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56     Chapter 3    Extensions to Mendel’s Laws


              product of allele A as protein A (no italics), and when ap-  genes interacts  additively to produce the phenotype of
              propriate, that of allele a as protein a (no italics).  seed color in lentils.
                                                                       Results obtained from self-crosses with the various
                                                                   types of F 2  lentil plants support a two-gene explanation.
              Additive Interactions Between Two Genes              Self-crosses of F 2  green individuals show that they are
                                                                   pure-breeding, producing an F 3  generation that is en-
              Controlling a Single Trait Can Produce               tirely green. Tan individuals generate either all tan off-
              Novel Phenotypes                                     spring, or a mixture of tan offspring and green offspring.
                                                                   Grays similarly produce either all gray, or gray and
              In the chapter opening, we described a mating of tan and   green. Self-crosses of brown F 2  individuals can have
              gray lentils that produced a uniformly brown F 1  genera-  four possible outcomes: all brown, brown plus tan,
              tion and then an F 2  generation containing brown, tan,   brown plus gray, or all four colors (Fig. 3.10b). The two-
              gray, and green lentil seeds. An understanding of how   gene hypothesis explains why:
              this can happen emerges from experimental results dem-
              onstrating that the ratio of the four F 2  colors is 9 brown :   ∙  only one green genotype exists: pure-breeding aa bb,
              3 tan : 3 gray : 1 green (Fig. 3.10a). Recall from Chapter 2   but
              that this is the same ratio Mendel observed in his analysis   ∙  two types of tans exist: pure-breeding AA bb as well
              of the F 2  generations from dihybrid crosses following   as tan- and green-producing Aa bb, and
              two independently assorting genes. In Mendel’s studies,   ∙  two types of grays exist: pure-breeding aa BB and
              each of the four classes consisted of plants that expressed   gray- and green-producing aa Bb, yet
              a combination of two unrelated traits. With lentils, how-  ∙  four types of browns exist: true-breeding AA BB,
              ever, we are looking at a single trait—seed color. The   brown- and tan-producing AA Bb, brown- and gray-
              simplest explanation for the parallel ratios is that a com-  producing Aa BB, and Aa Bb dihybrids that give rise
              bination of genotypes at two independently   assorting   to plants producing lentils of all four colors.



              Figure 3.10  How two genes interact to produce seed colors in lentils. (a) In a cross of pure-breeding tan and gray lentils, all
              the F 1  hybrids are brown, but four different phenotypes appear among the F 2  progeny. The 9:3:3:1 ratio of F 2  phenotypes suggests that seed
              coat color is determined by two independently assorting genes. (b) Expected results of selfing individual F 2  plants of the indicated phenotypes
              to produce an F 3  generation, if seed coat color results from the interaction of two genes. The third column shows the proportion of the F 2
              population that would be expected to produce the observed F 3  phenotypes. (c) Other two-generation crosses involving pure-breeding
              parental lines also support the two-gene hypothesis. In this table, the F 1  hybrid generation has been omitted.
              (a)  A dihybrid cross with lentil coat colors        (b)  Self-pollination of the F  to produce an F 3
                                                                                       2
                                                                   Phenotypes      Observed F 3      Expected Proportion
                                                                   of F  Individuals  Phenotypes     of F  Population*
                                                                                                       2
                                                                      2
                 P              AA bb        aa BB                    Green        Green                 1/16
                                                                      Tan          Tan                   1/16
                                                                      Tan          Tan, green            2/16
                 Gametes         A b          a B                     Gray         Gray, green           2/16
                                                                      Gray         Gray                  1/16
                                                                      Brown        Brown                 1/16
                                                                      Brown        Brown, tan            2/16
                                                                      Brown        Brown, gray           2/16
                                                                      Brown        Brown, gray, tan, green  4/16
                 F  (all identical)  Aa Bb    Aa Bb
                  1
                                                                   *This 1: 1: 2 : 2 : 1: 1: 2 : 2 : 4 F  genotypic ratio corresponds to a
                                                                                       2
                                                                   9 brown : 3 tan : 3 gray : 1 green F  phenotypic ratio.
                                                                                          2
                                                                   (c)  Sorting out the dominance relations by select crosses
                 F 2                       A B  A b  a B  a b
                                                                   Seed Coat Color of  F  Phenotypes and     Ratio
                                                                                        2
                                                                   Pure-Breeding Parents  Frequencies
                                       A B AA BB AA Bb Aa BB Aa Bb
                9    A– B– (brown)                                 Tan    green        231 tan, 85 green      3 : 1
                3    A– bb (tan)       A b AA Bb AA bb Aa Bb Aa bb  Gray  green        2586 gray, 867 green   3:1
                3    aa B– (gray)                                  Brown   gray        964 brown, 312 gray    3 :1
                1    aa bb (green)     a B Aa BB Aa Bb aa BB aa Bb  Brown  tan         255 brown, 76 tan      3 :1
                                                                   Brown   green       57 brown, 18 gray,     9 :3 : 3:  1
                                       a b Aa Bb Aa bb aa Bb aa bb                     13 tan, 4 green
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