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Modern Genetic Analysis Chapter 17. Population and Evolutionary Genetics
Random Events

If a population is finite in size (as all populations are) and if a given pair of parents has only a small number of offspring, then, even in the absence of all selective forces, the frequency of a gene will not be exactly reproduced in the next generation, because of sampling error. If, in a population of 1000 individuals, the frequency of a is 0.5 in one generation, then it may by chance be 0.493 or 0.505 in the next generation because of the chance production of a few more or a few less progeny of each genotype. In the second generation, there is another sampling error based on the new gene frequency, so the frequency of a may go from 0.505 to 0.511 or back to 0.498. This process of random fluctuation continues generation after generation, with no force pushing the frequency back to its initial state, because the population has no "genetic memory" of its state many generations ago. Each generation is an independent event. The final result of this random change in allelic frequency is that the population eventually drifts to p = 1 or p = 0. After this point, no further change is possible; the population has become homozygous. A different population, isolated from the first, also undergoes this random genetic drift, but it may become homozygous for allele A, whereas the first population has become homozygous for allele a. As time goes on, isolated populations diverge from each other, each losing heterozygosity. The variation originally present within populations now appears as variation among populations.

One form of genetic drift occurs when a small group breaks off from a larger population to found a new colony. This "acute drift," called the founder effect, results from a single generation of sampling, followed by several generations during which the population remains small. The founder effect is probably responsible for the virtually complete lack of blood group B in Native Americans, whose ancestors arrived in very small numbers across the Bering Strait at the end of the last Ice Age, about 20,000 years ago.

The process of genetic drift should sound familiar. It is, in fact, another way of looking at the inbreeding effect in small populations discussed earlier. Whether regarded as inbreeding or as random sampling of genes, the effect is the same. Populations do not exactly reproduce their genetic constitutions; there is a random component of gene frequency change.

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 m , 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 2Nm . 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 km 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.

MESSAGE
New mutations can become established in a population even though they are not favored by natural selection simply by a process of random genetic drift. Even new favorable mutations are often lost.

© 1999 by W. H. Freeman and Company. All rights reserved.