Chapter 15 Notes

Random Genetic Drift

Random Drift of Allele Frequencies

Allele Frequencies Change Whenever Individuals Have Different Numbers of Offspring

The mathematics of random reproduction, as illustrated in Figure 15.2, are explored further in Chapter 28.

Luria and Delbrück (1943) performed a classic experiment, the fluctuation test, showing that mutations that gave bacteriophage resistance occur randomly, before phage are present, rather than as an adaptive response to the selective challenge (pp. 345–346). Their experiment depends on the randomness of reproduction; we provide further details in Luria and Delbrück’s Fluctuation Test.

The Wright–Fisher Model Is a Standard Representation of Random Drift

Crow and Kimura (1970) is still the best reference on the Wright–Fisher model and on random genetic drift more generally. Felsenstein’s lecture notes are perhaps more accessible.

Figure 15.3 is taken from Buri (1956). Kerr and Wright (1954) performed similar experiments.

It is remarkable that the effect of drift on the mean of a quantitative trait is independent of its genetic basis. We explain why in Random Drift of Quantitative Traits.

Figure 15.4 is from Clayton et al. (1957). Rich et al. (1984) give another example of drift in a quantitative trait.

The Rate of Random Drift Is Determined by the Variance in Fitness

For more on the factors that influence effective population size, see Crow and Kimura (1970, Chapter 3.13).

Short-term factors reduce effective population size below census numbers by a substantial factor. See Nunney (1994) and Vucetich et al. (1997).

Coalescence

Genetic Ancestry Is Described by a Process Known as Coalescence

Detailed accounts of the coalescent process can be found in Donnelly and Tavaré (1995), Rosenberg and Nordborg (2002), and Hein et al. (2005). Wakeley (2008) provides a comprehensive and accessible account.

The large-scale survey of human single-nucleotide polymorphism (SNP) variation was published with the draft human genome in Sachidanandam et al. (2001).

Felsenstein (1992) discusses the inherent randomness of the coalescent process and explains why this makes pairwise measures such as nucleotide diversity highly variable.

We will see later that the properties of the coalescent process are reflected in the patterns of variation generated by mutation. We explore some of these basic properties in Properties of the Coalescent Process.

Genealogies Can Be Inferred from Sequences

Because the rate of coalescence in the recent past is extremely high, the tips of a genealogy are often too short to have accumulated unique mutations. Thus, the more recent parts of a genealogy cannot be resolved.

The Neutral Theory

The Rate of Neutral Divergence Equals the Mutation Rate

The neutral theory of molecular evolution was proposed independently by Kimura (1968) and by King and Jukes (1968); it was subsequently developed primarily by Motoo Kimura. (The neutral theory was also proposed by Alan Robertson [1967] but dismissed in the same paragraph.)

If the genes have been diverging for a long time, then there is an appreciable chance that two mutations might occur at precisely the same site. Because only one mutational change would then be detected, the actual extent of divergence would be underestimated (Chapter 27). However, when we are studying variation in DNA sequence within a species, or between closely related species, this is not a serious problem. We can assume that mutations are spread over so many possible nucleotide sites that each is unique, that is, we assume the infinite-sites model (p. 424).

Note that the rate of 1.2 × 10^–9 amino acid changes per year for α-globin, cited on p. 371, is consistent with the rate of one change per 6 Myr given here, because α-globin has 141 amino acids.

In The Absence of Selection, Neutral Variation Is Determined by a Balance between Mutation and Drift

Follow this link for a derivation of genetic variability under the infinite-alleles model.

Abundant Species Have Less Genetic Diversity Than Expected from the Neutral Theory

Estimates of diversity (π = 0.01) and mutation rate (µ = 3 × 10^–9 per site per generation) for Drosophila melanogaster are from Andolfatto and Przeworski (2000). Diversity estimates are based on 24 loci in regions of high recombination. The mutation rate is estimated from the divergence between the Drosophila obscura and D. melanogaster species groups, assuming ten generations per year and a split 30 Mya. (Estimates vary widely; for example, Sharp and Li [1989] use a value about half this, µ = 1.6 × 10^–9.)

Selander and Levin (1980) published one of the first surveys of genetic diversity in bacteria. Maynard Smith (1990) reviews later work. Feil and Spratt (2001) and Gupta and Maiden (2001) review the structure of diversity in bacterial populations, focusing on the extent of recombination.

Maynard Smith and Haigh (1974) first proposed that hitchhiking is more important than conventional random genetic drift in reducing diversity. This idea has recently been developed by Gillespie (2000, 2001).

Recombination and Random Drift

Recombination Breaks Up the Genome into Regions with Different Ancestry

The idea of a “mitochondrial Eve” became popular after Cann et al. (1987) published their survey of human mtDNA. However, it was often used in a misleading way.

Strictly, these arguments apply only to the nonrecombining region of the Y chromosome. There is a small pseudoautosomal region that recombines with the X chromosome and so has a different ancestry (see pp. 682–683).

Chang (1999) showed that at about log₂(N) generations in the past, an individual ancestral to the entire current population is likely to be found. NOTE WN15A Going back about twice as far, all individuals who are ancestors are likely to be ancestral to the entire present population. This assumes a pedigree version of the Wright–Fisher model, in which an individual’s two parents are drawn at random from the previous generation. Rohde et al. (2004) showed that human geographic structure does not alter these conclusions much.

Figure 15.12B,C is taken from Derrida et al. (1999).

Figure 15.13 is calculated using results in Barton and Etheridge (2003). The simulation assumes a very large and constant population.

The Pattern of Ancestry Depends on the Number of Recombination Events per Generation, N_ec

Figure 15.15 is from Patil et al. (2001).

Note that the Drosophila alcohol dehydrogenase example of Figure 13.14 is from a region of low recombination. Thus, blocks of sequence that share the same ancestry are longer than the 50 bp calculated in the text, making it possible to discern them reasonably clearly.

Figure 15.16 is taken from Maynard Smith (1990).

The figure of 2 × 10^–8 per base per generation for recombination rate in Drosophila is from Hey and Kliman (2002, Fig. 2b). Similar estimates are given in Andolfatto and Przeworski (2000). It is an average over males and females. Males have no recombination, and the rate in females is measured from laboratory crosses. (It is not straightforward to extract numbers from these papers: Hey and Kliman [2002] do not give units for R, and Andolfatto and Przeworski [2002] express recombination rate in terms of the product 2N_ec.)

Associations between Pairs of Alleles Are Measured by Linkage Disequilibrium

The CCR5 example is taken from Stephens et al. (1998). See also Novembre et al. (2005). The estimate of allele age in the text is based on a very simple calculation and is highly uncertain, both because of the random location of recombination events and because of the randomness of reproduction.

There has been some controversy about the merits of different measures of linkage disequilibrium. For example, Lewontin (1988) argues that D depends on allele frequencies and that the ratio D/D_max is more appropriate for comparing pairs of alleles with different frequencies. However, the appropriate measure depends on the question that is being asked. Often, the best approach is to fit a model of the evolutionary process rather than try to summarize complex data into a single measure (cf. Box 25.2).

The variance of pairwise linkage disequilibrium is derived by Avery and Hill (1979).

The Amount of Linkage Disequilibrium Varies Greatly along the Genome

Figure 15.19 is from Phillips et al. (2003). Because of its importance for human disease mapping, there is now a large literature on linkage disequilibrium in human populations (see, e.g., Ardlie et al. 2002).

Figure 15.20 is from Reich et al. (2002). A similar excess of the extent of linkage disequilibrium along the genetic map, over that expected from measured recombination rates and estimates of N_e, is seen in Drosophila (Andolfatto and Przeworski 2000).

Direct evidence for recombination hot spots comes from typing human sperm (Jeffreys et al. 1998; Kauppi et al. 2003; Jeffreys and May 2004): These directly observed hot spots usually coincide with hot spots inferred from patterns of linkage disequilibrium (Myers et al. 2005). (However, there is evidence that the location of hot spots shifts over evolutionary time [Jeffreys et al. 2005].) Direct estimates from large pedigrees also show that most recombination is in hot spots (Coop et al. 2008). The consistency between different approaches shows that patterns of linkage disequilibrium can be explained by recombination hot spots, without any strong influence from population structure.

Robertson and Hill (1983, p. 263) first noted tentative evidence for excess linkage disequilibrium in humans and suggested the two alternative explanations discussed here: variation in recombination rate along the genome and population structure.

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