Explain the law of independent assortment with a dihybrid cross example

Question

State Mendel’s Law of Independent Assortment. Illustrate it with a dihybrid cross between two pea plants, showing the expected phenotypic ratio in the F₂ generation.

Solution — Step by Step

Why This Works

The 9:3:3:1 ratio is exactly what you get if the two monohybrid ratios (3:1 for each trait) are multiplied independently:

$(3 \text{ Yellow}: 1 \text{ Green}) \times (3 \text{ Round}: 1 \text{ Wrinkled}) = 9:3:3:1$

This mathematical equivalence is proof that the two traits segregate independently. If they were linked (on the same chromosome), the ratio would deviate from 9:3:3:1.

Independent assortment occurs because homologous chromosomes line up independently at the metaphase plate during meiosis I. The orientation of one pair has no influence on the orientation of another pair.

Alternative Method — Forked Line Method

Instead of a 4×4 Punnett square, use the forked-line (branch) method:

Color alone (Yy × Yy): 3 Yellow : 1 Green

For each colour outcome, apply the shape ratio (Rr × Rr): 3 Round : 1 Wrinkled

Yellow branch: $3Y \times 3R = 9$ YR; $3Y \times 1r = 3$ Yr

Green branch: $1y \times 3R = 3$ yR; $1y \times 1r = 1$ yr

Result: 9:3:3:1 — same answer, faster method.

Common Mistake