What occurs when a few individuals from an original population move to a new area?

Genetic Drift and Evolutionary Theory

Genetic drift is at the core of the shifting-balance theory of evolution coined by Sewall Wright where it is part of a two-phase process of adaptation of a subdivided population. In the first phase, genetic drift causes each subdivision to undergo a random walk in allele frequencies to explore new combinations of genes. In the second phase, a new favorable combination of alleles is fixed in the subpopulation by natural selection and is exported to other demes by factors like migration between populations. Much of the basic theory of genetic drift was developed in the context of understanding the shifting-balance theory of evolution. Genetic drift has also a fundamental role in the neutral theory of molecular evolution proposed by the population geneticist Motoo Kimura. In this theory, most of the genetic variation in DNA and protein sequences is explained by a balance between mutation and genetic drift. Mutation slowly creates new allelic variation in DNA and proteins, and genetic drift slowly eliminates this variability, thereby achieving a steady state. A fundamental prediction of genetic drift theory is that the substitution rate in genes is constant, and equal to the mutation rate.

Abstract

Genetic drift was the second accepted mechanism of evolutionary change in genomes (before the term genome was even in use). The logic of these random changes in small populations, and even in larger populations over large numbers of generations, was sound. Modern genomics is now showing just how extensive the effects of genetic drift have been with genes and several chromosomal mutations. Genetic drift contrasts with the famed Hardy–Weinberg law, which predicts for large populations that the frequency of alternate neutral alleles will remain stable over the generations, but given enough time, random intergenerational changes in these frequencies are likely to eventually cause the elimination of some alleles and the fixation of others.

The Fate of a Newly Arisen Mutation in a Large Population

We first examine the impact of genetic drift on the evolutionary fate of a newly arisen mutation. Let A symbolize the group of all the old alleles at an autosomal locus, and let a be a newly arisen mutation at this locus that is initially present in only a single individual with the new genotype Aa. We initially regard this individual as a self-compatible, random-mating hermaphrodite (Hardy's assumptions for the Hardy–Weinberg law) with normal meiosis and no subsequent mutations producing new a alleles; that is, the a allele is unique in its mutational origin. The first step in the survival of this new mutant allele is to be passed on to a gamete during meiosis, whose pgf has already been given in Eq. (4.1). The chances for a surviving to the next generation also depend upon how many offspring the initial carrier, Aa, has. Suppose that the initial Aa carrier has n offspring. Then, the pgf for the total number of a alleles this individual passes on to the next generation is:

(4.5)h(z|n)=∏j=1ngj(z)=[g(z)]n

where gj(z) is the pgf for the meiotic event associated with offspring j. Eq. (4.5) reflects the fact that all meioses are independent events with the same pgf, g(z). The problem with Eq. (4.5) is that it assumes that we know n, the number of offspring born to the initial Aa individual that, in this simple model, survive to adulthood in the next generation. At this point we encounter another level of sampling that can contribute to genetic drift at the population level—not all individuals in general will have exactly the same number of surviving offspring even if the environment is constant and every offspring has the same probability of surviving. The random sampling of the number of surviving offspring produced by an individual can also be described by a series of probabilities, say pn, that represent the probability of having n surviving offspring. Eq. (4.5) is the conditional pgf given n, but now we can define the unconditional pgf as

(4.6)h(z)=∑n=0∞pnh(z|n)=∑n=0∞pn[g(z)]n

Note that if we define a new dummy variable t = g(z), then Eq. (4.6) becomes the pgf for the random variable n, the number of surviving offspring produced by an individual. Hence, the pgf h(g(z)) incorporates the effects of sampling meiotic events and sampling the number of surviving offspring on describing the total number of a alleles that survive into the next generation. For example, let us assume that n is from a Poisson distribution, a commonly used distribution for family size in idealized populations, as mentioned in Chapter 3. The pgf for a Poisson distribution is ek(t−1) where k is the mean number of surviving offspring of an Aa individual and t is the dummy variable. In this special case of Eq. (4.6), the pgf for the number of a alleles in the next generation is

(4.7)ek[g(z)− 1]=ek[12+12z−1]=ek2[z−1]

To find the probability of survival, it is easier to first find the probability of loss; that is, the probability that there are 0 copies of a in the next generation. Recall that this is found simply by setting the dummy variable to 0 to yield the probability of loss of the a allele in the next generation as e−k/2. If the total population size is approximately stable and the a allele is neutral (that is, it has no effect on the probabilities for the number of offspring), each of the individuals, including Aa, in this idealized population has an average of k = 2 offspring, and e−1 = 0.367879. Note that over a third of all new neutral mutants are lost by the very first generation after mutation just by the sampling processes that contribute to genetic drift. The probability of surviving just a single generation is 1-Probability(loss) = 0.632121.

To find the probability of surviving for just two generations, assume that n copies survived into the first generation. Because mating is at random and if we further assume the population is very large, these copies will almost certainly all be in Aa genotypes as the frequency of a is extremely rare (recall the Hardy–Weinberg law). Under these assumptions, each of the n copies of a that are in Aa individuals will also produce a random number of a copies in the next generation as described by the pgf given in Eq. (4.6); that is h(z). Because there are n carriers of a in the first generation, the total pgf for the second generation given n is [h(z)] n. However, n itself is a random variable described by pgf h(t), and we need to incorporate this fact to get the unconditional pgf for the second generation. Exactly like the derivation of Eq. (4.6), the unconditional pgf for the number of a alleles in the second generation is h(h(z)); that is, the dummy variable for the second generation is the pgf from the first generation. For the Poisson case, the pgf for the second generation is

(4.8)ek2[ek2[z− 1]−1]

Setting z = 0 and k = 2, Eq. (4.8) yields the probability of loss by the second generation to be 0.531464, so the probability of surviving for two generations is 0.468536. Thus, by just two generations, more than half of all new mutant alleles are lost by genetic drift. The recursion used to generate Eq. (4.8) can be repeated multiple times to obtain the pgf's of later generations (Schaffer, 1970). For example, the pgf for the third generation is h(h(h(z))). Table 4.1 shows the probabilities of loss of the mutant allele for the first 10 generations in our idealized population. As can be seen, very few mutants survive even just 10 generations of genetic drift.

Table 4.1. The Probabilities of a New Mutant Surviving Over the First Ten Generations After Its Occurrence as a Function of the Average Number of Offspring Produced by Individuals in the Population

The ultimate probability of survival (ups) can be found by solving the equation h(z) = z for 0 ≤ z ≤ 1, and an approximation to this solution that incorporates the impact of meiosis (Eq. 4.1) is (modified from Schaffer, 1970, which only deals with the haploid case):

(4.9)u ps≈k−2k+v

where v is the variance in the number of offspring. For the Poisson case, k = v, as mentioned in Chapter 3. Also, if k = 2 as in our example of a neutral allele in a stable population, ups = 0. This of course, is an approximation, and we will see later that the actual probability of survival in our assumed large population is extremely small in a large population but greater than 0.

Humans are unique among the large-bodied vertebrates in that we have had sustained population growth for at least the last 10,000 years with the beginning of agriculture (Coventry et al., 2010). To consider a growing population, Table 4.1 also presents the survival probabilities for a population in which the average number of surviving offspring per individual is 3. As can be seen, the probability of survival is consistently larger under population growth. Moreover, the approximate ultimate probability of survival is (from Eq. (4.9) with k = v = 3) 0.1667.

Up to now we have assumed that all individuals in the population have the same average number of offspring. However, other than the assumptions that the total population size is large and capable of indefinite growth, the k in our model of offspring number only refers to the average number of offspring by bearers of the new mutant a. Suppose the overall average number of offspring in the growing population were four, then an average size of just three offspring would mean extremely strong natural selection against the Aa individuals bearing the new, mutant allele (a 25% reduction in number of expected offspring in the next generation). As will be shown in Chapter 9, strong selection against a dominant mutant such as a would result in its rapid elimination when genetic drift and population growth are ignored. As Table 4.1 and the ups of 0.1667 show, even a strongly deleterious dominant allele can persist in the human gene pool. A recessive deleterious allele is even more sheltered against the effects of natural selection (Chapter 9), so such recessive deleterious alleles will have an even higher probability of persistence in the human gene pool. Indeed, deep sequencing studies reveal that humans have many more rare variants that appear deleterious over that expected in a constant-sized population (Coventry et al., 2010). Recall also from Chapter 3 the large number of rare variants that individual humans carry that are loss-of-function mutations or otherwise predicted to be deleterious (Gudbjartsson et al., 2015). The accumulation of deleterious mutations in the gene pool is sometimes called the mutational load, and humans have a uniquely high mutational load (Lynch, 2010). The concept of mutational load was first introduced by Muller (1950), who won the Nobel Prize for his work demonstrating that radiation can increase the mutation rate. Muller was concerned about an increase in radiation levels due to nuclear testing and the threat of nuclear war increasing the mutational load in humans, and Lynch was concerned with mutation rates and relaxed selection. However, population growth, and therefore indirectly agriculture, has played a much more important role in increasing the mutational load in humans. Demography and genetic drift are major evolutionary forces that have strongly shaped the unique nature of the human gene pool with its vast excess of rare, deleterious variants.

Finite Population Size

Genetic drift can cause nonrandom associations between alleles at different loci. While the expected value of pairwise gametic disequilibrium due to drift over many generations is zero, the variance is large for closely linked loci in small populations. The demographic structure of a population will affect the amount of gametic disequilibrium observed. A small founder population or a bottleneck in the recent past can cause significant gametic disequilibrium for closely linked loci. While less gametic disequilibrium will be generated by genetic drift in a rapidly growing population, gametic disequilibrium present before or during the early phase of the expansion will persist.

Abstract

Random genetic drift describes the stochastic fluctuations of allele frequencies due to random sampling in finite populations. Over time, genetic drift can lead to fixation or loss of genetic variants, thereby systematically eliminating diversity from a population. This trend is counterbalanced by mutations that continuously produce new variants. A number of powerful frameworks, such as coalescence theory, have been developed to study how these processes interact in shaping patterns of genetic diversity in populations. Random genetic drift and mutation also lie at the foundation of Kimura's neutral theory of evolution, which constitutes the standard null model of molecular population genetics.

Modifiers of Recombination and Genetic Drift in Large Populations

Genetic drift acts in all populations, and so the stochastic effects of finite population size can play a role in large populations as well. Under Hill–Robertson interference (discussed above), genetic linkage is seen to increase the amount of genetic drift near a selected locus, thus reducing the effective population size for the locus when either a beneficial mutation arises or in the presence of purifying selection against a deleterious allele. Keightley and Otto (2006) contrasted the probability of fixation for an allele modifying recombination with a neutral allele, and showed that purifying selection against repeated deleterious mutations provided an advantage to modifier alleles, causing them to fix with a higher probability. Surprisingly, this effect increased with increasing population size.

To understand this somewhat counter-intuitive result, we note that recombination frees the focal locus from Hill–Robertson interference, allowing deleterious mutations to be purged by selection. A larger number of polymorphic loci increases the opportunity for Hill–Robertson interference, which increases the advantage seen for recombination. Larger populations (where genetic drift is overall weaker) will maintain greater polymorphism, and thus see on average a greater amount of Hill–Robertson interference, and a larger advantage to recombination. The Keightley–Otto model gives a truly synthetic treatment of the role of negative disequilibrium where both selection and drift determine how selection on a new mutation affects the fate of other loci, and recombination frees loci from these shared fates.

Genetic Drift

Genetic drift is the change in allele frequencies in a population over time due to random sampling events (e.g., differences among individuals in survival or fecundity that are unrelated to their phenotype/genotype). Although the specific genetic consequences of genetic drift during a given demographic bottleneck are unpredictable, the overall effect of drift is to erode genetic diversity.

Effective population size, or Ne, is a measure of how sensitive a population is to genetic drift. Ne is defined as the size of a hypothetical, theoretically ideal population that would experience the same level of inbreeding, loss of heterozygosity, and genetic drift per generation as the real population in question (Kimura and Crow, 1963). Other factors besides the census size of a population will influence the change in allele frequencies over time (e.g., an uneven sex ratio, past fluctuations in population size, nonrandom variation in family size); by excluding these factors, Ne makes it possible to evaluate and compare measurements of drift across species with very different life histories. There are different ways to empirically estimate Ne over both short- and long-term time scales (see review by Hare et al., 2011), but Ne is virtually always smaller, and often much smaller, than the census size of a population. Frankham (1995) reviewed published estimates of Ne/N for wildlife species, and found that Ne averaged only 10–11% of total census size.

In large (unthreatened) populations, it takes a long time to see a major effect of genetic drift on allele frequencies; genetic diversity represents a balance between mutation and natural selection. However, when Nes<<1, where s is the selection coefficient describing the difference in fitness between two alleles, drift can counter selection, and the alleles will behave as if they are neutral (Wright, 1931). Thus through this mechanism, small populations may show greater maladaptation (i.e., mismatch between environment and mean phenotype) than larger ones. By similar logic, mildly deleterious mutations will tend to accumulate in small populations, because selection is ineffective at removing them. This can lead to ‘mutational meltdown’: as deleterious mutations become fixed, they drive down population growth rate (and size), making the population progressively more susceptible to fixation of future mutations (Lynch et al., 1995).

Genetic Drift and the Founder Effect

Genetic drift is the change in frequencies of alleles in a population due to chance. If a population is small then chance could determine whether a neutral allele becomes extinct or increases in frequency to fixation. If a population is very small then such random genetic drift could determine the fate of an allele even in the presence of moderately strong natural selection. In nature, however, it may be unusual for a population to stay small long enough for drift to occur – the population could become extinct, grow, or merge with another population. Tendencies to genetic drift will be opposed by gene flow. Hence if a fungus is abundant and widespread with copious spores capable of long distance dispersal, gene flow is likely to counteract any tendency to genetic drift. There is evidence for this in the cosmopolitan and abundant fungi Neurospora crassa, Puccinia graminis f. sp. tritici, and Schizophyllum commune.

There are, however, ways in which random events could determine the genetic structure of a population and the course of microevolution. One or a few individuals will not cover the genetic diversity in the population; many alleles present in the whole population will be absent from such a small set of individuals. A small set of individuals could occur as the result of a catastrophe almost destroying a population or by the dispersal of one or a few individuals to a new environment. The population resulting from such a founder effect will be genetically different from the one from which it originated. Many fungi live in environments that are highly favourable but transient, and will hence be liable to colonisation from one or a few spores when they arise, and population crashes when they disappear. Founder effects are likely to occur with such fungi and, if the fungi are not highly abundant, may not subsequently be overwhelmed by gene flow.

Australia provides lots of examples of single founder events: Puccinia striiformis – cause of yellow (stripe) rust of wheat – was introduced into Australia in 1979 (p. 263), as a single race from Europe, but mutations have now resulted in new pathotypes which differ from those in Europe. Similarly, Cryphonectria parasitica – cause of chestnut blight (pp. 287–289) – in North America has much less genetic diversity than in Asia, probably reflecting a founder effect. The dry-rot fungus, Serpula lacrymans, originated in northeast Asia, where it has most genetic variations. However, there is very little genetic variation in the founder populations across the globe (Figure 4.11). In some areas the indoor genetic populations are unique (e.g. Japan), representing a single founder event, whereas elsewhere (e.g. Australia), there is slightly more variation representing founder events from Japan and from Europe.

2.4.4 Genetic Drift

Genetic drift (also called random genetic drift) means a change in the gene pool strictly by chance fixation of alleles. The effects of genetic drift can be acute in small populations and for infrequently occurring alleles, which can suddenly increase in frequency in the population or be totally wiped out. The alleles thus fixed by chance (genetic sampling error) may be neutral—that is, they may not confer any survival or reproductive advantage. Therefore, for small populations, genetic drift can result in a significant change in gene frequency in a short period of time.

Genetic drift can be caused by a number of chance phenomena, such as differential number of offspring left by different members of a population so that certain genes increase or decrease in number over generations independent of selection, sudden immigration or emigration of individuals in a population changing gene frequency in the resulting population, or population bottleneck. Of these, population bottleneck can cause a radical change in allele frequencies in a very short time. A population bottleneck occurs when a population suddenly shrinks in size owing to random events, such as sudden death of individuals due to environmental catastrophe, habitat destruction, predation, or hunting. When the small number of surviving individuals gives rise to a new population, there is a radical change in the gene frequency in the resulting population, in which certain genes (including rare alleles) of the original population may radically increase in proportion while others may radically decrease or be wiped out completely, independently of selection. Additionally, the resulting population contains a small fraction of the genetic diversity of the original population. The founder effect is a severe case of population bottleneck and happens when a few individuals migrate out of a population to establish a new subpopulation. Random genetic drift accompanies such founder effect, to severely reduce the genetic variation that exists in the original population. In the new population, the founder effect can rapidly increase the frequency of an allele whose frequency was very low in the original population. If the allele is a disease-related allele, the founder effect can lead to the prevalence of the disease in the new population. An increase in a specific disease in a human population due to the founder effect is seen in the Old Order Amish of eastern Pennsylvania,66 and in the Afrikaner population of South Africa.67

The current Amish population has descended from a small number of German immigrants who settled in the United States during the eighteenth century. The incidence of Ellis–van Creveld syndrome (a form of dwarfism with polydactyly, abnormalities of the nails and teeth, and heart problems) is many times more prevalent in this Amish population than in the American population in general. The origin of this disease can be traced back to one couple, Samuel King and his wife, who came to the area in 1744. The mutated gene that causes the syndrome was passed along from the Kings and their offspring. The Amish population practices endogamy (individuals tend to mate within their own subgroup). Additionally, in this community the gene flow is centrifugal—that is, members may leave the community but outsiders do not join the community—therefore, there has been no introduction of exogenous genes into the Amish gene pool. As a result, the frequency of the disease gene has rapidly increased over generations.

Another example of founder effect comes from the Afrikaner population of South Africa, which is mainly descended from one group of European (mainly Dutch, but also German and French) immigrants that landed there in 1652. The present-day Afrikaner population has a very high prevalence of Huntington’s disease; over 200 affected individuals in more than 50 supposedly unrelated families have been found to be ancestrally related through a common progenitor in the seventeenth century. Thus, the root of the disease can be traced back over 14 generations to a common progenitor who supposedly carried the gene for Huntington’s disease. Huntington’s disease is an autosomal dominant disease caused by triplet (CAG) repeat expansion in the gene (and the mRNA), containing 40 to>100 CAG triplets. The onset and severity of the disease is directly correlated with the number of repeats.

III.G. Genetic Drift

Genetic drift involves the loss of alleles from a population by chance. Random fluctuations in allele frequencies in small populations reduce genetic variation, leading to increased homozygosity and loss of evolutionary adaptability to change.

The rate at which alleles are lost from a sexually reproducing population by genetic drift can be predicted. Sewall Wright (1969) developed the basic theoretical model in 1931 and showed analytically how the rate varies with population size. Actually, it is not the census size (N) that is important but rather the genetic effective population size (Ne). This parameter takes into account the fact that closely related individuals will share alleles by common descent. Monozygotic twins are genetically identical and therefore should be counted as one individual rather than two. Sibs share half their genes with each other and half with each of their parents and are therefore not equivalent to two genetically unrelated individuals. The genetic effective number of individuals in a population is therefore almost always less than the number of individuals counted by an ecologist. Ne can, under some breeding systems, be one or two orders of magnitude less than N. Consider, for example, the number of adults in a sexually reproducing population: In a monogamous species the census count of adults is useful, but in a harem species only 1 of the 10 males may be contributing to Ne. Ne can be variously defined in terms of unequal sex ratios among breeders, fluctuations in population size over several generations, and variance in family size (Lande and Barrowclough, 1987).

Wright (1969) defined the variance effective population size (Ne) as the number of individuals in an ideal population that would experience genetic drift at the same rate as the actual population. Ne can be defined and estimated in various ways using temporal ecological data, DNA sequences, and various methods of estimating migration rate. Some methods of estimation have theoretical value but little operational utility—it is almost impossible to determine the values that some algorithms require. Nevertheless, by estimating Ne one can assess the effects of different population management strategies. Unequal numbers of males and females, increased variance in family size, and temporal fluctuations in N all cause Ne to be much less than the census size, N. In many endangered populations Ne is only 10–30, and at such levels genetic variation becomes significant for a population's viability.