Law of Independent Assortment

The dihybrid cross — a cross between plants differing in two traits — gave Mendel the clue for his second law. When he crossed plants with round yellow seeds and wrinkled green seeds, the F₂ generation did not show just the two parental types. Instead, four phenotypes appeared: round yellow, wrinkled yellow, round green, and wrinkled green, in a ratio of 9:3:3:1.

Mendel noticed that this 9:3:3:1 ratio is actually the product of two independent 3:1 ratios. If you take the seed shape ratio (3 round : 1 wrinkled) and multiply it by the seed colour ratio (3 yellow : 1 green), you get exactly the four combinations:

(3 Round : 1 Wrinkled) × (3 Yellow : 1 Green) = 9 Round, Yellow : 3 Wrinkled, Yellow : 3 Round, Green : 1 Wrinkled, Green

This meant that the inheritance of seed shape had nothing to do with the inheritance of seed colour — the two traits were assorting independently of each other. Based on this and similar observations from other dihybrid crosses, Mendel proposed his Law of Independent Assortment.

To understand how this works at the level of gamete formation, consider the F₁ plant with genotype RrYy. During meiosis, the two alleles of each gene segregate. For the gene R/r, 50% of gametes get R and 50% get r. Now, each of these gametes must also carry an allele for seed colour — either Y or y. The key point is that the segregation of R and r is completely independent of the segregation of Y and y. So, among the gametes that carry R, half get Y and half get y. Similarly, among the gametes that carry r, half get Y and half get y.

The result is four equally frequent types of gametes — both in pollen and in eggs:

• RY (25%)
• Ry (25%)
• rY (25%)
• ry (25%)

When these four types of male and female gametes combine at random, the Punnett square gives 16 equally likely combinations. From these 16 squares, you can work out the genotypes and phenotypes of the F₂ plants. …