Two traits at once: the dihybrid cross

Two traits together

Mendel next asked a harder question. When a plant differs in two traits, are they passed on together, or separately? A cross that follows two pairs of traits is a dihybrid cross.

He took seed shape and seed colour:

• R for round seeds, dominant over r for wrinkled;
• Y for yellow seeds, dominant over y for green.

The F1 generation

He crossed a pure plant with round yellow seeds, RRYY, with a pure plant with wrinkled green seeds, rryy.

Each gamete of the first parent carries R and Y. Each gamete of the second carries r and y. So every F1 plant is RrYy, and every F1 seed is round and yellow. Both dominant forms show.

The F2 generation

Mendel let the F1 plants pollinate themselves, and sorted the F2 seeds. He found four kinds:

That is the ratio $9 : 3 : 3 : 1$. In one experiment he counted $315$ round yellow, $108$ round green, $101$ wrinkled yellow and $32$ wrinkled green seeds.

Look closely at the middle two. Round green and wrinkled yellow were in neither parent. They are new combinations of the traits.

Why the four kinds appear

An RrYy plant makes four kinds of gametes. The R or r copy goes into a gamete independently of the Y or y copy. So the gametes are RY, Ry, rY and ry, in equal numbers.

A Punnett square with four gametes on each side has $16$ boxes. Count the boxes of each phenotype and you get $9 : 3 : 3 : 1$.

Now look at one trait at a time. Round seeds are $9 + 3 = 12$ parts, and wrinkled seeds are $3 + 1 = 4$ parts. That is $12 : 4$, or $3 : 1$. Yellow to green is also $3 : 1$. Each trait on its own still follows the monohybrid ratio.

Independent inheritance

The new combinations show that seed shape and seed colour do not travel as a pair. Each trait is passed on independently of the other. This is the idea of independent inheritance.

It also explains why sexual reproduction gives so much variation. Every trait is shuffled on its own, so the young can carry new mixes that neither parent had.

Set the number of F2 seeds below and see how many of each kind to expect.

Try it in Python

The program makes the four gametes of an RrYy plant, pairs every gamete with every other, and counts the four kinds of seed.

Practise with new numbers

Common mistakes

• "The F1 of round yellow and wrinkled green is a mixture." Every F1 seed is round yellow, because both dominant forms show.
• "An RrYy plant makes two kinds of gametes." It makes four: RY, Ry, rY and ry.
• "The F2 has only the two parent kinds." It also has round green and wrinkled yellow, the new combinations.
• "9 : 3 : 3 : 1 breaks the 3 : 1 rule." Taken one trait at a time, each is still $3 : 1$.

Remember these

• A dihybrid cross follows two traits at once.
• Pure round yellow (RRYY) crossed with pure wrinkled green (rryy) gives an F1 all round yellow (RrYy).
• The F2 gives round yellow, round green, wrinkled yellow and wrinkled green in the ratio $9 : 3 : 3 : 1$.
• The new combinations show that the two traits are inherited independently.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. What is the genotype of the F1 seeds of a cross between RRYY and rryy, and what do they look like?

2. Write the four kinds of gametes made by an RrYy plant.

3. Name the two kinds of F2 seed that were in neither parent. What do they show?

4. In the F2, what is the ratio of yellow seeds to green seeds, whatever their shape?

5. Out of $16$ F2 seeds, how many do you expect to be both wrinkled and green? What is their genotype?