Tuesday, September 25, 2007

Random Genetic Drift and Population Size

One of the most persistent myths of evolutionary biology is that random genetic drift only occurs in small populations. You'll find this myth everywhere you look, even in textbooks that should know better. A few minutes ago I was looking for a simple way to explain this in the comments section of P-ter Accuses Me of Quote Mining when I came across this explanation in Modern Genetic Analysis by Anthony Griffiths, William Gelbart, Jeffrey Miller, and Richard Lewontin (1999 edition). This is the offspring of a textbook that David Suzuki started many years ago [ 17. Population and Evolutionary Genetics].
One result of random sampling is that most new mutations, even if they are not selected against, never succeed in entering the population. Suppose that a single individual is heterozygous for a new mutation. There is some chance that the individual in question will have no offspring at all. Even if it has one offspring, there is a chance of 1/2 that the new mutation will not be transmitted. If the individual has two offspring, the probability that neither offspring will carry the new mutation is 1/4 and so forth. Suppose that the new mutation is successfully transmitted to an offspring. Then the lottery is repeated in the next generation, and again the allele may be lost. In fact, if a population is of size N, the chance that a new mutation is eventually lost by chance is (2N − 1)/2N (For a derivation of this result, which is beyond the scope of this book, see Chapters 2 and 3 of Hartl and Clark, Principles of Population Genetics.) But, if the new mutation is not lost, then the only thing that can happen to it in a finite population is that eventually it will sweep through the population and become fixed. This event has the probability of 1/2N In the absence of selection, then, the history of a population looks like Figure 17-17. For some period of time, it is homozygous; then a new mutation appears. In most cases, the new mutant allele will be lost immediately or very soon after it appears. Occasionally, however, a new mutant allele drifts through the population, and the population becomes homozygous for the new allele. The process then begins again.

Even a new mutation that is slightly favorable selectively will usually be lost in the first few generations after it appears in the population, a victim of genetic drift. If a new mutation has a selective advantage of S in the heterozygote in which it appears, then the chance is only 2S that the mutation will ever succeed in taking over the population. So a mutation that is 1 percent better in fitness than the standard allele in the population will be lost 98 percent of the time by genetic drift.

The fact that occasionally an unselected mutation will, by chance, be incorporated into a population has given rise to a theory of neutral evolution, according to which unselected mutations are being incorporated into populations at a steady rate, which we can calculate. If the mutation rate per locus is μ, and the size of the population is N, so there are 2N copies of each gene, then the absolute number of mutations that will appear in a population per generation at a given locus is 2Nμ. But the probability that any given mutation is eventually incorporated is 1/2N so the absolute number of new mutations that will be incorporated per generation per locus is (2Nµ)(1/2N) = µ If there are k loci mutating, then in each generation there will be kμ newly incorporated mutations in the genome. This is a very powerful result, because it predicts a regular, clocklike rate of evolution that is independent of external circumstances and that depends only on the mutation rate, which we assume to be constant over long periods of time. The total genetic divergence between species should, on this theory, be proportional to the length of time since their separation in evolution. It has been proposed that much of the evolution of amino acid sequences of proteins has been without selection and that evolution of synonymous bases and other DNA that neither encodes proteins nor regulates protein synthesis should behave like a molecular clock with a constant rate over all evolutionary lineages. Different proteins will have different clock rates, depending on what portion of their amino acids is free to be substituted without selection.
This is an important conclusion. It shows that alleles are fixed in large populations by random genetic drift. I'd like it a lot if people would stop saying that drift only occurs in small populations.

18 comments :

  1. As always, there is a more sophisticated way to look at the issue. Drift can act rapidly in small populations, and therefore can be an important part of evolution. But it is a silly logical fallacy to assume that because it acts in small populations that it does not act in large populations. As the great philosopher Aristotle, no Nietsche, no Popper...wait, it was that philosopher Moran that said, "Drift happens."

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  2. One of the most persistent myths of evolutionary biology is that random genetic drift only occurs in small populations. You'll find this myth everywhere you look, even in textbooks that should know better.

    Which textbooks are these? Mine says that drift is far more important in small populations, much like the excerpt in this post did, really.

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  3. Okay, so some textbooks get it completely wrong and others only get it partially wrong.

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  4. While the point of drift having a role in fixation and elimination in even large populations is well taken, it's safe to say that all else being equal, the ratio of selection to drift in gene evolution is higher in larger populations than it is smaller ones. Generalizing further, the role of selection relative to drift in speciation is higher in anagenesis than it is in cladogenesis.

    Anyone disagree?

    Tupaia

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  5. As Larry of course knows, the population-size independence of the rate of fixation applies only to alleles that are EXACTLY neutral. Even a pretty small selection coefficient reintroduces a significant population dependence (i.e. Ohta's "near-neutral theory"), in which case selection IS relatively more important in large populations. And it's very rare that we have the data to tell whether an allele is strictly neutral or near-neutral.

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  6. Thanks for posting that very clear exposition.
    Since it was a comment of mine that prompted it, though, I'd like to point out the context: we were talking about the evolution of phenotypic traits, and the relative likelihood of attributing it to selection vs. drift. If we have identified a phenotypic trait of interest, then we have indirectly specified a particular mutation of origin, and given that specific mutation, its fixation by drift is far more likely in a small population. I regret wording that point in an over-generalized way in the first place.

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  7. I'm relatively new to this lark; previously my understanding of evolution was pretty simple, mutation, selection kind of stuff. I'm now getting to grips with the complex realities of evolution. With that context in mind, I hope people will excuse what might be a stupid question.

    Is the key question not whether or not genetic drift occurs in large populations, but how significant it is? If fixation time increases linearly with population size then does this mean that large populations are unlikely to be massively affected by it, simply because drift would take too long to have any major impacts?

    Assuming this to be the case, does the question then becomes whether or not anything can be done to large populations to increase the influence of drift? For example, subdividing them, a question that this paper (which I'm still trying to get my head around) investigates:

    Blythe, R.A. (2007) The propagation of a cultural or biological trait by neutral genetic drift in a subdivided population. Theoretical Population Biology, 71, 454-472.

    Also, with regards to this part of the textbook excerpt:

    So a mutation that is 1 percent better in fitness than the standard allele in the population will be lost 98 percent of the time by genetic drift.

    Does this basically mean that genetic drift swamps a lot of beneficial mutations? Quite a few of the papers that I've read that measure the fitness effects of BMs have values of between 1 and 5%. Will such beneficial mutations most likely be lost to these laboratory populations over time? To get significant evolutionary change via beneficial mutations requires ones with large fitness effects?

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  8. Is this "either disappear or take over the population"?

    As far as I can conceive, differences of fitness of genotypes may lead to greater probability of survival of some which are more frequent in the population, but usually we also have other less fit phenotypes represented, simply in smaller proportion, right?

    Though I understand conditions for equilibrium may be rare, there is such a thing as coexistence of different phenotypes within a population, this is well-documented; and any of these (not necessarily the fittest) could give origin to a new species.

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  9. Thinking through the implications of our appreciation of both neutral (drift) and non-neutral (selection and drift) gene evolution in large populations, it can be concluded that the Mayr-Gould notion that the isolation of small peripheral populations is the main or sole mechanism of speciation can be dispensed with as incorrect. Rather, the small isolate model is one of several mechanisms, since large, unbroken populations can evolve into new species through a combination of selection and drift (with selection being more important in this process the larger the population).

    Tupaia

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  10. To keep things clear that are easy to confuse, the probability of fixation given sufficient time of any particular neutral allele, including one of Sven's visible but neutral mutations, is equal to the rate at which it arises by mutation and is independent of population size. (So Sven's statement, if interpreted in this sense, is not correct). However the average TIME (in generations)to fixation of a neutral allele IS proportional to population size (allele frequencies show much more drastic random fluctuations each generation in a small population.) The latter fact is no doubt the source of (correct) statements that drift can have much more powerful effects in situations where population size is drastically but temporarily reduced eg. bottlenecks and founder effects.

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  11. Steve LaBonne says,

    As Larry of course knows, the population-size independence of the rate of fixation applies only to alleles that are EXACTLY neutral. Even a pretty small selection coefficient reintroduces a significant population dependence (i.e. Ohta's "near-neutral theory"), in which case selection IS relatively more important in large populations. And it's very rare that we have the data to tell whether an allele is strictly neutral or near-neutral.

    Steve is correct and I should have mentioned this in my article.

    Nevertheless, the main point is valid. Random genetic drift is not restricted to small populations. Furthermore, the very existence of an approximate molecular clock over periods of hundreds of millions of years indicates that fixation by drift in far more common than fixation by natural selection.

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  12. steve dimilo says,

    If we have identified a phenotypic trait of interest, then we have indirectly specified a particular mutation of origin, and given that specific mutation, its fixation by drift is far more likely in a small population.

    This is correct. If we're talking about a specific trait, say, ability to roll your tongue, then it is more likely to be fixed in a small population. However, if we're talking about neutral phenotypes in general then it is not correct to say that they can only become fixed in small populations.

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  13. One of the most persistent myths of evolutionary biology is that random genetic drift only occurs in small populations. You'll find this myth everywhere you look, even in textbooks that should know better.

    Okay, so some textbooks get it completely wrong and others only get it partially wrong.

    Really? Mention those textbooks, then. Griffiths et al, Suzuki, Hartl & Clark are mentioned, an d by implication have it right according to Larry, but the explanation above reads identical to Futuyma, and all seem a pretty direct lift from Kimura's monograph.

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  14. Furthermore, the very existence of an approximate molecular clock over periods of hundreds of millions of years indicates that fixation by drift in far more common than fixation by natural selection.
    One has to be a bit careful about qualifying this last statement. There is a selection (in the statistical not genetic sense) bias at work there, since you'll get sensible results for clock purposes only if you ARE looking at changes which are selectively neutral or very near-neutral. So I'm not so sure that molecular-clock studies per se provide a data base which can safely be generalized to make statements about the overall prevalance of neutral substitutions. Real tests of the neutral theory require an attempt to survey an unbiased database of substitutions. As is well known, despite the fact that tests with sufficient statistical power to reject the neutral hypothesis are not at all easy to design, such tests as have been performed have by no means always supported the theory.

    The neutral theory is popular because of its mathematical simplicity, but it's by no means an established fact that it provides an overall accurate picture of evolution.

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  15. Heleen says,

    Really? Mention those textbooks, then. Griffiths et al, Suzuki, Hartl & Clark are mentioned, an d by implication have it right according to Larry, but the explanation above reads identical to Futuyma, and all seem a pretty direct lift from Kimura's monograph.

    I expect most university genetics textbooks to get the explanation correct, and they do. I expect Futuyma to get it right and he certainly does.

    I was thinking about introductory biology textbooks—the source of most information about evolution for most students (and Professors). One of the best is Purves, Orians, Heller and Sadava. I'm looking at the 5th edition (1998). My old friend David Sadava is the lead author on the latest edition so things may have changed.

    In the 5th edition, the only mention of random genetic drift is in a short section titled "Genetic drift may cause large changes in small populations" (pp. 458-460).

    Incidentally, I have an old version of Hartl (1994) and he very much emphasizes that drift is a small population phenomenon (pp. 217-219).

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  16. I happen to have a copy of the 8th edition of Sadava et al. (formerly Purves et al.), copyright 2008 (though I've had it since March!).
    The section of genetic drift is about one page of text, with the same section heading alluded to above ("Genetic drift may cause large changes in small populations"). It's mostly about bottleneck and founder effects, but does include this sentence in the first paragraph: "Even in large populations, genetic drift can influence the frequencies of alleles that do not influence the survival and reproductive rates of their bearers."(p 494)
    In a later chapter ("The Evolution of Genes and Genomes") there is a shorter section called "Much of evolution is neutral" on mutations and drift at the molecular level.

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  17. Does the book give equations for fixation in mitochondrial genomes?

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