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Under the assumption that q is small compared to f, the approximate equilibrium allele frequency when mutation and selection reach a balance with consanguineous mating is equilibrium fs

Interact box 7.5 Natural selection and mutation

You can use PopGene.S2 to simulate the simultaneous action of natural selection and mutation. From the Drift menu select the Drift + Selection + Mutation. In the module dialog set Ne = 20, w^ = wAa = 1.0, and waa = 0.9 (or s = 0.1 with complete dominance for the A allele) and ^ = 1 x 10-3. Compute the expected equilibrium for these parameter values using equation 7.41 and then run the simulation.

Genetic drift will have a minimal effect on the outcome of allele frequencies as long as the effective population size is large. You can test this prediction by trying simulations with Ne = 10, 100, 500, and 1000 and comparing the equilibrium allele frequencies for each case.

(see Haldane 1940; Morton 1971). Since recessive deleterious mutations are only perceived by natural selection when homozygous, consanguineous mating increases the effectiveness of selection by increasing the proportion of homozygous genotypes in the population. This means that selection is more effective at eliminating the recessive homozygote (there are fewer heterozygotes that shelter the allele) and the equilibrium allele frequency for mutation-selection balance occurs at a lower allele frequency. It is counterintuitive that populations which cease consanguineous mating and engage in random mating may temporarily experience an increase in deleterious allele frequencies and a decrease in average fitness due to less effective natural selection.

7.4 Natural selection in genealogical branching models

• The problem with selection in genealogical branching models.

• Directional selection and the ancestral selection graph.

• Genealogies and balancing selection.

The final topic in this chapter is the process of natural selection in the context of genealogical branching models. Representing natural selection in genealogical branching models will require a change in perspective about how selection works and also an expansion of the ways that events are represented on genealogies. The major goal of this section is to introduce ways of modeling selection on genealogies to understand how the operation of natural selection might change the height and total branch length of genealogical trees compared with the case of coalescence patterns due to genetic drift alone.

Adding natural selection to the genealogical branching model introduces a serious complication to the Wright-Fisher model of sampling that the basic genealogical branching model is built on. Recall from Chapter 3 that the basic coalescent model assumes that when going one generation back in time, the chance that any two lineages coalesce is-. This

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