such theoretical reasons are nonexistent for phenotypes.

Personally, I think selection is more important than drift at the molecular level as well, for reasons having to do with those "genetically correlated" and "unlinked" assumptions. But to the extent that neutral evolution may be credible for many genes, it is much less credible for most phenotypes.

Here's what I tell my students:

To explain the evolution of a feature in ancient humans, genetic drift is my absolute last resort...right before sexual selection.

Why I don't like sexual selection is a topic for another day.

For now, on to genetic drift. Here's what Gould and Lewontin's famous "spandrels" paper has to say:

Have we not all heard the catechism about genetic drift: it can only be important in populations so small they are likely to become extinct before playing any sustained evolutionary role (but see Lande 1976) (Gould and Lewontin 1979:585-586).

With some math, we can show that the "catechism" is not literally true -- genetic drift can cause substantial phenotypic evolution in large populations. But ...

Some worked examples

Lande (1976) shows genetic drift can cause phenotypic evolution consistent with many examples in the fossil record:

This paper presents a statistical test for the hypothesis of evolution by random genetic drift, contingent on the effective population size. In examples from the fossil record, it is found that the rates of evolution equal to or greater than those observed have a significant probability of occurring by random genetic drift even in very large populations (Lande 1976:314-315).

Let's consider an example not examined by Lande. One of the most significant temporal trends in the early hominid species Australopithecus afarensis is a decrease in the length of the lower third premolar. This decrease in length is associated with a change in the morphology of the tooth, in which a more sectorial one-cusped form becomes less common and a more bicuspid form becomes more common. Lockwood et al. (2000) show that the P₃ length decreases from an average around 10.5 mm in the early, 3.5 Ma Laetoli sample down to an average around 8.5 mm in the latest 3.0 Ma Hadar sample. Estimating the standard deviation of the sample as a whole (including intermediate time periods at Hadar) is a bit complicated, but if we consider the mean as a moving average, then the standard deviation is between 1.0 and 1.5 mm. I'll assume 1.0 mm to be conservative.

Lande (1976) derives the distribution of phenotypic change due to genetic drift in a population with effective size N_e. The average change due to genetic drift is no change -- the most likely result of random sampling is no change at all. Populations can change in either direction (larger or smaller) due to random sampling, and larger amounts of change are increasingly less likely. More change is likely in smaller populations, so that the amount of change depends on the effective population size. Lande gives an expression for the effective population size N* at which the observed amount of change is at the 95 percent confidence limit:

If we assume h² = 0.5, t = 25,000 generations, and the standard deviation is 1, then N* is estimated as 12,000. Since the effective population size of all extant hominoid species is around 10,000, this estimate is fully consistent with the evolution of P₃ length by genetic drift alone.

In fact, it's pretty hard to find anything in human evolution that couldn't have evolved by drift alone, under these assumptions. For example, Wolpoff and I (2001) found that the Middle Pleistocene increase in cranial capacity was consistent with genetic drift in a population with N_e = 1.8 x 10⁶. The increase from early Neandertals to Würm Neandertals was less likely to occur by drift alone -- our estimate of N_e = 1.2 x 10³ is quite a bit less than 10,000. On the other hand, there would be many who would argue that the effective population size in Europe alone really was that small, and that therefore the Neandertals increased their cranial capacity by genetic drift also.

Now, the increase in endocranial volume in humans is one of the most impressive long-term evolutionary trends in mammals. If even that is explicable by genetic drift, then it is pretty clear that we don't ever need natural selection at all.

So I should really like genetic drift, right? I mean, it explains everything, doesn't it?

The fallacy

Of course, what is actually going on is that we have chosen a null hypothesis that is especially hard to refute. This means we should expect a lot of type II error: using this method, we can't reject the hypothesis of genetic drift even if it isn't the right answer.

What is worse, even if we were to show that the amount of phenotypic change is too great for a given effective population size, there will always be someone to argue that the effective population size was smaller in the past. So genetic drift is a moving target -- it is effectively impossible to reject.

The operative problems here are (i) a relatively small amount of change over (ii) a very long period of time. This combination will usually be consistent with Lande's derivation for genetic drift and reasonable effective population sizes -- particularly if we cannot establish in advance what effective population size is actually reasonable.

There is a big contrast between a long timescale and a short timescale in this comparison. Natural selection is certainly much faster than genetic drift on a short timescale -- the time to fixation of an adaptive allele by selection proceeds as the logarithm of population size, while the fixation time by drift proceeds linearly with population size. Genetic drift can change a population quickly, but only if the population is very small. Selection can change a large population quickly.

The fallacy is the assumption that the difference between selection and drift over short timescales also is a difference over long timescales. There is some ultimate limit on the evolution of any character. Selection may make a mouse the size of a cat in a few hundred generations, but even assuming that those cat-sized mice can stick around, there is no reason to think that dog-sized mice will be better! At some point, selection will stabilize -- and for most characters the amount of change permitted by stabilizing selection is not too great. Sampled at time intervals of many hundreds of generations, selection may look exactly like genetic drift.

What to do

People think about genetic drift because of its mathematical convenience. Sampling error is predictable, and the repeated occurrence of sampling error over many generations follows well-known probability distributions.

Selection is predictable too, but it requires you to actually know something about ecology. We often don't know anything, and when we do, we usually have some particular relationship in mind, which needs to be tested. So, we test the hypothesis of neutrality, with all its mathematical simplicity.

But remembering that the null hypothesis is sometimes -- maybe even often -- true doesn't mean that we should be satisfied with any particular test of that null. For neutral evolution of phenotypes, there are more powerful tests than evolutionary rates. The problem is that these "tests" are not in large part quantitative, but instead are logical or qualitative.

For example, it is very likely that human brains increased in size under selection because there should clearly have been selection against larger brains because of their energetic costs. The rate of evolution does not factor in here, and is in fact irrelevant to the assessment of selection.

The case does require a more complex model than simple directional selection -- instead it involved a structured model in which the force of selection is mostly stabilized by a counterforce of selection. It also begs an explanation for why the change should have proceeded at a given rate -- for example, was it slow because of environmental constraints? Such constraints would seem a likely explanation for the rate of change of dental size in Australopithecus afarensis.

But when most people talk about genetic drift, their reality doesn't seem to include the mathematical consequences of genetic drift.

For one thing, genetic drift is sloooooow. It affects allele frequencies on a time scale in generations proportional to the effective population size.

We sometimes hear that it is a bad thing to doubt the power and ubiquity of genetic drift. This doubt is sometimes equated with adaptationism, taken as the uncritical assumption of selection as a null hypothesis.

References:

Gould SJ, Lewontin RC. 1979. The spandrels of San Marco and the Panglossian paradigm: a critique of the adaptationist programme. Proc R Soc Lond B 205:581-598.

Lockwood CA, Kimbel WH, Johanson DC. 2000. Temporal trends and metric variation in the mandibles and dentition of Australopithecus afarensis. J Hum Evol 39:23-55.

Hawks J, Wolpoff MH. 2001. The accretion model of Neandertal evolution. Evolution 55:1474-1485.

Following up on yesterday's post on annoying misconceptions, I noticed Razib had posted his own candidate:

My problem is not an misconception, it is a pet peeve. As I've noted before, random genetic drift is a catchall explanation for everything.

Well, I thought that was worth a post of its own instead of an update, because it probably annoys me even more than the species divergence thing.

It is a periodic revelation for me how many committed Darwinists don't use or understand natural selection. I think they place natural selection somewhere between Santa Claus and the Tooth Fairy -- useful to explain a few really strange phenomena, but pretty much irrelevant to evolution.

There is, of course, some reason to be cautious about selection. A little selection goes a long way toward explaining almost any pattern of evolution. Selection can make populations stay the same, and it can make them change. It can make them change fast, or it can make them change slowly. And at the genetic level, there are good reasons to suppose that many nucleotide changes don't have a phenotypic effect -- necessary for them to be selected. So it is reasonable a lot of the time to take neutrality (and therefore, genetic drift) as a null hypothesis for change.

Null hypotheses aren't there to be believed, they are there to be tested! Neutrality is a better null hypothesis because the hypothesis of some kind of selection is harder to refute. But neutrality is pretty hard to refute too, at least for the kind of evidence we usually have at hand.

It doesn't help at the molecular level that clearly non-neutral patterns of variation can be explained by extreme demographic changes (and no selection), or selection. Which hypothesis do we choose then? Most people pick neutrality, but not always for good reasons.

Nor does it help that morphological change over long time spans tends to average to very small amounts per unit time. That pattern of change is thoroughly consistent with genetic drift, but equally consistent with slowly changing stabilizing selection. And depending on the density of fossil sampling, it is often consistent with occasional pulses of strong directional selection.

Testing the difference between these hypotheses statistically is murderously hard with fossil samples. So what do we accept provisionally?

Myself, I'm a natural selection man. Accident is overrated.

You know, there's something depressing about collecting a bunch of annoying misconceptions -- and I suppose reading all of them must be sort of annoying itself. Of course, there's always the hope that writing about them might have some effect ...

Ackermann and Cheverud (2004) consider the pattern of selection necessary to change a nonrobust australopithecine cranium (i.e. Sts 5) into a robust australopithecine or early Homo cranium. To do this, they measure seven fossil specimens (KNM-ER 1470, KNM-ER 1813, KNM-ER 3733, KNM-ER 406, KNM-WT 17000, SK 48, and Sts 5), taking eight linear measurements on each (nasion-nasale, nasion-frontomalare, nasale-anterior nasal spine, anterior nasal spine-intradentale superior, anterior nasal spine-zygomaxillare superior, frontal-maxillary nasal suture point-zygomaxillare superior, and zygomaxillare superior-frontomalare). These are all facial measurements, so the question is the degree to which gross facial dimensions change over time.

They also have samples of humans, chimpanzees, and gorillas to provide a model of within-population facial variation. These comparative samples are used as follows:

Phenotypic within-population V/CV matrices for the facial variables from all three living primate populations were obtained by using the residual CV matrix from a multiple ANOVA with the eight traits as the dependent variables and subspecies as the independent variable, thus pooling the CV across subspecies, and were then simplified to their principal components (PCs). The PCs of the within-population V/CV matrix are ordered by their level of V (eigenvalues) and are uncorrelated with one another so that on the scale of the PCs, the within-population V/CV martix is a simple diagonal matrix with no CVs among components. PC scores are calculated for each fossil population by multiplying trait means by the standardized within-population PC loadings. The between-population V for each PC can then be calculated as the V among these population mean PC scores; these values are given in Table 2 along with the within-population Vs (eigenvalues) for each extant model (Ackermann and Cheverud 2004:17947).

I had to read that through a few times before I got it, and since I'll surely forget it, I quoted it verbatim.

From the values for each group, the amount of morphological change is estimated between the hominid populations. Random drift is expected to cause evolutionary divergence between populations in a way that is proportional to the within-population variation of traits. In other words, traits that are highly variable within populations should also vary highly between populations, and two traits that are correlated within populations should both vary in the same way between populations. By examining the PC scores within populations, they eliminate the correlations, and can consider whether the within and between-population differences are linearly related. Under the hypothesis of genetic drift, the slope of a regression between the two should be 1.0. Greater divergence time increases the expected between-population difference, but the relation with within-population variance of each trait should remain linear and with a slope of 1.0 (17948).

Since these are PC scores, it is hard for me to figure out quite what deviations from this model would mean. For example, there is undoubtedly variation about the regression line, but how much variation is too much to be consistent with the model? If the slope deviates from 1.0, that means that the high variance traits are either significantly more or less different than they should be, or the low variance traits are significantly higher in between-variation difference than they should be (they would seem unlikely to be lower than expected). And are the PC's drawn from living hominoid populations really applicable to the fossils? After all, the three contemporary species generate different PC's, and the fossil taxa are analyzed three different ways here as a result. Does the significant result in the robust australopithecines mean that they really were subject to selection, or that they fit the pattern of variation in living hominoids poorly? Since these variances are pooled into classes (australopiths, robusts, Homo), it is hard to tell.

The hominid data seem difficult to shoehorn into Lande's (1976) predictions about drift. The expectation for the degree of change over time for a trait within a population is no change. In an infinitely large set of populations, the degree of change in a single trait is expected to be distributed normally, with a variance determined by the within-population variance of the trait. What that means is that if there are a large set of populations that have diverged simultaneously from a common ancestor, the degree of variance among those populations should be predicted by the degree of variance within the populations. But for the early hominids we do not have a large range of populations; we have a set of pairwise contrasts. I should also mention that we do not have a sample of species means; we have a sample of individuals drawn from species at different times and places. For example, the "australopith" class equals the "robust" class plus Sts 5. Together, all this should mean that the scatter plot of between-population difference against within-population variance should be exactly that--a scatter.

For the significant results, Ackermann and Cheverud (2004) estimate the degree of selection necessary on each linear measurement to create the observed amount of change. These values are smoothed across a map of the face to create a graphic picture of selection intensity. This is not a real quantification of selection in terms of deaths, since each measure used here may really be linked to one or more correlated traits that affect mortality in early hominid populations.

Their results indicate that robust australopithecines emerged through a selective process operating on the shape of the upper and lower face, while early Homo did not exhibit a significant divergence from the predictions of genetic drift among the specimens sampled. They describe this result (17951):

[A]lthough the initial divergence of Homo from the australopiths may have involved selection, divergence after this time (at least in the facial characters analyzed) could have occurred through random processes alone. In other words, much of the facial diversity seen in the Homo lineage from ~2.5 million to 1 million years ago may result from random evolutionary processes, rather than adaptive evolution. Other studies have shown that craniofacial diversity in most populations of modern humans can be explained by random processes. Lynch (1990) suggests that the development of cultural inheritance could have released many of the morphological traits of humans from the pressures of stabilizing selection. This study supports that idea and supplies it with a temporal context, potentially providing direct biological evidence of a shift early on in this lineage toward nonbiological adaptation (i.e., culture) as early hominins increasingly relied on technology. Because drift tends to play a larger role in shaping diversity when populations are finite, these results also may reflect a demographic revolution toward increasingly isolated and widespread populations.

The time range cited here is probably overstating matters, considering their sample of 3 specimens. Indeed, the great size disparity among the early Homo fossils used here may have some effect on the results. I would posit that it is not time yet to accept the null hypothesis of drift, considering the failure to detect the fairly profound selection on size among the specimens. The fact that the variation among these specimens correlates linearly with the variation within the comparative samples does not prove drift; there are a number of ways that selection on facial shape might result in such a pattern. Consider for example that the gorilla comparative model (which has the greatest degree of within-sample variation and would best match the two-specimen distance of KNM-ER 1470 and KNM-ER 1813) yields a regression for the early Homo sample with an R² of 0.01. In other words, the scatter is super-high, and doesn't really prove or disprove anything. The chimpanzee and human models are very close to a slope of 1.0, and have less scatter; but their variance is arguably a worse model for early Homo including H. habilis.

For the robust australopithecines, Wood and Lieberman (2001) found that the traits that vary most within the lineage are those that are related to masticatory strain; the fact that these characters are much less variable between robust taxa (indicated by the very low regression slope found in this study) is not especially surprising: this would seem to indicate strong stabilizing selection on variable characters within taxa rather than directional selection on robust facial morphology over time.

I think a stronger study would control better by sample, with larger samples compared to each other and specific evolutionary hypotheses being tested (for example, are all early Homo erectus specimens, including Dmanisi, significantly divergent from Homo habilis?). I won't say that more features should be added, because until there are more specimens, there is no point whatsoever in adding features from a statistical point of view. Indeed, more focused questions might require that variable number be reduced. A resampling test that could determine if a very small number of traits are consistent with drift would be useful here. Even if this were simply a test of the regression, it might be handy, but especially if it tested drift directly without recourse to a regression. In particular, if such a test could directly compare pairs of species samples instead of variance within multiple-species samples, it would be a more useful test.

References:

Ackermann RR and Cheverud JM. 2004. Detecting genetic drift versus selection in human evolution. Proc Natl Acad Sci U S A 101:17946-17951.