Why accelerated adaptive evolution is faster evolution

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)/2Ne, where Ne 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 (2Neu for an autosomal locus). But the rate of fixation is inversely proportional to population size (1/2Ne). 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 (4Ne 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.

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