1. Introduction

In the previous genetics tutorials, we’ve looked at variations on crosses that involved a single gene, with two alleles (or three, in the case of blood type). But what happens when two (or more) genes are being transmitted at the same time?

2. From Segregation of Alleles (Mendel’s 1^st principle) to Dihybrid Crosses

The table below shows seven of the traits in garden peas that Gregor Mendel, the founder of genetics, experimented with as he was figuring out the principles of genetics in the 1850s and 60s.

Mendel’s principle of segregation of alleles came out of his experiments with monohybrid crosses. In these crosses, Mendel crossed true-breeding varieties that differed in one trait to create a hybrid. For example, if Mendel wanted to create a hybrid for seed color, he’d cross a true-breeding plant with round seeds with a true-breeding plant that produced wrinkled seeds. The result would be a hybrid plant with round seeds (because round is the dominant allele).

We’ve seen that a monohybrid cross produces offspring in a 3 to 1 ratio, with 3 offspring showing the dominant trait for each one showing the recessive trait. Here’s the Punnett square. We’ll use the letter “R” to represent the allele for round seeds (the dominant trait) and “r” to represent the allele for wrinkled seeds, which is recessive.

	R	r
R	RR	Rr
r	Rr	rr

75% of the offspring have genotypes RR or Rr, giving them round seeds. 25% have wrinkled seeds (genotype rr).

Why is this called the principle of segregation? The name reflects Mendel’s insight that parents possess two alleles for a trait. When that parent creates offspring, he/she/it only passes on one of its two alleles. The alleles separate (or segregate) during gamete formation.

Along with figuring out the principle of segregation, Mendel also experimented with dihybrid crosses: crosses in which individuals were hybrid for two traits, such as stem height and flower color.

Follow what Mendel did through the interactive reading below.

3. Solving Dihybrid Crosses and Related Problems

Mendel’s principle of independent assortment is important to know about in its own right. It’s also the basis of many dihybrid cross genetics problems that you’ll be asked to solve in a typical introductory college-level/AP biology course.

In solving dihybrid cross problems, the toughest part, for most students, seems to be figuring out the gametes that the parents can produce. Here’s an example, working with Mendel’s peas.

Try to solve these problems on your own before looking at the answer.

SAMPLE PROBLEM 1

In peas, round seed texture (R) is dominant over wrinkled seeds (r). Yellow seed color (Y) dominates over green (y). What is the genotype of an organism that is heterozygous round and heterozygous yellow? What gametes could this organism form?

Step 1: Figure out the genotype of the parents

The parent is described as heterozygous round and heterozygous yellow. That means it’ll be RrYy

Step 2: Use the FOIL algorithm to determine what gametes this parent can make.

FOIL (which I mentioned in the interactive reading above) stands for First, Outside, Inside, Last.

• “First” means the first allele in each pair. “R” is the first allele in “Rr,” and “Y” is the first allele in “Yy.” So, the first alleles in the genotype RrYy are RY. That’s the first possible gamete.
• Outside means the two outermost alleles. In RrYy that’s Ry. That’s the second possible gamete.
• Inside means the two innermost alleles. In RrYy that’s rY. 
• Last means the two last alleles in each pair. In RrYy that’s ry

So, the four possible gametes are RY, Ry, rY, and ry.

SAMPLE PROBLEM 2

The setup is the same as in problem 1: In peas, round seed texture (R) is dominant over wrinkled seeds (r). Yellow seed color (Y) dominates over green (y). What is the genotype of an organism that is homozygous round and heterozygous yellow? What gametes could this organism form?

Step 1: Figure out the genotype of the parents

The parent is described as homozygous round and heterozygous yellow. That means it’ll be RRYy.

Step 2: Use the FOIL algorithm to determine what gametes this parent can make.

• “First” means the first allele in each pair. So, the first alleles in the genotype RRYy are RY. That’s the first possible gamete.
• Outside means the two outermost alleles. In RRYy that’s Ry. That’s the second possible gamete.
• Inside means the two innermost alleles. In RRYy that’s RY. 
• Last means the two last alleles in each pair. In RRYy that’s Ry

If you list the four alleles derived using FOIL, you’ll see RY, Ry, RY, and Ry. The last two are repeats, which means that this parent can produce only two types of gametes: RY and Ry

SAMPLE PROBLEM 3

Let’s put these two problems together.

In peas, the allele for round seeds (R) is dominant over the allele for wrinkled seeds (r). Yellow seed color (Y) dominates over green (y). What is the result of a cross between a dihybrid Round Yellow parent and a parent that is homozygous round and heterozygous yellow?

STEP 1: Figure out the genotype of the parents. Look at problems 1 and 2 above. The genotypes are RrYy x RRYy.

STEP 2: Figure out the genotype of the gametes each parent can make.

Look at problems 1 and 2 above for the solution.

RrYy: RY, Ry, rY, ry

RRYy: RY and Ry.

STEP 3: Set up a Punnett Square.

In introducing dihybrid crosses, we used a Punnett square which was 4 squares x 4 squares, to accommodate all the possible gametes. But in the cross above, one parent can only form two types of gametes. So you can set up your Punnett square in a 4 x 2 grid, like this:

	RY	Ry	rY	ry
RY
Ry

STEP 4: Complete your Punnett square by combining the alleles in the gametes to see the possible offspring.

	RY	Ry	rY	ry
RY	RRYY	RRYy	RrYY	RrYy
Ry	RRYy	RRyy	RrYy	Rryy

STEP 5: Analyze the offspring.

When we were doing monohybrid crosses, I had you list both the genotypes and phenotypes of the offspring. With dihybrid crosses, you mostly have to report phenotypes and their frequency.

In this case, the analysis is simplified because none of the offspring are wrinkled, so there are only two phenotype categories. I’m going to put a ♥ in all the squares with offspring that are round and yellow (R_Y_) and a ♦ in all the squares that have offspring that are round and green (R_yy).

	RY	Ry	rY	ry
RY	RRYY♥	RRYy♥	RrYY♥	RrYy♥
Ry	RRYy♥	RRyy♦	RrYy♥	Rryy♦

75% of the offspring are round and yellow

25% of the offspring are round and green.

4. Practice Problems

Solve the following problems in your student learning guide. Then flip the card to check your answer.

 

Next Steps

1. High School Biology: For most high school courses, this tutorial will end this unit on Genetics.
2. AP or College Bio: Continue  to Linked Genes (the next tutorial)
3. Return to the Genetics Main Menu