Genetic Drift
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[edit] Definition
Genetic drift may be defined as the random component in the change of allele frequencies in the gene pool.
[edit] Neutral drift
We might begin our examination of genetic drift by looking at its effect on neutral differences between variant alleles of the same gene: that is, differences which do not affect the genetic fitness of the organisms involved, and which are therefore unaffected by natural selection. In this section, we shall tend to speak as though all genetic variation is neutral: this may very nearly be true.
We shall also tend to speak as though the population of a species stays the same over time: this, again, is not a bad approximation to what we find in nature. It is possible to work out what happens if the population size is allowed to vary, but this article is intended only as an introduction to the field.
We shall show the mathematical working behind our results; for the benfit of those readers who don't like math, We shall provide a short qualitative summary of the results at the end of each subsection.
[edit] The random walk
For convenience we shall discuss a gene with only two alleles, which we shall call A and B: what we say will apply equally well where there is greater genetic diversity.
So, suppose we have two alleles, A and B, neither having any selective advantage over the other, in a certain ratio in a gene pool. We cannot expect this ratio to remain stable, because the reproductive chances of the two allele types will depend to a certain extent on chance. In any particular generation, the carriers of one or the other type of allele may be eaten by predators, or fail to find a mate --- or be struck by lightning, for that matter.
This means that the allele frequencies will vary in what mathematicians call a random walk: they will fluctuate up and down randomly (see graph opposite).
This random walk will finish when one of the alleles reaches fixation: i.e. every gene in the gene pool is of this type; and, by the same token, the other allele is exctinct in the gene pool. The graph opposite shows this: the A allele reaches fixation, the B allele goes extinct. It is inevitable, given enough time, that one or the other of the two alleles would become fixed, because for a random walk to keep the allele frequencies in the middle of the graph, without the frequency of the A allele hitting either 0% or 100%, would take an infinite series of coincidences.
Summary: Because of genetic drift, the ultimate fate of every neutral variation within a gene pool is either extinction or fixation.
[edit] New mutations and neutral drift
When a new neutral mutation arises (let us say one A allele in a gene pool otherwise consisting of B alleles) then the process of genetic drift begins. And it begins with the A allele very close to extinction: the random walk begins right next to the bottom of the graph of the allele frequency of A. This means that the random walk is much more likely to take the allele frequency of A to extinction than to fixation.
By a neat trick, we can calculate exactly how much more likely extinction is than fixation: this depends on the size of the effective population (the part of the population which is not too old or too young to breed) and on the ploidy of the organisms involved, i.e. how many copies of each chromosome they possess.
Consider a diploid species having an effective population Ne of 50. Then we may regard the gene pool as having 100 copies of the gene. Suppose one of them is of type A and all the others of type B. Let us mentally label the B type alleles from B1 - B99. We may then think of B1 - B99 as being 99 more neutral "variants" of the gene, though the only difference between them is the mental labels we've put on them.
Now, as we have stated, the fate of every neutral variation must either be extinction or fixation. This means that if we wait long enough, every copy of the gene in the gene pool will be descended from allele B17, say, or B94 --- or from A. Now, because A is a neutral mutation, it stands an equal chance with the B alleles of achieving fixation. So in this case, it has a 1/100 chance of achieving fixation, and a 99/100 chance of reaching extinction in the gene pool.
In general, then, the chances of fixation of a new neutral mutation are 1 / fNe, where f gives the ploidy of the species in question (1 for haploid, 2 for diploid, et cetera).
Summary: The probability that a new neutral mutation will end up being fixed in the gene pool is inversely proportional to the size of the population.
[edit] Substitution and the genetic clock
This leads to a further rather neat result. Let μ be the rate at which neutral mutations occur, given as probability of mutation per nucleotide per generation. Then there will be μfNe mutations per site per generation in the population. Of these, only a fraction will go on to fixation, this fraction being given, as we have shown, by 1/fNe. It follows that the rate of substitution (i.e. the fixation of new alleles, replacing the old ones) is given by μfNe/fNe --- which is just equal to μ. In other words, the rate of substitution per site per generation in the entire gene pool is equal to the rate of mutation per nucleotide per generation in the individual. The fact that large populations reduce the probability of a new allele being fixed is exactly cancelled out by the fact that new mutations are more likely to arise in larger populations.
This means that the rate of substitution is independent of fluctuations in population size. To know how many substitution events should take place over a given period of time, all we need to know is the rate at which mutations take place. This means that if we have two isolated gene pools which once had a common ancestor, and we know their mutation rate, we can work out how long the two gene pools have been separated by counting the number of different substitution events in the two gene pools.
Summary: The rate at which substitution of new alleles for old takes place in the gene pool does not depend on population size. We can use this fact to estimate the time of divergence of two separate gene pools. For more detail, see our main article on Molecular Clocks.
[edit] Neutral drift and genetic diversity
As we have shown, under neutral drift, each allele must tend either to fixation or extinction; so neutral drift reduces genetic diversity. On the other hand, new mutations increase genetic diversity.
We can calculate the results of this process.
Let us call the proportion of variant alleles in the gene pool H (for heterozygosity). Let the rate of mutation, as in the subsection above, be given by μ. The probability that such a mutation will affect a site which already exhibits variation is given by H; the chance that it will increase the number of sites with variant alleles is therefore 1 - H. Hence, mutation will increase the proportion of genes with variant alleles by μ(1 - H) per generation.
On the other hand, genetic drift, as we have shown, will remove a proportion 1/fNe of the variation per generation. So we can write the difference equation from one generation to the next as:
Hnew = Hold + μ(1 - Hold) - Hold/fNe.
The important thing to notice here is that when the amount of variation H is small, then we will have μ(1 - Hold) > Hold/fNe and the amount of variation in the gene pool will increase, and conversely when the amount of variation is large then it will decrease.
This means that if we leave the population constant for long enough, then eventually it will reach equilibrium --- the point at which the rate of increase of diversity by mutation is exactly balanced out by the decrease of diversity by genetic drift. This is the equilibrium heterozygosity, which we shall call H*: the point at which Hnew = Hold. So, from our difference equation above, we get:
H* = H* + μ(1 - H*) - H*/fNe
Solving this equation for H*, we get:
H* = μfNe/(1 + μfNe)
You will notice that the larger Ne is, the nearer H* approaches 1. This means that a smaller gene pool will have less genetic diversity than a larger one --- a fact of great concern to conservationists.
We can use this equation to learn about the past demographics of a species. For example, cheetahs have much less genetic diversity than we would expect from the size of the cheetah population: from this it is reasonable to deduce that at some time in the past it was squeezed through a population bottleneck, and that this happened sufficiently recently that it has not yet been able to recover its genetic diversity.
We may note in passing that if the legend of Noah's Ark was true, as asserted by creationists, the genetics of every land species would show signs of having passed through an exceedingly tight population bottleneck a mere 4000 years ago: this would stick out like a sore thumb in the genetic record, and is, of course, not the case.
Summary: Given the size of the population and the rate of mutation, we can say how much diversity there should be in a gene pool if the population size has kept reasonably stable. By comparing this figure to actual genetic diversity, we can learn about the demographic history of a species.
[edit] Drift with selection
In this section we shall look at the effect of genetic drift on alleles which are not neutral, and discuss briefly the interaction of genetic drift with natural selection
[edit] Drift and advantageous alleles
An allele which carries with it some benefit is not immune to neutral drift. The creatures possessing it have an advantage over the creatures that don't, but the edge is often slight, and it does not make them immune to the accidents that life may spring on them.
The result of this is that the frequency of an adaptive allele in the gene pool, like the frequency of a neutral allele, will go on a "random walk" until it eventually achieves either fixation or extinction. The only difference is that the random walk of the advantageous allele is biased by natural selection, so that there will each step in the random walk is more likely to be up rather than down the graph of allele frequency.
As with neutral mutations, the most likely fate of a new adaptive mutation (unless the associated benefit is absolutely huge) is to drift out of the gene pool almost as soon as it appears, and for the same reason: it starts off its random walk just above extinction level.
The likely fate of any new mutation, good, bad, or neutral, is for genetic drift to remove it from the population. The effect of natural selection is to make the fixation of advantageous alleles much more likely than the fixation of disadvantageous alleles.
But this is still not very likely: it is far from a certainty. The benefit of an advantageous allele over the others is often expressed in terms of selective advantage (denoted by s). To explain this concept by example, if allele A has a selective advantage of 0.02 over allele B, this means that for every 1 child a carrier of allele B may expect to produce and have reach breeding age, a carrier of allele A may expect 1.02 such children.
It was first calculated by J.B.S. Haldane that if the population is reasonably large, and the benefit of the mutation reasonably small, then the probability that it will reach fixation is approximately 2s. So a new mutation with a selective advantage of 0.02 has a 4% chance of achieving fixation. The odds are not good: they are merely much, much better that for maladaptive mutations; which is what makes adaptive evolution possible.
Summary: Because of genetic drift, a beneficial mutation still has only a slim chance of achieving fixation. Natural selection gives new and beneficial mutations a much greater chance of achieving fixation than harmful mutations, but this is not to say that the fixation of any particular beneficial mutation is inevitable or even likely.
[edit] Drift and disadvantageous alleles
In principle, a sufficiently large number of accidents could cause a harmful mutation to achieve fixation in any population, however large, so long as the mutation was not so harmful as to invariably cause either death before breeding age or complete sterility.
In practice, the series of coincidences required would have to be unfeasibly enormous. A new and harmful mutation has to deal both with the tendency of genetic drift to remove any new variant from the gene pool and with the pressure of natural selection: and this is a powerful combination.
This fact is, of course, of concern to conservationists: to conserve a species, it is not enough to maintain a small population, because as time passes, genetic drift will cause the substitution of more and more harmful mutations in the gene pool. The rule of thumb used by ecologists is the 50/500 rule --- 50 individuals are needed for the short-term genetic health of a species, and 500 in the long term.
Summary: Because of genetic drift, harmful mutations stand a realistic chance of being fixed in the gene pool if the population is very small.
[edit] Misconceptions
There are a number of mistakes and misconceptions concerning genetic drift.
[edit] Overlooking genetic drift
The most common mistake people make about genetic drift is to simply ignore it and its importance in the theory of evolution. But genetic drift can, as we have seen, fix alleles just like natural selection; nor is it impossible that a sufficient amount of neutral drift can lead to speciation.
We find natural selection more interesting --- glamorous, even --- because it explains the adaptation of organisms to their environment. But the study of neutral drift can tell us interesting things too; and certainly any mathematical model of evolution has to incorporate genetic drift at a very fundamental level. If we oversimplify the theory of evolution to "random mutation and natural selection", then this will do OK for understanding many of its qualitative aspects, but it would not allow us to construct a quantitative model.
[edit] "Darwinism" and genetic drift
The very first person to overlook the importance of genetic drift in evolution was, of course, Charles Darwin. He had the best of excuses: modern genetics had not at that time been invented.
When "neutralists", as they were called, tried to put genetic drift in its proper place in the theory of evolution, sometimes against stiff opposition, they referred to their opponents as "Darwinists", meaning that they placed too much emphasis on Darwin's concept of natural selection as the driving force for evolution, and didn't give sufficient credit to the concept of genetic drift. By disparaging "Darwinism", they do not, of course, mean to disparage the theory of evolution, of which genetic drift is, indeed, an integral part. On the other hand, there are scientists who to this day use "Darwinism" as a synonym for the modern theory of evolution, just as one might speak of "Newtonian" dynamics such as Newton never dreamed of.
This ambiguity is, naturally, a creationist's paradise, since, depending on usage, the word "Darwinism" as used by the kind of distinguished scientist whose authority they crave, could either refer to the theory of evolution, or to an outmoded concept of the theory of evolution, depending on the scientist. So, through ignorance or malice, they have the opportunity to quote-mine perfectly respectable scientists as attacking "Darwinism", as though they were attacking either the theory or the historical fact of evolution.
