Book Viewer

Short Contents | Full Contents | Other books @ NCBI

Modern Genetic Analysis Chapter 17. Population and Evolutionary Genetics
The Effect of Sexual Reproduction on Variation

The evolutionary theorists of the nineteenth century encountered a fundamental difficulty in dealing with Darwin's theory of evolution through natural selection. The possibility of continued evolution by natural selection is limited by the amount of genetic variation. But biologists of the nineteenth century, including Darwin, believed in one form or another of blending inheritance, a model postulating that the characteristics of each offspring are some intermediate mixture of the parental characters. Such a model of inheritance has fatal implications for a theory of evolution that depends on variation.

Suppose that some trait (say, height) has a distri-bution in the population and that individual members of that population mate more or less at random. If intermediate individuals mated with each other, they would produce only intermediate offspring according to a blending model. The mating of a tall with a short individual also would produce only intermediate offspring. Only the mating of tall with tall individuals and short with short individuals would preserve extreme types. The net result of all matings would be an increase in intermediate types and a decrease in extreme types. The variance of the distribution would shrink, simply as a result of sexual reproduction. In fact, it can be shown that the variance is cut in half in each generation, so that the population would be essentially uniformly intermediate in height before very many generations had passed. There then would be no variation on which natural selection could operate. This was a very serious problem for the early Darwinists; it made it necessary for Darwin to assume that new variation is generated at a very rapid rate by the inheritance of characters acquired by individuals during their lifetimes.

The rediscovery of Mendelism changed this picture completely. Because of the discrete nature of the Mendelian genes and the segregation of alleles at meiosis, a cross of intermediate with intermediate individuals does not result in all intermediate offspring. On the contrary, extreme types (homozygotes) segregate out of the cross. To see the consequence of Mendelian inheritance for genetic variation, consider a population in which males and females mate with each other at random with respect to some gene locus A; that is, individuals do not choose their mates preferentially with respect to the partial genotype at the locus. Such random mating is equivalent to mixing all the sperm and all the eggs in the population together and then matching randomly drawn sperm with randomly drawn eggs.

The outcome of such a random pairing of sperm and eggs is easy to calculate. If, in some population, the allele frequency of Ais 0.60 in sperm and eggs, then the chance that a randomly chosen sperm and a randomly chosen egg are both Ais 0.60 × 0.60 = 0.36. Thus, in a random-mating population with this allele frequency, offspring will be 36% A / A. In the same way, the frequency of a / a offspring will be 0.40 × 0.40 = 0.16. Heterozygotes will be produced by the fusion either of an A sperm with an a egg or of an a sperm with an A egg. If gametes pair at random, then the chance of an A sperm and an a egg is 0.60 × 0.40, and the reverse combination has the same probability, so the frequency of heterozygous offspring is 2 × 0.6 × 0.4 = 0.48. Moreover, the process of random mating has done nothing to change allele frequencies, as can be checked easily by calculating the frequencies of the alleles A and a among the offspring by using the method described on page 538. So the proportions of homozygotes and heterozygotes in each successive generation will remain the same.

Genetics in Process 17-2 gives a general form of this equilibrium result.

MESSAGE
Mendelian segregation has the property that random mating results in an equilibrium distribution of genotypes after only one generation, so genetic variation is maintained.

The equilibrium distribution

is called the Hardy-Weinberg equilibrium after those who independently discovered it. (A third independent discovery was made by the Russian geneticist Sergei Chetverikov.)

The Hardy-Weinberg equilibrium means that sexual reproduction does not cause a constant reduction in genetic variation in each generation; on the contrary, the amount of variation remains constant generation after generation, in the absence of other disturbing forces. The equilibrium is the direct consequence of the segregation of alleles at meiosis in heterozygotes.

Numerically, the equilibrium shows that, irrespective of the particular mixture of genotypes in the parental generation, the genotypic distribution after one round of mating is completely specified by the allelic frequency p. For example, consider three hypothetical populations:

The allele frequency p of A in the three populations is

So, despite their very different genotypic compositions, they have the same allele frequency. After one generation of random mating, however, each of the three populations will have the same genotypic frequencies:

and they will remain so indefinitely.

One consequence of the Hardy-Weinberg proportions is that rare alleles are virtually never in homozygous condition. An allele with a frequency of 0.001 occurs in homozygotes at a frequency of only one in a million; most copies of such rare alleles are found in heterozygotes. In general, because two copies of an allele are in homozygotes but only one copy of that allele is in each heterozygote, the relative frequency of the allele in heterozygotes (in contrast with homozygotes) is, from the Hardy-Weinberg equilibrium frequencies,

which for q = 0.001 is a ratio of 999:1. The general relation between homozygote and heterozygote frequencies as a function of allele frequencies is shown in Figure 17-3.

In our derivation of the equilibrium, we assumed that the allelic frequency p is the same in sperm and eggs. The Hardy-Weinberg equilibrium theorem does not apply to sex-linked genes if males and females start with unequal gene frequencies.

The Hardy-Weinberg equilibrium was derived on the assumption of "random-mating," but we must carefully distinguish two meanings of that process. First, we may mean that individuals do not choose their mates on the basis of some heritable character. Human beings are random-mating with respect to blood groups in this first sense, because they generally do not know the blood type of their prospective mates, and, even if they did, it is unlikely that blood type would be used as a criterion for choice. In the first sense, random-mating will occur with respect to genes that have no effect on appearance, behavior, smell, or other characteristics that directly influence mate choice.

There is a second sense of random mating that is relevant when there is any subdivision of a species into subgroups. If there is genetic differentiation between subgroups so that the frequencies of alleles differ from group to group and if individuals tend to mate within their own subgroup (endogamy), then with respect to the species as a whole, mating is not at random and frequencies of genotypes will depart more or less from Hardy-Weinberg frequencies. In this sense, human beings are not random mating, because ethnic and racial groups differ from one another in gene frequencies and people show high rates of endogamy, not only within major races, but also within local ethnic groups. Spaniards and Russians differ in their ABO blood group frequencies, Spaniards marry Spaniards, and Russians marry Russians, so there is unintentional nonrandom mating with respect to ABO blood groups.

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