A dihybrid cross examines two characteristics, each governed by a single gene with two alleles. In this instance, seed form (R = rounded, dominant; r = creased, recessive) and seed hue (Y = golden, dominant; y = verdant, recessive) are evaluated. Both parental organisms are heterozygous (RrYy), possessing the RrYy genotype for both traits.
To ascertain the phenotypic proportion of the progeny, we analyze the inheritance of both traits according to Mendel’s law of independent assortment, which posits that alleles for distinct traits segregate independently during gamete creation. The potential gametes from each RrYy parent are RY, Ry, rY, and ry.
Employing a Punnett square for a dihybrid cross (RrYy × RrYy) enables the calculation of phenotypic outcomes. However, for expediency, we can utilize the phenotypic proportions derived from Mendel’s experiments:
- For each trait independently, a mating between two heterozygotes (e.g., Rr × Rr) yields a 3:1 phenotypic ratio (3 dominant : 1 recessive).
- For seed form: 3 rounded (RR or Rr) : 1 creased (rr).
- For seed hue: 3 golden (YY or Yy) : 1 verdant (yy).
Given that the traits assort independently, the combined phenotypic proportion for the dihybrid cross is computed by multiplying the proportions of the individual traits:
- Rounded, golden: \( \frac{3}{4} \text{(rounded)} \times \frac{3}{4} \text{(golden)} = \frac{9}{16} \)
- Rounded, verdant: \( \frac{3}{4} \text{(rounded)} \times \frac{1}{4} \text{(verdant)} = \frac{3}{16} \)
- Creased, golden: \( \frac{1}{4} \text{(creased)} \times \frac{3}{4} \text{(golden)} = \frac{3}{16} \)
- Creased, verdant: \( \frac{1}{4} \text{(creased)} \times \frac{1}{4} \text{(verdant)} = \frac{1}{16} \)
Consequently, the phenotypic proportion of the progeny is 9 rounded, golden : 3 rounded, verdant : 3 creased, golden : 1 creased, verdant, or 9:3:3:1.