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Griffiths AJF, Miller JH, Suzuki DT, et al. An Introduction to Genetic Analysis. 7th edition. New York: W. H. Freeman; 2000.

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An Introduction to Genetic Analysis. 7th edition.

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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 slightly more or slightly fewer 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.0

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 24-15. 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.

Figure 24-15. The appearance, loss, and eventual incorporation of new mutations in the life of a population.

Figure 24-15

The appearance, loss, and eventual incorporation of new mutations in the life of a population. If random genetic drift does not cause the loss of a new mutation, then it must eventually cause the entire population to become homozygous for the mutation (more...)

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.

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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.

Another consequence of the interaction of random and selective forces is that the effectiveness of the selective force in driving population composition depends on population size. The magnitude of the random effect is proportional to the reciprocal of population size, 1/N, whereas the magnitude of a deterministic force depends on the migration rate, m, or mutation rate, μ, or selection coefficient, s. Thus we can say, roughly, that migration and mutation are effective if

Image ch24e48.jpg

The same is true of selection; selection is effective only if Ns ≥ 1. When Ns is small because selection is weak or population size is small, then mutations are effectively neutral, even though there is some selection of them. Small populations will be less affected by selection than large populations even under otherwise identical conditions. For example, human populations were very small for nearly all the history of our species, having grown large only in the past few hundred generations. Thus, we may expect to find that many mutations that are now under selection were effectively neutral for a long time and may have reached high frequency by chance.

By agreement with the publisher, this book is accessible by the search feature, but cannot be browsed.

Copyright © 2000, W. H. Freeman and Company.
Bookshelf ID: NBK21995

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