"The catechism about genetic drift"

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 Ne. 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 Ne = 1.8 x 106. The increase from early Neandertals to Würm Neandertals was less likely to occur by drift alone -- our estimate of Ne = 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.