Laws of Inheritance

Core Concepts

Mendel's second experiments: two traits at once

Mendel crossed true-breeding round, yellow plants (RRYY) with true-breeding wrinkled, green plants (rryy). All F1 seeds were round and yellow — both dominant — with genotype RrYy. If the two traits were inherited as a unit, self-fertilizing the F1 would simply reproduce the parental combinations. Instead the F2 contained all four combinations — round-yellow, round-green, wrinkled-yellow, wrinkled-green — close to 9:3:3:1 (his published counts for seed shape and color: 315 : 108 : 101 : 32). The two non-parental combinations (round-green, wrinkled-yellow) were the decisive observation: the alleles of the two genes must be combining freely during gamete formation.

The law of independent assortment

The law of independent assortment states that alleles of genes on different chromosomes are distributed to gametes independently: the segregation of one gene's alleles has no effect on another's. A plant with genotype RrYy therefore produces four gamete types — RY, Ry, rY, ry — in equal proportions (1/4 each), one allele of each gene, the two choices independent. The physical basis is meiosis: at metaphase I, homologous pairs line up randomly, and the orientation of one pair is independent of every other pair. Independent assortment, like crossing over, creates new allele combinations that neither parent possessed as a package.

The dihybrid Punnett square and the 9:3:3:1 ratio

For a dihybrid cross (RrYy × RrYy), each parent produces four gamete types, so the Punnett square is 4 × 4 with 16 cells. Because R and Y are dominant, the 16 equally likely genotypes collapse into four phenotypes: 9/16 round-yellow (RY), 3/16 round-green (Ryy), 3/16 wrinkled-yellow (rrY), and 1/16 wrinkled-green (rryy) — the 9:3:3:1 ratio. Two points: the ratio is phenotypic (9 distinct genotypes lie beneath it), and it holds only when both genes assort independently and show complete dominance. You can also count directly: 3/4 × 3/4 = 9/16 for both dominant phenotypes.

Probability shortcuts: product rule and forked-line method

The 16-cell square becomes unwieldy for three or more traits, but the product rule removes the need: because each gene assorts independently, the probability of any trait combination is the product of the single-gene probabilities. For RrYy × RrYy, the chance of a round seed is 3/4 and of a yellow seed 3/4, so round and yellow is 3/4 × 3/4 = 9/16; wrinkled and green is 1/4 × 1/4 = 1/16. The forked-line method (branch diagram) applies the same idea visually: split the cross trait by trait and multiply along each branch. With n independently assorting genes, the fraction of offspring showing all n dominant phenotypes is (3/4)ⁿ, and a heterozygote for n genes produces 2ⁿ gamete types.

Limits of independent assortment: linked genes

Independent assortment has a crucial boundary: it applies only to genes on different chromosomes (or genes far enough apart on the same chromosome that crossing over separates them freely). Genes close together on the same chromosome travel into gametes together — they are linked — and their inheritance deviates from 9:3:3:1, with parental combinations overrepresented. Linkage was invisible to Mendel (his seven genes lie on only four chromosomes, some on the same one but far apart enough to assort) and was discovered decades later in Morgan's fruit flies — the subject of the next chapter. The "laws" of inheritance are probabilistic rules with a chromosomal basis, not iron guarantees.

Common Confusions