1. Introduction

In the previous 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?

To see the answer, we’re going to look at the genetics experiments performed by Gregor Mendel in the 1850s and 1860s.

While Mendel’s life and career are outside the scope of AP Biology, you can learn more about his story on Wikipedia.

2. Mendel’s 1^st Experiments: Monohybrid Crosses and Segregation of Alleles

The table below shows seven of the traits in garden peas that Mendel experimented with as he was figuring out the principles of genetics.

Why did Mendel work with peas? For one thing, they were easily available in true-breeding varieties. True breeding is roughly synonymous with homozygous. What it meant for Mendel is that a plant with yellow seeds could be crossed with another plant with yellow seeds and all the offspring would have yellow seeds. It’s similar to breeding a poodle with another poodle: the offspring will be poodles.

Mendel’s first series of experiments involved monohybrid crosses. 

In these experiments, Mendel crossed varieties that differed in one trait. In other words, Mendel would cross a true-breeding pea plant with yellow seeds with one that had green seeds. The result would be a hybrid. In this context, hybrid is synonymous with heterozygous. In these crosses, Mendel called the parents the P generation (for parental) and the offspring the F₁ generation. (F₁ is for “first fillial.” “Fillial” means pertaining to sons or daughters, as in fillial piety).   

From our previous study of genetics, we can figure out what happened. The green-seed trait disappears in the first generation, so we can assume that green is recessive and yellow is dominant. As a result, all of the F₁s are yellow heterozygotes.

The Punnett square (a mathematical tool that Mendel didn’t have at his disposal), looks like this.

	Y	Y
y	Yy	Yy
y	Yy	Yy

100% of the offspring are Yy: heterozygotes with yellow seeds.

Mendel’s next move was a monohybrid cross. In a monohybrid cross, you cross two hybrids.

As we’ve previously seen when we were learning about sickle cell anemia, 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 know that each of the F₁s is a heterozygote.

	Y	y
Y	YY	Yy
y	Yy	yy

75% of the offspring have genotypes YY or yy, giving them yellow seeds. 25% have green seeds (genotype yy).

Mendel’s monohybrid crosses revealed some of the key principles of genetics. These include the idea of dominant and recessive traits, and what Mendel called the principle of segregation. Why 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.

Note that we saw this in our introduction to genetics when we saw how sickle cell anemia can be inherited. Each of Hunter Haymore’s parents was a heterozygote carrier of the sickle cell allele. During meiosis, these alleles separated, with one of the two alleles sent to each parent’s gametes. That’s segregation of alleles.

3. Dihybrid Crosses and Independent Assortment

Mendel’s next series of experiments involved 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.

4. 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 an AP biology course.

In solving dihybrid cross problems, the toughest part, for most students, is 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.

5. Practice Problems

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

6. What’s next?

Continue to Topic 5.3 – 5.5 part 5: Linkage and Recombination (the next tutorial in AP Bio Unit 5)