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146    Chapter 5    Linkage, Recombination, and the Mapping of Genes on Chromosomes


              Figure 5.14  Inferring the location of a crossover event. Once you establish the order of genes involved in a three-point cross, it
              is easy to determine which crossover events gave rise to particular recombinant gametes. Note that double crossovers are needed to
              generate gametes in which the gene in the middle has recombined relative to the parental combinations for the genes at the ends. Such
              events include the 2-strand DCO in part (d) as well as 3-strand DCOs (not shown).
                                            vg                 pr           b
                (a)    Parental chromosomes
                                            vg                 pr           b       Sister chromatids
                                                  Region 1         Region 2                          Homologous
                                                                                                     chromosomes
                                            vg +               pr +         b +                      of F  females
                                                                                                       1
                                            vg +               pr +         b +     Sister chromatids
                (b)   Crossover in region 1                             Resultant chromatids
                       vg                 pr            b                 vg                pr            b
                       vg                 pr            b                 vg                pr +          b +
                       vg +               pr +          b +              vg +               pr            b
                       vg +               pr +          b +              vg +               pr +          b +
                (c)   Crossover in region 2                             Resultant chromatids
                       vg                 pr            b                 vg                pr            b
                       vg                 pr            b                 vg                pr            b +
                       vg +               pr +          b +              vg +               pr +          b
                       vg +               pr +          b +              vg +               pr +          b +
                (d)   Double crossover; one crossover in each region    Resultant chromatids
                       vg                 pr            b                 vg                pr            b
                       vg                 pr            b                 vg                pr +          b
                       vg +               pr +          b +              vg +               pr            b +
                       vg +               pr +          b +              vg +               pr +          b +



                outside genes vg and b, even though not one but two ex-    ambiguous. A two-point cross involving y and r gave a re-
              changes must have occurred between them.             combination frequency of 42.9, but the sum of all the inter-
                  Because of the existence of double crossovers, the    vening distances was 55.0 (review Fig. 5.12). This discrepancy
              vg ↔ b distance of 17.7 m.u. calculated in the previous sec-  occurred because the two-point cross ignored double cross-
              tion does not reflect all of the recombination events pro-  overs that might have occurred in the large interval between
              ducing the gametes that gave rise to the observed progeny.   the y and r genes. The data summing the smaller intervening
              To correct for this oversight, it is necessary to adjust the   distances accounted for at least some of these double cross-
              recombination frequency by adding the double crossovers   overs by catching recombinations of gene pairs between y and r.
              twice, because each individual in the double crossover   Moreover, each smaller distance is less likely to encompass
              groups is the result of two exchanges between vg and b. The   a double crossover than a larger distance, so each number for
              corrected distance is                                a smaller distance is inherently more accurate.
                                                                       Note that even a three-point cross like the one for vg,
                 252 + 241 + 131 + 118 + 13 + 13 + 9 + 9   × 100   pr, and  b ignores the possibility of two recombination
                                  4197                             events taking place in, say, region 1. For greatest accuracy,
                 = 18.7 m.u.                                       it is always best to construct a map using many genes sepa-
                                                                   rated by relatively short distances.
              This value makes sense because you have accounted for all
              of the crossovers that occur in region 1 as well as all of the
              crossovers in region 2. As a result, the corrected value of   Interference: Fewer double crossovers
              18.7 m.u. for the distance between vg and b is now exactly   than expected
              the same as the sum of the distances between vg and pr   In a three-point cross following three linked genes, of the
              (region 1) and between pr and b (region 2).          eight possible genotypic classes, the two parental classes
                  As previously discussed, when Sturtevant originally   contain the largest number of progeny, while the two  double
              mapped several X-linked genes in Drosophila by two-point   recombinant classes, resulting from double crossovers, are
              crosses, the locus of the rudimentary wings (r) gene was   always the smallest (see Fig. 5.11). We can understand why
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