Mendel carried out a number of dihybrid crosses for pairs of characteristics and always obtained a 9:3:3:1 ratio in the F₂. This ratio makes perfect sense in light of the principle of segregation and the concept of dominance if we add a third principle, which Mendel recognized in his dihybrid crosses: the principle of independent assortment (Mendel’s second law). This principle states that alleles at different loci separate independently of one another.

A common mistake is to think that the principle of segregation and the principle of independent assortment refer to two different processes. The principle of independent assortment is really an extension of the principle of segregation. The principle of segregation states that the two alleles at a locus separate when gametes are formed; the principle of independent assortment states that, when these two alleles separate, their separation is independent of the separation of alleles at other loci.

Let’s see how the principle of independent assortment explains the results that Mendel obtained in his dihybrid cross. Each plant possesses two alleles encoding each characteristic, and so the parental plants must have had genotypes RR YY and rr yy (Figure 3.8a). The principle of segregation tells us that the alleles for each locus separate and that one allele for each locus passes to each gamete. The gametes produced by the round, yellow parent therefore contain alleles RY, whereas the gametes produced by the wrinkled, green parent contain alleles ry. These two types of gametes unite to produce the F₁, all with genotype Rr Yy. Because round is dominant over wrinkled and yellow is dominant over green, the phenotype of the F₁ will be round and yellow.

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When Mendel allowed the F₁ plants to self-fertilize to produce the F₂, the alleles for each locus separated, with one allele going into each gamete. This is where the principle of independent assortment becomes important. Each pair of alleles can separate in two ways: (1) R separates with Y and r separates with y to produce gametes RY and ry or (2) R separates with y and r separates with Y to produce gametes Ry and rY. The principle of independent assortment tells us that the alleles at each locus separate independently; thus, both kinds of separation take place with equal frequency, and all four types of gametes (RY, ry, Ry, and rY) are produced in equal proportions (Figure 3.8b). When these four types of gametes are combined to produce the F₂ generation, the progeny consist of ⁹/₁₆ round and yellow, ³/₁₆ wrinkled and yellow, ³/₁₆ round and green, and ¹/₁₆ wrinkled and green, resulting in a 9:3:3:1 phenotypic ratio (Figure 3.8c).