In four o'clock plants, many flower colors are observed. In a cross involving two true-breeding strains, one crimson and the other white, all of the \(P_{1}\) generation were rose color. In the \(F_{2}\), four new phenotypes appeared along with the \(P_{1}\) and \(F_{1}\) parental colors. The following ratio was obtaincd: \(1 / 16\) erimson \(2 / 16\) orange \(1 / 16\) yellow \(2 / 16\) magenta \(4 / 16\) rose \(2 / 16\) pale yellow \(4 / 16\) white Propose an explanation for the inheritance of these flower colors.

The two parental strains with crimson and white flowers were true-breeding, meaning they were homozygous for their respective flower color genes. When crossed, the \(P_{1}\) generation showed an intermediate rose color, suggesting incomplete dominance.

Examine the ratio of flower colors in the \(F_{2}\) generation: \(1 / 16\) crimson \(2 / 16\) orange \(1 / 16\) yellow \(2 / 16\) magenta \(4 / 16\) rose \(2 / 16\) pale yellow \(4 / 16\) white The pattern follows a \(1:2:1:2:4:2:4\) ratio, which is derived from the product of two \(1:2:1\) ratios, suggesting that two separate gene interactions are responsible for the flower color inheritance.

Assign two pairs of alleles, \(C\) and \(Y\), which control the crimson and yellow pigments in the flowers, respectively. The homozygous recessive genotype for both pairs of alleles will be white (e.g., \(ccyy\)).

Now, combine the genotypes of alleles \(C\) and \(Y\) with the observed phenotypes: \(1 / 16\) crimson: \(CCYY\) \(2 / 16\) orange: \(CCYy\) \(1 / 16\) yellow: \(CCyy\) \(2 / 16\) magenta: \(CcYY\) \(4 / 16\) rose: \(CcYy\) \(2 / 16\) pale yellow: \(Ccyy\) \(4 / 16\) white: \(ccyy\)

The inheritance of flower colors in this case appears to be controlled by two separate genes with incomplete dominance, one responsible for crimson pigment (\(C\)) and the other for yellow pigment (\(Y\)). The \(C\) allele determines the degree of crimson pigmentation, with \(CC\) being fully crimson, \(Cc\) being partially crimson, and \(cc\) having no crimson pigment. The \(Y\) allele determines the degree of yellow pigmentation, with \(YY\) being fully yellow, \(Yy\) being partially yellow, and \(yy\) having no yellow pigment. The ratio of flower colors in the \(F_{2}\) generation can be explained by the interactions between these two genes and their alleles, revealing the \(1:2:1:2:4:2:4\) ratio. This suggests a dihybrid inheritance pattern with incomplete dominance at play.