The Recombination Fraction

To continue here the discussion of recombination that we began in Sect. 3.2, consider a backcross and two loci that are polymorphic with respect to the two pure inbred strains used for the backcross. The first strain is an a/b homozygote and the second strain is an A/B homozygote. Regardless of which crossovers may occur during the formation of the outcross, the Fi mouse must be an (A/B, a/b) heterozygote. When the Fi mouse is backcrossed with the inbred a/b mouse, then the gametes of the resulting offsprings can be (a/b, a/b) or (A/B, a/b) in the case of no recombination. Alternatively, if a recombination does occur, the possible pairs of gametes are (a/B,a/b) or (A/b, a/b). The probability of each pair of gametes is (1 — 6)/2 in the former case and 6/2 in the latter. The observed genotype in the case of no recombination in the Fi meiosis will be either aa and bb or Aa and Bb. In the case of recombination, the observed genotype will be either aa and Bb, or Aa and bb. Consequently, the presence of a recombination can be determined from the observed genotypes. It is convenient to summarize the distribution of the four possibilities in a tabular form. See Table 4.1 for such a summary.

Knowing the genotype at the marker, the genotypic status at the QTL can be partly predicted. Specifically, if the genotype at the marker is bb, then the genotype at the QTL is aa with probability 1 — 6, and it is Aa with probability 6. Similarly, if the genotype at the marker is Bb then the genotype at the QTL is Aa with probability 1 — 6, and it is aa with probability 6.

Table 4.1. Distribution of observed genotypes at a pair of linked markers in the backcross design

Genotype

aa

Aa

total

bb

(1 - e)/2

e/2

1/2

Bb

e/2

(1 - e)/2

1/2

total

1/2

1/2

1

0 0

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