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.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.
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.
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].