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X42

of A and B alleles is equal. For example, the double heterozygotes AB/ab and Ab/aB have the same number of A and B alleles and so we can reasonably assume they have equal fitness values (Table 7.2). This assumption allows us to equate the fitnesses of those double heterozygotes where recombination plays a role in the gametes that are produced. Applying this assumption to equation 7.6, we can set w14 = w23 and then the r(w14x1x4 + w23x2x3) term becomes rw14(x1x4 + x2x3) to give v1(i+1)

This helps because the gametic disequilibrium parameter D is the difference between the product of the coupling gametes and the product of the repulsion gametes (see equation 2.24). In the notation of this section D = X1X4 X2X3. We can then substitute -D for x1x4 + x2x3 in equation 7.7 to give x- (W-^- + W17x2 + W^x^ + ^14x4)

- rw14D

Equation 7.8 shows that the frequency of AB gametes after one generation of natural selection is a function of three things. First, the viabilities of the three genotypes that produce AB gametes can change genotype frequencies and thereby impact the frequency of AB gametes in the next generation (recombination does not alter the frequency of AB gametes produced by the AB/AB, AB/Ab, and AB/aB genotypes). Then, an additional part of the frequency of AB gametes is determined by the combination of recombination, fitness values of the double heterozygotes, and initial gametic disequilibrium in the population. Double heterozygotes could be more or less frequent than expected by random mating as measured by D. Also the frequency of recombination and the relative fitness of the genotypes will determine how many AB gametes are produced. If D and r could be ignored, the frequency of AB gametes would be analogous to the frequency of one of the four possible gametes for a single locus with four alleles.

Expanding on the idea that the four gamete frequencies can be treated like the frequencies of four alleles at one locus, we can utilize some of the expressions developed earlier in the chapter for a single locus. The marginal fitness for each of the two-locus gametes (w;) is obtained by summing the frequency-weighted fitness value of each of the gametes that a given gamete could pair with to make a genotype:

Similarly, the average fitness of the population is the frequency-weighted average of the fitness values for all of the possible gamete combinations:

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