So unless the recombination rate between the marker locus and QTL is zero, which it almost never is, a and d are actually larger than the estimates of a and O from a single-marker QTL mapping experiment.

To see that a and O are minimum estimates, let's reconsider the example above but assume a different recombination rate. The estimated phenotypic effect of the QTL (a) is a constant. The observed difference in body mass between the GM M and GM M marker class means is 8 kg, yielding an estimate of 2a = 8 or a = 4 by equation 9.33. If the recombination rate is r = 0, then by equation 9.40 a = 4 kg/ (1 - 2(0)) = 4 kg. However, if the recombination rate between the marker locus and the QTL is r = 0.25 instead, then by equation 9.35, a = 4 kg/(1 - 2(0.25)) = 8 kg. For dominance, if r = 0 then by equation 9.41, d = 2 kg/(1 - 2(0))2 = 2 kg. However, if r = 0.25 then by equation 9.41, d = 2 kg/(1 - 2(0.25))2 = 8 kg. Therefore, the inferred true phenotypic effect of the QTL (a) and its degree of dominance (d) are both a function of the recombination rate between the marker locus and the QTL. The degree of dominance (d/a) inferred with r = 0 is 2/4 = 0.5. In contrast, the degree of dominance inferred with r = 0.25 is 8/8 = 1.0.

In this example, a recombination rate of 0.25 rather than zero doubles both the perceived true effect

Problem box 9.2 Compute the effect and dominance coefficient of a QTL

Sax (1923) was the first to carry out a QTL mapping analysis. He showed evidence for a QTL explaining continuous variation in the trait of seed weight of the common bean (Phaseolus vulgaris) based on differences in the phenotypic means of plants that differed in seed color. The P1 individuals had seed weights of 48 and 21 centigrams (cg) and were homozygous for different alleles (P and p) for a codominant gene that affects seed color. Using seed color patterns to determine genetic marker classes, the mean seed weights in the F2 individuals were

_M1 M1 jm2m2

Using the data collected by Sax, estimate a and N for the QTL for seed weight assuming that r = 0.2 and r = 0. What is the effect of the QTL in terms of the percentage of phenotypic difference between the P1 individuals? Did Sax identify a major gene for seed weight?

of the QTL and the perceived degree of dominance. With a higher recombination rate, the QTL has a larger effect on the phenotype but not all of this effect is reflected in the marker class means since recombination breaks down the association between QTL genotypes and marker locus genotypes. As the randomizing effect of recombination between a QTL and a marker locus increases, the smaller the difference between GM M and GM M becomes for a QTL. With free recombination between the QTL and the marker locus, GM M and GM M are expected to be equal because there is no association between the QTL and the marker locus genotypes.

QTL mapping with multiple marker loci

QTL mapping that utilizes numerous genetic marker loci is now routine. It is then possible to utilize all pairs of genetic markers for QTL mapping. The advantage of such flanking-marker QTL analysis or interval mapping is that the resulting estimates of a and O are not confounded with the recombination rate. Interval mapping is carried out with an F2 mating design like that shown in Fig. 9.15 to produce F1 individuals heterozygous at the two marker loci as well as the QTL. Figure 9.16 shows the arrange-

Genotype of Fl individual

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