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(a) Independent assortment
                                                                          Orientation I
                                                                      A
                                                                                                         B
                                                                                B
                                                                                                         B
                                                                      A
                                                                                B
                                                                                b
                                                                      a
                                                                                                         b
                                                                                                A
                                                                                b
                                                                                                         b
                                                                      a
                                                                                        Meiosis I
                                                                                                         B
                                                                      A
                                                                                B
                                                                                                a
                                                                                B
                                                                      A
                                                                                                         B
                                                                                                a
                                                                                                A
                                                                                                         b
                                                                      a
                                                                                b
                                                                                                A
                                                                      a
                                                                                b
                                                                                                         b
                                                                                 A
                                                                     A
                                                                                                           a
              142    Chapter 5    Linkage, Recombination, and the Mapping of Genes on Chromosomes  Meiosis II a  a a A  Orientation II
                                                                                 B
                                                                                              B
                                                                                                           B
                                                                     B
                                                                     a           a            A            A
                                                                                                           b
                                                                                              b
                                                                     b
                                                                                 b
              Figure 5.10  Why RF = 50% in a dihybrid for genes on nonhomologous chromosomes. (a) Nonhomologous chromosomes
              line up randomly with respect to one another so that meiosis results in all parental gametes (left) or all recombinant gametes (right) with
              equal frequency. (b) Meioses that occur with one crossover between one gene and the centromere generate all four gamete types with
                                                                                                Recombinant gametes
                                                                         Parental gametes
              equal frequency.
              (a) Independent assortment                           (b) Crossover between the centromere and one gene
                      Orientation I            Orientation II
                                                                      A         B               A        B
                 A         B               a        B                 A         B               A        B
                 A         B               a        B                 a         b               a        b
                 a         b               A        b                 a         b               a        b
                 a         b               A        b
                                                                                        Meiosis I
                                    Meiosis I
                                                                      A         B               A        B
                 A         B               a        B                 a         B               A        b
                 A         B               a        B
                                                                      A         b               a        B
                 a         b               A        b                 a         b               a        b
                 a         b               A        b
                                                                                        Meiosis II
                                   Meiosis II
                                                                     a           A            A            A
                A           A            a            a              B           B            B            b
                B           B            B            B
                                                                     A           a            a            a
                a           a            A            A              b           b            b            B
                b           b            b            b
                                                                    Recombinant   Parental     Parental   Recombinant
                    Parental gametes        Recombinant gametes       gametes     gametes      gametes     gametes
              (b) Crossover between the centromere and one gene
              Recombination Frequencies Between                        Importantly, experiments have established that genes lo-
              Two Genes Never Exceed 50%            B              cated very far apart on the same chromosome also show re-
                           B
                 A
                                           A
                 A         B               A        B              combination frequencies of approximately 50%. To understand
              If the definition of linkage is that the proportion of recom-  why this is true, consider the different meioses that contribute
                                                    b
                                           a
                           b
                 a
              binant classes is smaller than that of parental classes, a re-  to the pool of gametes counted in a testcross experiment.
                 a
                                           a
                                                    b
                           b
              combination frequency of less than 50% indicates linkage.   When two genes are very close together on the same chromo-
              But what can we conclude about the relative location of   some, only two kinds of meioses are likely to occur: those with
              genes if roughly equal numbers of parental and recombi-  no crossovers (an NCO meiosis in Fig. 5.9a and Fig. 5.11) and
                                    Meiosis I
              nant progeny exist? And does it ever happen that recombi-  rarer meioses with a single crossover (SCO in Fig. 5.9b and
              nants are in the majority?   A        B              Fig. 5.11). An NCO meiosis yields only parental gametes,
                           B
                 A
                                           A
                 a We already know one situation that can give rise to a   while an SCO event produces 50% recombinant gametes.
                           B
                                                    b
              recombination frequency of 50%. Genes located on different   These closely spaced genes are linked because some meioses
              (that is, nonhomologous) chromosomes will obey Mendel’s   (NCOs) do not make any recombinant-type gametes.
                                                    B
                 A
                           b
                                           a
              law of independent assortment for two reasons. First, the two   When the two genes are farther apart, SCOs become
                                                    b
                           b
                                           a
                 a
              chromosomes can line up on the spindle during meiosis I in   more frequent, and in some meioses, two crossovers be-
              either of two equally likely configurations. As a result, when   tween A and B (DCO meioses) can also occur (Fig. 5.11).
                                   Meiosis II
              summed over the products of many meioses, the number of   DCO meioses can be one of four different types; two, three,
              parental and recombinant gametes will be equal (Fig. 5.10a).   or all four nonsister chromatids may cross over. Because
                                                      A
                            A
                                         A
                a
              Second, if a crossover occurs between any one gene and the   the four DCO events are equally frequent, the average frac-
                            B
                B
                                         B
                                                      b
              centromere, that meiosis will produce two parental and two   tion of recombinant gametes produced by DCOs is 50%
              recombinant gametes (Fig. 5.10b). Thus, if genes A and B are   (see equation at the bottom of Fig. 5.11). The same is true
                A
                                                      a
                            a
                                         a
              on nonhomologous chromosomes, a dihybrid will produce   for triple crossover events, quadruple crossover events, etc.
                            b
                                                      B
                b
                                         b
              all four possible types of gametes (A B, A b, a B, and a b)   (not shown). Thus, even if the two genes are far enough
              with approximately equal frequency.    Recombinant   apart on the same chromosome that at least one crossover
                             Parental
                                          Parental
               Recombinant
                 gametes     gametes      gametes      gametes
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