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Figure 9.16 Interval mapping utilizes two marker loci (A and B) that sit on either side of a QTL. An individual with the genotype shown can produce two types of gametes if there is no recombination, four type of gametes if there is a single recombination event, and two types of gametes from a double recombination event. The expected gamete frequencies are a function of the recombination rates.

ment of two marker loci that flank a QTL in an F1 individual along with the eight types of gametes (two coupling, four single recombinants, and two double recombinants) that can be produced by an F1 individual. These eight F1 gametes can be combined to make nine two-locus marker genotypes and 28 possible F2 genotypes. The recombination rate between the marker loci, r, can be estimated from the two-locus marker genotype frequencies in the F2 progeny. Assuming no interference (or that recombination rates rA and rB are independent), then r = rA + rB - 2rArB.

Using the expected gamete frequencies shown in Fig. 9.16, the mean phenotypic value of each marker genotype can be derived. Table 9.6 shows the derivation of the expected phenotypic value for the marker genotypes A1A1B1B1 and A1A2B1B2. As for QTL mapping based on a single genetic marker, the portion of the mean genotypic value for the entire F2 population is referred to as GA0PA B B and GAOpa B B . These population mean genotypic values are the sum of the genotype-frequency-weighted genotypic values for each QTL genotype associated with a

two-locus marker genotype. Since —-— of all individuals in the F2 population are expected to have an A1A1B1B1 marker genotype, we can multiply by a 4

factor of -

)2 to obtain the actual genotypic mean of that subset of individuals in the F2 population with A1A1B1B1 marker genotypes or GA A BB . The expected frequency of the A1A2B1B2 genotype is used to obtain the actual genotypic mean of F2 individuals with A1A2B1B2 marker genotypes or GA A BB . The expected genotypic means of the remaining seven possible marker-class means as well as a regression method to estimate a and O are given in Haley and Knott (1992).

Like QTL mapping based on a single genetic marker, the phenotypic value of the A1A1B1B1 marker genotype is a function of both the additive and dominance effects of the QTL. In contrast, the expected phenotypic value of the A1A2B1B2 marker genotype is a function only of d. Therefore, the A1A2B1B2 marker-class mean value provides an estimate of the dominance coefficient independent of a. Once the value of d is estimated, then other marker-class means can be used to estimate the value of a. As with single-marker QTL analysis, a statistically significant difference between marker-class mean values indicates that a QTL is present between a pair of genetic marker loci.

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