Population Genetics. Matthew B. Hamilton

the action of natural selection to increase the absolute value of D and the action of recombination to bring D back to zero cancel each other out. The point where the two processes are exactly equal in magnitude but opposite in their effects is where gametic disequilibrium will be maintained in a population. It is important to recognize that the amount of steady‐state gametic disequilibrium depends on which genotypes have high fitness values, so natural selection and recombination could also act in concert to accelerate the decay of gametic disequilibrium more rapidly than just recombination alone.

      Interact box 2.3 Gametic disequilibrium under both recombination and natural selection

      To simulate the combined action of recombination and natural selection on gametic disequilibrium, use the program Populus, which can be obtained by following the link on the text website.

      In version 5.5 of Populus, use the Natural Selection menu to choose the Two‐Locus Selection simulation. Set pAB = pab = 0.5 and pAb = paB = 0.0 as a case where there is maximum gametic disequilibrium initially. Use fitness values of wAaBb = 1, all others = 0.5 and wAAbb = waaBB = 1, all others = 0.5 to generate strong natural selection via epistasis. Finally, try recombination values of r = 0.5 and 0.05. Focus your attention on the D vs. t plot. What do the two different fitness cases do to levels of gametic disequilibrium and how effective is recombination in opposing or accelerating this effect?

      To see the details behind the recombination and natural selection model of gametic disequilibrium, a spreadsheet version of this model is available in Microsoft Excel format. The spreadsheet model will allow you to see all the calculations represented by formulas along with a graph of gametic disequilibrium over time. You can vary the recombination rate, initial gamete frequencies, and relative fitness values to see how they impact change in D and determine its eventual equilibrium.

       Mutation

Alleles change from one form to another by the random process of mutation, which can either increase or decrease gametic disequilibrium. First consider the case of mutation producing a novel allele not found previously in the population. Since a new allele is present in the population as only a single copy, it is found only in association with the other alleles on the chromosome strand where it originated. Thus, a novel allele produced by mutation would initially increase gametic disequilibrium. Should the novel allele persist in the population and increase in frequency, then recombination will work to randomize the other alleles found with the novel allele and eventually dissipate the gametic disequilibrium. Mutation can also produce alleles identical to those currently present in a population. In that case, mutation can contribute to randomizing the combinations of alleles at different loci and thereby decrease levels of gametic disequilibrium. On the other hand, if the population is at gametic equilibrium mutation can create gametic disequilibrium by changing the frequencies of gamete haplotypes. However, it is important to recognize that mutation rates are often very low and the gamete frequency changes caused by mutation are inversely proportional to population size, so that mutation usually makes a modest contribution to overall levels of gametic disequilibrium. A simulation study showed that excluding any alleles at a frequency of less than 5–10% from estimates of D can eliminate most of the gametic disequilibrium attributable to recent mutations (Hudson 1985).

       Mixing of diverged populations

The mixing of two genetically diverged populations, often termed admixture, can produce substantial levels of gametic disequilibrium. This is caused by different allele frequencies in the two source populations that result in different gamete frequencies at gametic equilibrium. Recombination acts to produce independent segregation but it does so only based on the allele frequencies within a group of mating individuals. Table 2.13 gives an example of gametic disequilibrium produced when two populations with diverged allele frequencies are mixed equally to form a third population. In the example, the allele frequency divergence is large, and admixture produces a new population where gametic disequilibrium is 64% of its maximum value. In general, gametic disequilibrium due to the admixture of two diverged populations increases as allele frequencies become more diverged between the source populations, and the initial composition of the mixture population approaches equal proportions of the source populations.

       Mating system

      As covered earlier in this chapter, self‐fertilization and mating between relatives increase homozygosity at the expense of heterozygosity. An increase in homozygosity causes a reduction in the effective rate of recombination because crossing over between two homozygous loci does not alter the gamete haplotypes produced by that genotype. The effective recombination fraction under self‐fertilization is

(2.39)

where s is the proportion of progeny produced by self‐fertilization each generation. This is based on the expected fixation index at equilibrium (Haldane 1924; see Figure 2.13). Figure 2.22 shows the decay in gametic disequilibrium predicted by Eq. 2.39 for four self‐fertilization rates in the cases of free recombination (c = 0.5) and well as tight linkage (c = 0.05). Self‐fertilization clearly increases the persistence of gametic disequilibrium, with marked effects at high selfing rates. In fact, the predominantly self‐fertilizing plant Arabidopsis thaliana exhibits gametic disequilibrium over much longer regions of chromosome compared to outcrossing plants and animals (see review by Flint‐Garcia et al. 2003, Kim et al. 2007).

Table 2.13 Example of the effect of population admixture on gametic disequilibrium. In this case, the two populations are each at gametic equilibrium given their respective allele frequencies. When an equal number of gametes from each of these two genetically diverged populations are combined to form a new population, gametic disequilibrium results from the diverged gamete frequencies in the founding populations. The allele frequencies are: population 1 p₁ = 0.1, p₂ = 0.9, q₁ = 0.1, q₂ = 0.9; population 2 p₁ = 0.9, p₂ = 0.1, q₁ = 0.9, q₂ = 0.1. In population 1 and population 2, gamete frequencies are the product of their respective allele frequencies as expected under independent segregation. In the mixture population, all allele frequencies become the average of the two source populations (0.5) with D_max = 0.25.

Gamete	Gamete frequency	Population 1	Population 2	Mixture population
A1B1	g 11		0.01	0.81	0.41
A2B2	g 22		0.81	0.01	0.41
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