frequency of each new mutation. Here we use a new symbol to express the fixation probability because the probability of fixation for neutral mutations (PF) may well be different when a mutation is in gametic disequilibrium with a selected site than when a mutation is independent.

Assume that we have a neutral locus with two alleles A and a. The frequency of the A allele is x and the frequency of the a allele is therefore 1 - x. Further assume that this neutral locus is completely linked to another locus where all alleles are under the influence of very strong positive natural selection. Let's imagine that a new mutation occurs at the selected locus that is infinitely advantageous and so goes to fixation instantly. What is the probability that the A allele at the neutral locus is also fixed due to hitch-hiking? The A allele at the neutral locus has a frequency of x and therefore there is also the probability x that the new advantageous mutation at the selected locus is linked to the A allele. Thus, there is the probability x that the A allele will sweep to fixation with the new mutation at the selected locus. However, the probability that the A allele is fixed by genetic drift is also x since that is the initial frequency of the A allele. Therefore, even complete linkage to the selected allele does not alter the fixation probability for the A allele.

Birky and Walsh (1988) work through a more general analytical case and present the results of simulations, all showing that neither positive nor negative natural selection will change substitution rates at neutral sites. This occurs because the increased probability of substitution of the copies of a neutral allele linked to a selected site is counterbalanced by a decrease of exactly the same amount in the probability of fixation of all the neutral allele copies that are not linked to a selected site.

Chapter 8 review

• The neutral theory is a widely used null hypothesis in molecular evolution, predicting patterns and rates of DNA sequence change under the assumption that all mutations have no fitness advantage or disadvantage. Even though genetic drift leads to fixation or loss, neutral alleles experience a random walk to these end points that results in transient genetic variation.

• Neutral theory predicts that polymorphism, or genetic variation within populations, is a function of the effective population size and the mutation rate. Larger effective population sizes or higher mutation rates result in higher levels of equilibrium polymorphism.

• Neutral theory predicts that the rate of divergence, the accumulation of fixed nucleotide differences between two species, is a function of only the mutation rate.

• Nearly neutral theory uses the assumption that many mutations are effectively neutral because their selection coefficients are less than the pressure of genetic drift. When 4Nes = 1, genetic drift and natural selection are equally likely to dictate the fate of a new mutation.

• Apparent divergence between two DNA sequences may be underestimated because of multiple hit mutations or homoplasy. Nucleotide substitution models serve to correct observed divergence for multiple hits, giving a better estimate of actual divergence.

• Nucleotide diversity (n) and the number of segregating sites (S) are two measures of DNA sequence polymorphism that can be used to estimate 0 = 4Ne|.

• The molecular clock hypothesis uses the neutral theory prediction that divergence occurs at a constant rate over time to estimate the time that has elapsed since the two sequences shared a common ancestor.

• Heterogeneity in the rate of divergence over time is common and leads to difficulty equating divergence with time since divergence.

• Under a Poisson process model, the variance in substitution rates should equal the mean substitution rate to give an index of dispersion of one. The index of dispersion is often not equal to one, suggesting either that the substitution rate is not dictated by purely neutral processes or that the Poisson model is not an apt description of the neutral substitution process.

• Rate heterogeneity can be consistent with neutral evolution such as when mutation rates are constant per generation but generations span different lengths of time. Alternatively, rate heterogeneity may be caused by natural selection that changes the probability of substitution for mutations depending on their fitness.

• The HKA and MK tests examine the neutral prediction that polymorphism and divergence should be proportional since both are functions of the mutation rate. Tajima's D compares 0 estimated from nucleotide polymorphism and the number of segregating sites, which are expected to be equal under neutrality. Mismatch distributions are expected to be bimodal under the standard neutral model. These are not tests only for the action of natural selection, since population structure and changes in the effective population size through time also lead to rejection of the null hypothesis.

• Mutations acted on by natural selection can alter levels of polymorphism at linked neutral nucleotide sites. Genetic hitch-hiking reduces polymorphism at neighboring sites because positive selection will bring a mutation and linked neutral mutations to fixation but drive other mutations to loss in the process. Negative selection against some new mutations also reduces polymorphism at linked sites in a process called background selection. Balancing selection can elevate polymorphism at linked neutral sites because long-lived allele copies accumulate numerous mutations over time.

• Divergence rates of neutral nucleotide sites are not impacted by natural selection at linked nucleotide sites.

Further reading

Motoo Kimura provided a readily accessible review of neutral theory in:

Kimura M. 1989. The neutral theory of molecular evolution and the world view of neutralists. Genome 31: 24-31.

For a review of the nearly neutral theory see:

Ohta T. 1992. The nearly neutral theory of molecular evolution. Annual Reviews of Ecology and Systematics 23: 263-86.

A non-technical overview of molecular clock concepts, methods, and applications can be found in:

Bromham L. and Penny D. 2003. The modern molecular clock. Nature Reviews Genetics 4: 216-24.

A review of possible explanations for the overdispersed molecular clock can be found in:

Culter DJ. 2000. Understanding the overdispersed molecular clock. Genetics 154: 1403-17. Edward Hooper's popular 1999 book The River: a Journey to the Source of HIV and AIDS (Little, Brown and Co., Boston, MA) examined in detail evidence connecting the origin of HIV and polio vaccination campaigns. While all of these ideas have been discredited, the book makes interesting reading as science fiction. John Gillespie's 1991 classic book The Causes of Molecular Evolution (Oxford University Press, New York) is a wide-ranging discussion and review of empirical data as well as models of molecular evolution and the molecular clock.

For a review of empirical studies where directional or balancing natural selection has been invoked to explain observed polymorphism, see:

Hedrick PW. 2006. Genetic polymorphism in heterogeneous environments: the age of genomics. Annual Review of Ecology Evolution and Systematics 37: 67-93.

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