Genetic drift

Genetic drift is a process that causes a population's allele frequencies to change from one generation to the next simply as a result of chance. This happens because reproductive success within a population is variable, with some individuals producing more offspring than others. As a result, not all alleles will be reproduced to the same extent, and therefore allele frequencies will fluctuate from one generation to the next. Because genetic drift alters allele frequencies in a purely random manner, it results in non-adaptive evolutionary change. The effects of drift are most profound in small populations where, in the absence of selection, drift will drive each allele to either fixation or extinction within a relatively short period of time, and therefore its overall effect is to decrease genetic diversity. Genetic drift will also have an impact on relatively large populations but, as we shall see later in this chapter, a correspondingly longer time period is required before the effects become pronounced. Genetic drift is an extremely influential force in population genetics and forms the basis of one of the most important theoretical measures of a population's genetic structure: effective population size (Ne). Because genetic drift and Ne are inextricably linked, we will now spend some time looking at how Ne differs from census population size (Nc), how it is linked to genetic drift, and what this ultimately means for the genetic diversity of populations.

What is effective population size?

A fundamental measure of a population is its size. The importance of population size cannot be overstated because, as we shall see throughout this text, it can influence virtually all other aspects of population genetics. From a practical point of view, relatively large populations are, all else being equal, more likely to survive than small populations. This is why the World Conservation Union (IUCN) uses population size as a key variable, considering a species to be critically endangered if it consists of a population that numbers fewer than 50 mature individuals. Taken in its simplest form, population size refers simply to the number of individuals that are in a particular population -- this is the census population size (Nc). From the point of view of population genetics, however, a more relevant measure is the effective population size (Ne).

The Ne of a population reflects the rate at which genetic diversity will be lost following genetic drift, and this rate is inversely proportional to a population's Ne. In an ideal population Ne = Nc, but in reality this is seldom the case. If an actual population of 500 individuals is losing genetic variation through drift at a rate that would be found in an ideal population of 100 individuals, then this population would have Nc = 500 but Ne = 100, in other words it will be losing diversity much more rapidly than would be expected in an ideal population of 500. An Ne/Nc ratio of 100/500 = 0.2 would not be considered unusually low; one review calculated the average ratio of Ne/Nc in wild populations, based on the results of nearly 200 published results, as approximately 0.1 (Figure 3.3; Frankham, 1995). We will now look at three of the most common reasons why Ne is often much smaller than Nc: uneven sex ratios, variation in reproductive success, and fluctuating population size. At the end of this section we will return to an explicit discussion of the relationship between Ne, genetic drift, and genetic diversity.

Figure 3.3 A review of published studies revealed a range of Ne/Nc values in insects, molluscs, fish, amphibians, reptiles, birds, mammals and plants. Note that although Ne is often much less than Nc, it is a theoretical measurement and under some conditions can be greater than Nc (data from Frankham, 1995, and references therein)

Ne/Nc

Figure 3.3 A review of published studies revealed a range of Ne/Nc values in insects, molluscs, fish, amphibians, reptiles, birds, mammals and plants. Note that although Ne is often much less than Nc, it is a theoretical measurement and under some conditions can be greater than Nc (data from Frankham, 1995, and references therein)

What influences Ne?

Sex ratios Unequal sex ratios generally will reduce the Ne of a population. An excess of one or the other sex may result from adaptive parental behaviour. Although the mechanisms behind this are not well understood, there is increasing evidence for parental manipulation of offspring sex ratios in a number of taxo-nomic groups, including some bird species, which may be responding to environmental constraints such as a limited food supply (Hasselquist and Kempenaers, 2002). Even if the overall sex ratio in a population is close to 1.0, the sex ratio of breeding adults may be unequal, and it is the relative proportion of reproductively successful males and females that ultimately will influence Ne. In elephant seal populations, for example, fighting between males for access to harems is fierce. This intense competition means that within a typical breeding season only a handful of dominant males in each population will contribute their genes to the next generation, whereas the majority of females reproduce. This disproportionate genetic contribution results in an effectively female-biased sex ratio. The effect of an unequal sex ratio on Ne is approximately equal to:

where Nef is the effective number of breeding females and Nem is the effective number of breeding males. The importance of the sex ratio can be illustrated by a comparison of two hypothetical populations of house wrens (Troglodytes aedon), which tend to produce an excess of females when conditions are harsh (Albrecht, 2000). Each of these populations has 1000 breeding adults. In the first population, conditions have been favourable for several years and so the Nef of 480 was comparable to the Nem of 520. The Ne therefore would be:

The second population, however, has been experiencing relatively harsh conditions for some time. As a result, the Nef is 650 but the Nem is only 350. The Ne in this population is:

In this example, the Ne/Nc in the first population, which had almost the same number of males and females, was 998/1000 = 0.998. The Ne/Nc in the second population, with its disproportionately large number of females, was 910/1000 = 0.910. Although the Ne/Nc ratio was smaller in the second population, the reduction in Ne that is attributable to uneven sex ratios was actually relatively low in both of these hypothetical populations compared to what we would find in many wild populations. According to one survey of multiple taxa, uneven sex ratios cause effective population sizes to be an average of 36 per cent lower than census population sizes (Frankham, 1995), although not surprisingly there is considerable variation both within and among species.

Variation in reproductive success Even if a population had an effective sex ratio of 1:1, not all individuals will produce the same number of viable offspring, and this variation in reproductive success ( VRS) will also decrease Ne relative to Nc. In some species the effects of this can be pronounced. Genetic and demographic data were obtained from a 17-year period for a steelhead trout (Oncorhynchus mykiss) population in Washington State, and variation in reproductive success was found to be the single most important factor in reducing Ne (Ardren and Kapuscinski, 2003). When this trout population is at high density, i.e. when Nc is large, females experience increased competition for males, spawning sites and other resources. The successful competitors will produce large numbers of offspring whereas the less successful individuals may fail to reproduce. In other species, variation in reproductive success may have relatively little influence on Ne. The relatively high Ne/Nc ratio in balsam fir (Abies balsamea; Figure 3.4) has been attributed partly to overall high levels of reproductive success in this windpollinated species (Dodd and Silvertown, 2000).

The effects of reproductive variation on Ne can be quantified if we know the VRS of a population. Reproductive success reflects the number of offspring that each individual produces throughout its lifetime and therefore can be determined from a single breeding season in short-lived species, although individuals with multiple breeding seasons must be monitored for the requisite number of years. Long-term monitoring of a population of Darwin's medium ground finch (Geospiza fortis) on the Galapagos archipelago provided an estimated VRS of 7.12 (Grant and Grant, 1992a). The effects of VRS on Ne can be calculated as follows:

If the census population size of G. fortis is 500 on a particular island, then the influence of variation in reproductive success on Ne will be:

Therefore, even if the sex ratio is equal, the variation in the number of chicks that each individual produces will cause Ne to be substantially smaller than Nc.

VRS may be highest in clonal species. In the freshwater bryozoan (moss animal) Cristatella mucedo (Figure 3.5), clonal selection throughout the growing season means that some clones are eliminated whereas others reproduce so prolifically

Figure 3.4 Balsam fir (Abies balsamea). Wind pollination in this species helps to maintain overall high levels of reproductive success, and this helps to keep the Ne/Nc ratios high within populations. Photograph provided by Mike Dodd and reproduced with permission

that the Nc of a population may be in the tens of thousands by the end of the growing season (Freeland, Rimmer and Okamura, 2001). Because clonal selection is decreasing the proportion of unique genotypes throughout the summer (Figure 3.6), the VRS must be substantial, with some clones producing no offspring and others producing large numbers of young. In the most extreme scenario, some populations ofbryozoans and other clonal taxa may become dominated by a single clone that experiences all of the reproductive success within that population, and when this happens the effective population size is virtually one (Freeland, Noble and Okamura, 2000). If this occurs in a population with a large Nc, the Ne/Nc ratio will approach zero.

Figure 3.5 A close-up photograph showing a portion of a colony of the freshwater bryozoan Cristatella mucedo. These extended tentacular crowns are approximately 0.8 mm wide and capture tiny suspended food particles. Photograph provided by Beth Okamura and reproduced with permission

0 25 50 75 100 125 150 175 200 Relative date

Figure 3.6 Linear regression of ln-relative date (sampling date represented as number of days after 1 January) versus total number of alleles in a UK population of the freshwater bryozoan Cristatella mucedo (redrawn from Freeland, Rimmer and Okamura, 2001). Clonal selection has reduced the genetic diversity of this population throughout the growing season, even though the number of colonies increased during this time. This leads to a reduction in the Ne/Nc ratio

0 25 50 75 100 125 150 175 200 Relative date

Figure 3.6 Linear regression of ln-relative date (sampling date represented as number of days after 1 January) versus total number of alleles in a UK population of the freshwater bryozoan Cristatella mucedo (redrawn from Freeland, Rimmer and Okamura, 2001). Clonal selection has reduced the genetic diversity of this population throughout the growing season, even though the number of colonies increased during this time. This leads to a reduction in the Ne/Nc ratio

Fluctuating population size Regardless of a species' breeding biology, fluctuations in the census population size from one year to the next will have a lasting effect on Ne. A survey of multiple taxa suggested that fluctuating population sizes have reduced the Ne of wild populations by an average of 65 per cent, making this the most important driver of low Ne/Nc ratios (Frankham, 1995). This is because the long-term effective population size is determined not by the Ne averaged across multiple years, but by the harmonic mean of the Ne (Wright, 1969). The harmonic mean is the reciprocal of the average of the reciprocals, which means that low values have a lasting and disproportionate effect on the long-term Ne. A population crash in one year, therefore, may leave a lasting genetic legacy even if a population subsequently recovers its former abundance. A population crash of this sort is known as a bottleneck and it may result from a number of different factors, including environmental disasters, over-hunting or disease.

Because fluctuations in population size have such lasting effects on genetic diversity, we will take a more detailed look at bottlenecks later in this chapter. For now, we will limit ourselves to looking at how fluctuating population sizes influence Ne, which can be calculated as follows:

Ne = t/[(l/Nei) + (1/Nez) + (1/N*) ■■■ + (1/Net)] (3.10)

where t is the total number of generations for which data are available, Ne1 is the effective population size in generation 1, Ne2 is the effective population size in generation 2, and so on.

The fringed-orchid (Platanthera praeclara) is a globally rare plant that occurs in patches of tallgrass prairie in Canada. The Ne of most populations is substantially reduced by fluctuations in population size from one year to the next. If a population had a census size of 220, 70, 40 and 200 during each of the past four years, and we assume that Ne/Nc = 1.0, then the effects that these fluctuations would have had on the Ne can be calculated as:

Ne = 4/[(1/220) + (1/70) + (1/40) + (1/200)] Ne = 82

Even though this population rebounded from the bottleneck that it experienced in years 2 and 3, this temporary reduction in Nc means that the current Ne/Nc ratio is only 82/200 = 0.41. Note that we have limited our example to a 4-year period for the sake of simplicity, although a longer period is needed for an accurate estimation of Ne.

So far we have looked at how individual factors -- sex ratios, VRS, and fluctuating population sizes - can influence Ne. In each of the preceding sections we calculated the effects of a single variable on Ne, but in reality all of these variables can simultaneously influence a population's Ne. We are highly unlikely to have enough information to calculate individually the reduction in Ne that is attributable to each relevant variable. In the next section, therefore, we will move away from examining the effects of single variables and instead look at how we can calculate a population's overall Ne regardless of which factors have caused the biggest reduction in Ne.

Calculating Ne

There are three general approaches for estimating Ne. The first of these, based on long-term ecological data, requires accurate census sizes and a thorough understanding of a population's breeding biology, neither or which are available for most species. A second approach is based on some aspect of a population's genetic structure at a single point in time, e.g. heterozygosity excess (Pudovkin, Zaykin and Hedgecock, 1996) or linkage disequilibrium (Hill, 1981). The application of mutation models to parameters such as these can provide estimates of Ne, although this approach is not used widely because it makes many assumptions about the source of genetic variation and can be influenced strongly by demographic processes such as immigration (Beaumont, 2003).

The third approach, which is considered by many to be the most reliable, requires samples from two or more time periods that are separated by at least one generation. Several different methods can then be used to calculate Ne from the variation in allele frequencies over time. At this time, the most widely used method is based on Nei and Tajima's (1981) method for calculating the variance of allele frequency change (Fc) as follows:

where K = the total number of alleles and i = the frequency of a particular allele at times x and y, respectively. This value then can be used to calculate Ne while correcting for sample size and Nc by using the following equation (after Waples, 1989):

where t = generation time, S0 = sample size at time zero and St = sample size at time t.

The temporal variance in allele frequencies was used to calculate the Ne of crested newt ( Triturus cristatus) populations that were sampled from ponds in western France. Researchers first were able to obtain an accurate census size of these populations using a standard mark--recapture method. As they were counted, individuals were marked by removing toes, which then were used as sources of DNA for deriving genetically based estimates of Ne. The census

Table 3.5 Some estimates of Ne/Nc. In all these examples, Ne was calculated using a method based on the temporal variance in allele frequencies

Species

Steelhead trout (Oncorhynchus mykiss) Domestic cat (Felis catus)

Red drum, a marine fish

(Sciaenops ocellatus) Crested newt ( Triturus cristatus) Marbled newt ( T. marmoratus)

Shining Fungus beetle

( Phalacrus substriatus) Carrot ( Daucus carota) Grizzly bear (Ursus arctos) Apache silverspot butterfly

(Speyeria nokomis apacheana) Pacific oyster ( Crassostrea gigas)

Giant toad (Bufo marinus)

Ne/Nc

0.73

Reference

Ardren and Kapuscinski (2003) Kaeuffer, Pontier and Perrin (2004)

Turner, Wares and Gold (2002)

Ingvarsson and Olsson (1997)

Le Clerc et al. (2003) Miller and Waits (2003) Britten et al. (2003)

Hedgecock, Chow and Waples (1992)

Easteal and Floyd (1986)

population size in one pond was approximately 77 newts in 1989 and 73 newts in 1998. The variance in allele frequencies between 1989 and 1998, based on eight microsatellite loci, provided an Ne estimate of approximately 12 and an Ne/Nc ratio of 0.16 (Jehle et al., 2001). Other examples of Ne/Nc ratios that have been calculated from temporal changes in allele frequencies are given in Table 3.5.

Estimating Ne from the variance in allele frequencies can be logistically challenging because of the time and expense involved in sampling the same population in multiple years. Obtaining samples from museums is one answer to this, although museum specimens are a finite resource and not all species will have sufficient representation. Furthermore, some taxa such as soft-bodied invertebrates are not amenable to preservation in museums, and in many cases plants will be underrepresented. Practical limitations may also arise from the availability of markers; because it is based on allele frequencies, the temporal method ideally should be done with data from co-dominant loci. Dominant data such as AFLPs can also be used, although, as noted earlier, accompanying estimates of allele frequencies will assume Hardy--Weinberg equilibrium, which may be unrealistic.

Perhaps the biggest drawback to estimating Ne from the temporal variance in allele frequencies is the assumption that all changes in allele frequencies are a result of genetic drift. This does not allow for the possibility that immigrants from other populations are introducing new alleles and therefore altering allele frequencies through a process that is completely separate from genetic drift. As we will see in the next chapter, most populations receive immigrants with some regularity, and therefore this assumption is unlikely to be met. This problem has been partially addressed by a recently developed maximum likelihood (ML) approach that estimates Ne from temporal changes in allele frequencies in a way that partitions the effects of both immigration and genetic drift (Wang and Whitlock, 2003).

Maximum likelihood is a general term for a statistical method that first specifies a set of conditions underlying a particular data set, and then determines the likelihood that these particular conditions would have given rise to the data in question. In the case of Ne, conditions may include a particular evolutionary history of the alleles in question, and maximum likelihood would be used to calculate the probability that different scenarios would have resulted in the observed variance in allele frequencies (Berthier et al., 2002). Maximum likelihood is a powerful approach, although it is computationally demanding and analytically complex. For these reasons it has avoided the mainstream so far, although its popularity is increasing as computers become more powerful and software becomes more user-friendly, and it may soon become the analytical method of choice for several aspects of molecular ecology including estimates of Ne.

Wang and Whitlock's (2003) method is an extremely promising development in the quest for accurate estimates of Ne. However, it does require data from a sufficient number of variable markers to allow the detection of even relatively small changes in allele frequencies; this may be particularly demanding when Ne is relatively large and migration rates are relatively small. In addition, it requires allele frequency data from both the population under investigation (focal population) and the populations from which immigrants may be originating (potential source populations). Assuming that the latter can be identified, one option is to pool data from all possible source populations and estimate the extent to which their collective contribution of migrants to the focal population has influenced the variance in allele frequencies that might otherwise be attributed entirely to drift. This method was applied to a metapopulation of newts ( Triturus cristatus and T. marmoratus) in France. The Ne/Nc ratios ranged from 0.07 to 0.51 when researchers assumed that changes in allele frequencies were solely a result of drift, and were 0.05 - 0.65 when they allowed for the effects of immigrants (Jehle et al., 2005). Because it aims to separate the effects that genetic drift and migration have on changing allele frequencies, this approach marks a significant step forward in the quantification of Ne. Although none is perfect, methods for estimating Ne have become increasingly refined in recent years, and this trend will undoubtedly continue because accurate estimates of Ne are crucial for understanding many different aspects of population genetics and evolution.

Effective population size, genetic drift and genetic diversity

We started this section by identifying genetic drift as one of the key processes that influences the genetic diversity of populations. We will now return to that concept by looking at the specific relationship between Ne, genetic drift and genetic diversity. The genetic diversity of a population will be reduced whenever an allele reaches fixation (attains a frequency of 1.0) because, when this occurs, the population has only one allele at that particular locus. The probability that a novel mutation will become fixed in a population as a result of genetic drift is 1/(2Ne) for diploid loci, in ohter words it is inversely proportional to the population's Ne (Figure 3.7). Since the rate at which alleles drift to fixation also represents the rate at which all other alleles at that locus will be lost, 1/(2Ne) can be considered as the rate at which genetic variation will be lost within a population as a result of genetic drift.

The predictable relationship between Ne and genetic drift means that if we know the effective size of a population and its current genetic diversity (measured as expected heterozygosity), and if we assume that the population size remains essentially constant, we can calculate what the heterozygosity will become after a given time period as:

where Ht and H0 represent heterozygosity at time t and time zero, respectively. Time intervals refer to generations, not years (although they will of course be the same if the generation time is 1 year). The predicted heterozygosity at time t is represented more commonly as a proportion of the heterozygosity at time zero:

This tells us what proportion of the initial heterozygosity will be remaining after t generations. We can use this equation to compare the expected changes in hetero-zygosity in two hypothetical populations of crested newts that have a generation time of 1 year. The first population lives in a lake and retains an effective population size of approximately 200 for a period of 10 years. The second population inhabits a small pond and has an Ne of approximately 40 for the same time period. From Equation 3.14 we can estimate the proportional change in heterozygosity as:

Ht/H0 =[1 - 1/(2 x 200)]10 = [0.9975]10 = 0.975 for the lake population, and as:

for the pond population. This means that the lake population will lose approximately 2.5 per cent of its initial heterozygosity in ten generations, whereas the smaller pond population will lose around 12 per cent of its heterozygosity.

The rate of drift does not depend solely on a population's Ne; it is also influenced by the population sizes of the genome in question (Table 3.6 and Figure 3.7). Since the population sizes of plastids and mitochondria are effectively

0.25

0 50 100 150 200 250 300

Figure 3.7 The probability that a neutral mutation will reach fixation in any given generation reflects the rate at which genetic variation will be lost following genetic drift. In this figure, the probability of fixation is given for diploid loci, calculated as 1/(2Ne), and for mitochondrial haplotypes, which is calculated as 1/Nef (here we have assumed that half of the breeding population is female; see Table 3.6). Note that the probability of fixation (and the accompanying loss of alleles) following genetic drift is inversely proportional to the effective population size a quarter those of nuclear genomes in diploid species, they will lose genetic variation at a faster rate than most nuclear genes (Figure 3.7). Returning to our example of crested newts, we know that the rate at which genetic variation is lost from diploid nuclear genes is 1/2Ne per generation, which is around 1/400 = 0.0025 in the lake population of 200 individuals. Table 3.6 tells us that in the same population, assuming that half of the Ne is female, mitochondrial variation will be lost at the much faster rate of approximately 1/100 = 0.01 per generation.

Table 3.6 The rate at which genetic variation is lost each generation following genetic drift will depend on the population size of the locus in question. Adapted from Wright (1969)

Relative population size

Rate at which variation is lost each generation

Haploid

1/Ne

Diploid

1/(2Ne)

Tetraploid

1/(4Ne)

Plastid DNA

1/Nefa

mtDNA

1/Nefa

"This is true for taxa in which plastid DNA (including cpDNA) and mtDNA are maternally inherited, because Nef is the effective number of females in a population.

"This is true for taxa in which plastid DNA (including cpDNA) and mtDNA are maternally inherited, because Nef is the effective number of females in a population.

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