Two characters and independent assortment

The law of segregation describes one gene at a time. Mendel next asked what happens when you follow two genes at once: do their alleles travel together as a package, or does each gene go its own way?

A cross that follows two characters

A cross that tracks two characters at the same time is a two-factor cross. Mendel crossed a true-breeding plant with yellow, round seeds (YYRR) to a true-breeding plant with green, wrinkled seeds (yyrr). Yellow (Y) is dominant to green (y), and round (R) is dominant to wrinkled (r).

The first parent can make only YR gametes and the second only yr gametes, so every F₁ plant is YyRr. Offspring that are heterozygous for two genes like this are dihybrids. As expected from dominance, all the F₁ plants had yellow, round seeds. The real test came when the F₁ plants fertilized themselves.

Two hypotheses, two predictions

Mendel could imagine two ways the alleles might behave when a YyRr plant makes gametes:

If the alleles stayed linked in their original pairs, no F₂ plant could show a new mix of traits; every one would look like one of the original P-generation parents. If they sorted independently, new combinations (yellow wrinkled and green round) would appear.

Check yourselfUnder linked assortment, would crossing two YyRr F₁ plants give any yellow, wrinkled F₂ offspring?

No. Each F₁ plant would make only YR and yr gametes, so the F₂ would show just the parental combinations, 3 yellow, round : 1 green, wrinkled.

The 9:3:3:1 result

Mendel’s F₂ plants showed all four phenotypes, close to a 9:3:3:1 ratio. With four kinds of gametes from each parent, a Punnett square has 4 × 4 = 16 boxes, and they group like this:

The two middle classes are the new combinations, the ones the linked hypothesis said could never happen. Their appearance ruled it out. Mendel saw the same pattern for every pair of characters he tested.

The law of independent assortment

These results gave Mendel’s law of independent assortment: the alleles of different genes assort independently of each other during the process that gives rise to gametes.

In practice, which seed-color allele a gamete gets tells you nothing about which seed-shape allele it gets. A gamete with Y is just as likely to carry r as R. That is why a dihybrid makes four kinds of gametes in equal numbers.

Independent assortment holds for genes on different chromosomes. Two genes that sit close together on the same chromosome tend to be inherited together and don’t assort independently, an exception called linkage. Mendel knew nothing about chromosomes, yet their behavior turns out to explain both of his laws.

Check yourselfA pea plant is YyRr. If the two genes assort independently, what kinds of gametes can it make, and in what proportions?

Four kinds, YR, Yr, yR, and yr, each making up one-fourth of the gametes.