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Modern Genetic Analysis Chapter 17. Population and Evolutionary Genetics
The Sources of Variation

The variational theory of evolution has a peculiar self-defeating property. If evolution occurs by the differential reproduction of different variants, we expect the variant with the highest rate of reproduction eventually to take over the population and all other genotypes to disappear. But then there is no longer any variation for further evolution. The possibility of continued evolution therefore is critically dependent on renewed variation.

For a given population, there are three sources of variation: mutation, recombination, and immigration of genes. However, recombination by itself does not produce variation unless alleles are segregating already at different loci; otherwise there is nothing to recombine. Similarly, immigration cannot provide variation if the entire species is homozygous for the same allele. Ultimately, the source of all variation must be mutation.

Variation from Mutations

Mutations are the source of variation, but the process of mutation does not itself drive evolution. The rate of change in gene frequency from the mutation process is very low because spontaneous mutation rates are low (Table 17-7 on page 548). The mutation rate is defined as the probability that a copy of an allele changes to some other allelic form in one generation. Suppose that a population were completely homozygous A and mutations to a occurred at the rate of 1/100,000. Then in the next generation the frequency of a alleles would only be 1.0 × 1/100,000 = 0.00001 and the frequency of A alleles would be 0.99999. After yet another generation of mutation, the frequency of a would be increased by 0.99999 × 1/100,000 = 0.000009 to a new frequency of 0.000019, whereas the original allele would be reduced in frequency to 0.999981. It is obvious that the rate of increase of the new allele is extremely slow and that it gets slower every generation because there are fewer copies of the old allele still left to mutate. A general formula for the change in allele frequency under mutation is given in Genetics in Process 17-3.

MESSAGE
Mutation rates are so low that mutation alone cannot account for the rapid evolution of populations and species.

It is not possible to measure locus-specific mutation rates for continuously varying characters, but the rate of accumulation of genetic variance can be determined. Beginning with a completely homozygous line of Drosophila derived from a natural population, 1/1000 to 1/500 of the genetic variance in bristle number in the original population is restored each generation by spontaneous mutation.

Variation from Recombination

The creation of genetic variation by recombination can be a much faster process than its creation by mutation. When just two chromosomes with "normal" survival, taken from a natural population of Drosophila, are allowed to recombine for a single generation, they produce an array of chromosomes with 25 to 75 percent as much genetic variation in survival as was present in the entire natural population from which the parent chromosomes were sampled. This is simply a consequence of the very large number of different recombinant chromosomes that can be produced even if we take into account only single crossovers. If a pair of homologous chromosomes is heterozygous at n loci, then a crossover can take place in any one of the n 1 intervals between them, and, because each recombination produces two recombinant products, there are 2(n 1) new unique gametic types from a single generation of crossing-over, even considering only single crossovers. If the heterozygous loci are well spread out on the chromosomes, these new gametic types will be frequent and considerable variation will be generated. Asexual organisms or organisms, such as bacteria, that very seldom undergo sexual recombination do not have this source of variation, so new mutations are the only way in which a change in gene combinations can be achieved. As a result, asexual organisms may evolve more slowly under natural selection than sexual organisms.

Variation from Migration

A further source of variation is migration into a population from other populations with different gene frequencies. The resulting mixed population will have an allele frequency that is somewhere intermediate between its original value and the frequency in the donor population. Suppose a population receives a group of migrants whose number is equal to, say, 10 percent of its native population size. Then the newly formed mixed population will have an allele frequency that is a 0.90:0.10 mixture between its original allele frequency and the allele frequency of the donor population. If its original allele frequency of A were, say, 0.70, whereas the donor population had an allele frequency of only, say, 0.40, the new mixed population would have a frequency of 0.70 × 0.90 + 0.40 × 0.10 = 0.67. Genetics in Process 17-4 derives the general result. The change in gene frequency is proportional to the difference in frequency between the recipient population and the average of the donor populations. Unlike the mutation rate, the migration rate (m) can be large, so the change in frequency may be substantial.

We must understand migration as meaning any form of the introduction of genes from one population into another. So, for example, genes from Europeans have "migrated" into the population of African origin in North America steadily since the Africans were introduced as slaves. We can determine the amount of this migration by looking at the frequency of an allele that is found only in Europeans and not in Africans and comparing its frequency among blacks in North America.

We can use the formula for the change in gene frequency from migration if we modify it slightly to account for the fact that several generations of admixture have taken place. If the rate of admixture has not been too great, then (to a close order of approximation) the sum of the single-generation migration rates over several generations (let's call this M) will be related to the total change in the recipient population after these several generations by the same expression as the one used for changes due to migration. If, as before, P is the allelic frequency in the donor population and p0 is the original frequency among the recipients, then

so

For example, the Duffy blood group allele Fya is absent in Africa but has a frequency of 0.42 in whites from the state of Georgia. Among blacks from Georgia, the Fya frequency is 0.046. Therefore, the total migration of genes from whites into the black population since the introduction of slaves in the eighteenth century is

When the same analysis is carried out on American blacks from Oakland (California) and Detroit, M is 0.22 and 0.26, respectively, showing either greater admixture rates in these cities than in Georgia or differential movement into these cities by American blacks who have more European ancestry. In any case, the genetic variation at the Fy locus has been increased by this admixture.

The Origin of New Functions

Point mutations or chromosomal rearrangements are themselves a limited source of variation for evolution because they can only alter a function or change one kind of function into another. To add quite new functions requires expansion in the total repertoire of genes through duplication and polyploidy, followed by a divergence between the duplicated genes, presumably by the usual process of mutation. Expansion of the genome by polyploidy has clearly been a frequent process, at least in plants.

When the total DNA of the genome has expanded, only a few base substitutions in a gene may be required to provide it with a new function. For example, B. Hall has experimentally changed a gene to a new function in Escherichia coli. In addition to the lacZ genes specifying the usual lactose-fermenting b -galactosidase activity in E. coli, another structural gene locus ebg specifies another b -galactosidase that does not ferment lactose, although it is induced by lactose. The natural function of this second enzyme is unknown. Hall was able to alter this gene into one specifying an enzyme that ferments another substrate, lactobionate. To do so, it was necessary to alter the regulatory element to a constitutive state and to produce three successive structural-gene mutations.

MESSAGE
Evolution would come to a stop by running out of variation if new genetic variation were not added to populations by mutation, recombination, and migration. Ultimately, all new variation is derived from gene and chromosome mutations.

Inbreeding and Assortative Mating

Random mating with respect to a locus is common, but it is not universal. Two kinds of deviation from random mating must be distinguished. First, individuals may mate with each other nonrandomly because of their degree of common ancestry; that is, their degree of genetic relationship. If mating between relatives occurs more commonly than would occur by pure chance, then the population is inbreeding. If mating between relatives is less common than would occur by chance, then the population is said to be undergoing enforced outbreeding, or negative inbreeding.

Second, individuals may tend to choose each other as mates, not because of their degree of genetic relationship but because of their degree of resemblance to each other at some locus. Bias toward mating of like with like is called positive assortative mating. Mating with unlike partners is called negative assortative mating. Assortative mating is never complete.

Inbreeding and assortative mating are not the same. Close relatives resemble each other more than unrelated individuals on the average, but not necessarily for any particular trait in particular individuals. So inbreeding can result in the mating of quite dissimilar individuals. On the other hand, individuals who resemble each other for some trait may do so because they are relatives, but unrelated individuals also may have specific resemblances. Brothers and sisters do not all have the same eye color, and blue-eyed people are not all related to one another.

Assortative mating for some traits is common. In humans, there is a positive assortative mating bias for skin color and height, for example. An important difference between assortative mating and inbreeding is that the former is specific to a trait, whereas the latter applies to the entire genome. Individuals may mate assortatively with respect to height but at random with respect to blood group. Cousins, on the other hand, resemble each other genetically on the average to the same degree at all loci.

For both positive assortative mating and inbreeding, the consequence to population structure is the same: there is an increase in homozygosity above the level predicted by the Hardy-Weinberg equilibrium. If two individuals are related, they have at least one common ancestor. Thus, there is some chance that an allele carried by one of them and an allele carried by the other are both descended from the identical DNA molecule. The result is that there is an extra chance of homozygosity by descent, to be added to the chance of homozygosity (p2 + q2) that arises from the random mating of unrelated individuals. The probability of homozygosity by descent is called the inbreeding coefficient (F). Figure 17-4 and Genetics in Process 17-5 illustrate the calculation of the probability of homozygosity by descent. Individuals I and II are full sibs because they share both parents. We label each allele in the parents uniquely to keep track of them. Individuals I and II mate to produce individual III. If individual I is A1 / A3 and the gamete that it contributes to III contains the allele A1, then we would like to calculate the probability that the gamete produced by II is also A1. The chance is 1/2 that II will receive A1 from its father, and, if it does, the chance is 1/2 that II will pass A1 on to the gamete in question. Thus, the probability that III will receive an A1 from II is 1/2 × 1/2 = 1/4, and this is the chance that IIIthe product of a full-sib matingwill be homozygous by descent.

Such close inbreeding can have deleterious consequences. Let's consider a rare deleterious allele a that, when homozygous, causes a metabolic disorder. If the frequency of the allele in the population is p, then the probability that a random couple will produce a homozygous offspring is only p2 (from the Hardy-Weinberg equilibrium). Thus, if p is, say, 1/1000, the frequency of homozygotes will be 1 in 1,000,000. Now suppose that the couple are brother and sister. If one of their common parents is a heterozygote for the disease, they may both receive it and may both pass it on to their offspring. As the calculation shows, the rarer the gene, the worse the relative risk of a defective offspring from inbreeding. For more-distant relatives, the chance of homozygosity by descent is less but still substantial. For first cousins, for example, the relative risk is 1/16p compared with random mating.

Systematic inbreeding between close relatives eventually leads to complete homozygosity of the population, but at different rates, depending on the degree of relationship. Which allele is fixed within a line is a matter of chance. If, in the original population from which the inbred lines are taken, allele A has frequency p and allele a has frequency q = 1 p then a proportion p of the homozygous lines established by inbreeding will be homozygous A / A and a proportion q of the lines will be a / a. Inbreeding takes the genetic variation present within the original population and converts it into variation between homozygous inbred lines sampled from the population (Figure 17-5).

Suppose that a population is founded by some small number of individuals who mate at random to produce the next generation. Assume that no further immigration into the population ever occurs again. (For example, the rabbits now in Australia probably have descended from a single introduction of a few animals in the nineteenth century.) In later generations, then, everyone is related to everyone else, because their family trees have common ancestors here and there in their pedigrees. Such a population is then inbred, in the sense that there is some probability of a gene's being homozygous by descent. Because the population is, of necessity, finite in size, some of the originally introduced family lines will become extinct in every generation, just as family names disappear in a closed human population because, by chance, no male offspring are left. As original family lines disappear, the population comes to be made up of descendants of fewer and fewer of the original founder individuals, and all the members of the population become more and more likely to carry the same alleles by descent. In other words, the inbreeding coefficient F increases, and the heterozygosity decreases over time until finally F reaches 1.00 and heterozygosity reaches 0.

The rate of loss of heterozygosity per generation in such a closed, finite, randomly breeding population is inversely proportional to the total number (2N) of haploid genomes, where N is the number of diploid individuals in the population. In each generation, 1/2N of the remaining heterozygosity is lost, so

where Ht and H0 are the proportions of heterozygotes in the tth and original generations, respectively. As the number t of generations becomes very large, Ht approaches zero.

Which of the original alleles becomes fixed at each locus is a chance matter. If allele Ai has frequency pi in the original population, then the probability is pi that eventually the population will become homozygous Ai / Ai. Suppose that a number of isolated island populations are founded from some large, heterozygous mainland population. Eventually, if these island populations remain completely isolated from one another, each will become homozygous for one of the alleles at each locus. Some will be homozygous A1 / A1, some A2 / A2, and so forth. Thus, the result of this form of inbreeding is to cause genetic differentiation between populations.

MESSAGE
Once again, we see that inbreeding is a process that converts genetic variation within a population into difference between populations by making each separate population homozygous for a randomly chosen allele.

Within each population, there is a change in allelic frequency from the original pi to either 1 or 0, depending on which allele is fixed, but the average allelic frequency over all such populations remains pi. Figure 17-6 shows the distribution of allelic frequencies among islands in successive generations, where p(A1) = 0.5. In generation 0, all populations are identical. As time goes on, the gene frequencies among the populations diverge and some become fixed. After about 2N generations, every allelic frequency except the fixed classes (p = 0 and p = 1) is equally likely, and about half the populations are totally homozygous. By the time 4N generations have gone by, 80 percent of the populations are fixed, half being homozygous A / A and half being homozygous a / a.

The process of differentiation by inbreeding in island populations is slow, but not on an evolutionary or geological time scale. If an island can support, say, 10,000 individuals of a rodent species, then, after 20,000 generations (about 7000 years, assuming 3 generations per year), the population will be homozygous for about half of all the loci that were initially at the maximum of heterozygosity. Moreover, the island will be differentiated from other similar islands in two ways. For the loci that are fixed, many of the other islands will still be segregating, and others will be fixed at a different allele. For the loci that are still segregating in all the islands, there will be a large variation in gene frequency from island to island, as shown in Figure 17-6.

The Balance between Inbreeding and New Variation

Any population of any species is finite in size, so all populations should eventually become homozygous and differentiated from one another as a result of inbreeding. Evolution would then cease. In nature, however, new variation is always being introduced into populations by mutation and by some migration between localities. Thus, the actual variation available for natural selection is a balance between the introduction of new variation and its loss through local inbreeding. The rate of loss of heterozygosity in a closed population is 1/2N so any effective differentiation between populations will be negated if new variation is introduced at this rate or higher. If m is the migration rate into a given population and m is the rate of mutation to new alleles, then roughly (to an order of magnitude) a population will retain most of its heterozygosity and will not differentiate much from other populations by local inbreeding if

or if

For populations of intermediate and even fairly large size, it is unlikely that Nµ 1. For example, if the population size is 100,000, then the mutation rate must exceed 105, which is somewhat on the high side for known mutation rates, although it is not an unknown rate. On the other hand, a migration rate of 105 per generation is not unreasonably large. In fact

Thus, the requirement that Nm is equivalent to the requirement that

or that

irrespective of population size. For many populations, more than a single migrant individual per generation is quite likely. Human populations (even isolated tribal populations) have a higher migration rate than this minimal value, and, as a result, no locus is known in humans for which one allele is fixed in some populations and an alternative allele is fixed in others (see Table 17-6).

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