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3.2 Extensions to Mendel for Two-Gene Inheritance   65


                       categories, for the sake of simplicity, we have looked at   Although the possibilities for variation are manifold,
                       examples in which one allele of each gene in a pair showed   none of the observed departures from Mendelian  phenotypic
                       complete dominance over the other. But for any type of   ratios contradicts Mendel’s genetic laws of segregation and
                       gene interaction, the alleles of one or both genes may ex-  independent assortment. The alleles of each gene still seg-
                       hibit  incomplete dominance  or codominance, and these   regate as he proposed. Interactions between the alleles of
                       possibilities increase the potential for phenotypic diversity.   many genes simply make it harder to unravel the complex
                       For example, Fig. 3.21 shows how incomplete dominance   relation of genotype to phenotype.
                       at both genes in a dihybrid cross results not in a collapse of
                       several genotypic classes into one but rather an expansion—
                       each of the nine genotypes in the dihybrid cross F 2  corre-
                       sponds to a different phenotype.                    Breeding Studies Help Geneticists
                          A simple biochemical explanation for the pheno-  Determine Whether One or Two Genes
                       types in Fig. 3.21 is similar to that for incomplete domi-  Determine a Trait
                       nance in Fig. 3.3b, where the amount of red pigment
                       produced was proportional to the amount of an enzyme.   How do geneticists know whether a particular trait is
                       The difference here is that purple pigmentation requires   caused by the alleles of one gene or by two genes interact-
                       the action of two enzymes, A and B, and one is more ef-  ing in one of a number of possible ways? Breeding tests
                       ficient than the other, resulting in one gene (in this case,   can usually resolve the issue. Phenotypic ratios diagnostic
                       the A gene) contributing more to the purple phenotype   of a particular mode of inheritance (for instance, the 9:7
                       than the other gene.                                or 13:3 ratios indicating that two genes are interacting)
                                                                           can provide the first clues and suggest hypotheses. Fur-
                                                                           ther breeding studies can then show which hypothesis is
                                                                           correct.
                       Figure 3.21  With incomplete dominance, the interaction   As an example, a mating of one strain of pure-breeding
                       of two genes can produce nine different phenotypes   white albino mice with pure-breeding brown results in
                       for a single trait. In this example, two genes produce purple   black hybrids; and a cross between the black F 1  hybrids
                                          2
                                    1
                       pigments. Alleles A  and A  of the first gene exhibit incomplete   produces 90 black, 30 brown, and 40  albino offspring.
                                          1
                                                2
                       dominance, as do alleles B  and B  of the second gene. The two   What is the genetic constitution of these phenotypes? We
                       alleles of each gene can generate three different phenotypes, so   could assume that we are seeing the 9:3:4 ratio of reces-
                       double heterozygotes can produce nine (3 × 3) different colors in    sive epistasis and hypothesize that two interacting genes
                       a ratio of 1:2:2:1:4:1:2:2:1.
                                                                           (call them  B and  C)  control color. In this model, each
                                                  1 2
                                              1 2
                               1 2
                                  1 2
                             A A  B B        A A  B B                      gene has completely dominant and recessive alleles, and
                       F  (all                                             the homozygous recessive of one gene is epistatic to both
                        1
                       identical)                                            alleles of the other gene (Fig. 3.22a). This idea makes
                                            1
                                                           2
                                                                   2
                                                    1
                                           A  B 1  A  B 2  A  B 1  A  B 2  sense, but it is not the only hypothesis consistent with
                                                                           the data. 
                                                                     1 2
                                                      1 2
                                                  1 1
                                                             1 1
                                                          1 2
                                                                 1 2
                                              1 1
                                      1
                                           1 1
                                     A  B 1  A A  B B A A   B B  A A  B B A A   B B  We might also explain the data—160 progeny in
                                                                           a ratio of 90:30:40—by the activity of one gene
                                              1 2
                                                  1 1
                                                      2 2
                                                          1 2
                                      1
                                           1 1
                                                                     2 2
                                                             1 2
                                                                 1 2
                                     A  B 2  A A  B B A A   B B A A  B B A A   B B  (Fig. 3.22b). According to this one-gene hypothesis, al-
                       F 2                                                 binos would be homozygotes for one allele (B B ),
                                                                                                                         1 1
                                                                 2 2
                                                          2 2
                                              1 1
                                                             1 1
                                                  1 2
                                                      1 2
                                           1 2
                                                                     1 2
                                      2
                                     A  B 1  A A  B B A A  B B A A  B B A A  B B  brown mice would be homozygotes for a second allele
                                                                                                                         1 2
                                                                           (B B ), and black mice would be heterozygotes (B B )
                                                                             2 2
                                                      2 2
                                                          2 2
                                                                     2 2
                                      2
                                           1 2
                                                             1 2
                                                                 2 2
                                                  1 2
                                              1 2
                                     A  B 2  A A  B B A A  B B A A  B B A A  B B  that have their own novel phenotype because B  and B
                                                                                                                            2
                                                                                                                     1
                                                                           are incompletely dominant. Under this system, a mating
                                           1 1
                                               1 1
                                 1        A A    B B  purple shade 9       of black (B B ) to black (B B ) would be expected to
                                                                                                     1 2
                                                                                      1 2
                                               1 2
                                                                                      2 2
                                                                                                                 1 1
                                           1 1
                                                                                                    1 1
                                 2        A A   B B   purple shade 8       produce 1 B B  brown : 2 B B  black : 1 B B  albino, or
                                               1 1
                                           1 2
                                 2        A A   B B   purple shade 7       40 brown : 80 black : 40 albino. Is it possible that the
                                               2 2
                                           1 1
                                 1        A A   B B   purple shade 6       30 brown, 90 black, and 40 albino mice actually counted
                                                                           were obtained from the inheritance of a single gene?
                                               1 2
                                           1 2
                                 4        A A   B B   purple shade 5       Intuitively, the answer is yes because the ratios 40:80:40
                                           2 2
                                               1 1
                                 1        A A  B B    purple shade 4       and 30:90:40 do not seem that different. We know that if
                                           1 2
                                               2 2
                                 2        A A   B B   purple shade 3       we flip  a coin 100 times, it doesn’t always come up
                                           2 2
                                               1 2
                                 2        A A  B B    purple shade 2       50 heads : 50 tails; sometimes it’s 60:40 just by chance.
                                                                           So, how can we decide between the two-gene and the
                                           2 2
                                               2 2
                                 1        A A  B B    purple shade 1  (white)  one-gene model?
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