By the end of this lesson you should be able to:

  1. Describe the work of Gregor Mendel leading to his discover of ‘heritable factors’
  2. Predict offspring using Punnett square for monohybrid, dihybrid and trihybrid crosses
  3. Use the multiplication and addition rule to determine offspring outcomes
  4. Identify type of mechanisms that do not satisfy Mendelian genetics

Who was Gregory Mendel?

At this point we have covered the mechanics of mitosis and meiosis. You now obviously know about genes and chromosomes. These biomolecules determine the characteristic phenotypes we inherit from our parents. But, did you know that before the discovery of these “heritable factors”, scientists were able to conduct breeding experiments and to a great extend accurately predict phenotype outcomes? It’s true. Thank Gregor Mendel. Mendel was the monk and scientist who discovered heredity in the 1800’s. His insights came from his experiments with peas. It is not a mystery why he used peas. They were used due to the following advantages –

  1. Availability in different varieties
  2. Ability to grow and mature quickly
  3. Ability to produce a large offspring
  4. Ability to easily control pollination between plants   

Mendel’s Experiment

Mendel started his experiment by crossing true-breeding peas. A true-breeding plant is one that can only produce a certain phenotype. For example, only purple or white flowers. This is because they were homozygous for the dominant trait. It was not that Mendel was able to somehow run tests in a molecular biology lab to determine dominance. He had to depend on observation. So, if after many generations the plant only produced purple or white flowers, he concluded that they were true-breeding. 

The crossing of true-breeding parents is called hybridization. The true-breeding parent is called the P (parental) – generation, and the hybrid offspring is called the F1 (first filial) generation. When two F1 generation cross with each other, we get the F2 (second filial) generation. 

Mendel discovered that when he did monohybrid crosses, the F2 generation had a phenotype ratio of 3:1. For example 3 purple flours and 1 white flour. This was true regardless of the phenotype he was breeding e.g., seed color, seed shape, pod shape, pod color, and stem length.

A monohybrid cross is a cross between the P generation that differs by only a single trait. See the example below. Capital letter indicate dominant trait.

Today, Geneticists can conduct similar experiments to determine the genetic characteristics of an organism. For example, let’s say you have a plant that has purple flower. Its alleles may be PP, or Pp (where P = purple and p = white). Which one is it? To find out, you would have to cross the “mystery plant” with a true-breeding plant having the recessive trait (i.e., white – pp).

Scenario 1: If the mystery plant has PP alleles. Then all F1 would be purple 

Scenario 2: If the mystery plant has Pp alleles. Then 50% of F1 would be purple and 50% white 

Mendel’s experiments were not just limited to monohybrid crosses. He also did dihybrid crosses where the parent generation differed in two traits. When he did this, he found that the ratio of phenotypes was not 3:1 as shown earlier, but 9:3:3:1.

How to Determine Genotypes of a Dihybrid Cross

Use the following steps to work out a dihybrid cross.

  1. Write down the parent cross
  2. Draw the Punnett square (a dihybrid cross will have a Punnett square with 16 boxes)
  3. Use the FOIL method (first, outside, inside, last) to come up with the gamete combinations
  4. On the top and left of the Punnett square, write down the gamete combination from the parent
  5. Fill the boxes of the Punnett square to show the possible genotypes  

Here is an example.

Determine the F2 generation from a cross between YYRR and yyrr. Where Y = yellow seed, y = green seed, R = round seed, and r = wrinkled seed. (Notice that the two parents represent true-breeds)

Step 1

YYRR x yyrr

Step 2


Step 3

You will have 8 possible ways to combine the gametes.

Step 4 and 5

Since we are going to the F2 generation, we will have to repeat the steps to combine the offspring of the F1 generation. That is, YyRr x YyRr.


Coimplete the Punnett Square for the F2 generation. Notice the 9:3:3:1 ratio.

Punnett Square for F2

How to Determine Genotypes of a Trihybrid Cross

We have just looked at a dihybrid cross, and as you can see the Punnett square had 16 squares. Consider what would happen if you had a trihybrid cross. Now your gamete possibility is 8 instead of 4. Thus, you would need an 8 x 8 Punnett square (64 individual squares). This can be quite daunting. The example below is a trihybrid cross between PpYyRr and Ppyyrr.

Do not try to use the FOIL method for this problem. We need a different strategy. Follow these steps instead.

  1. Write down the genotype of the parent
  2. Draw a line through the first letter, second letter, and then the last one which can either go in the R direction of r direction. Therefore, the first two gametes are PYR and PYr
  • Go back to the first letter, but this time draw the line through the y instead of Y and through R and r. Therefore, the gametes you will get are PyR and Pyr
  • Now instead of starting with the first letter P, start with p and draw a line through Y followed by R and then r to get pYR and pYr.
  • Are you getting the hang of it? Start with p again, but this time draw a line through y and then R and r to get pyR and pyr. 

Now you can follow the same procedure above to find the possible gametes for Ppyyrr.

A Punnett square for this trihybrid cross would look like this?


Daunting isn’t it? Lucky for you, there is an easier way to predict genotypes using statistics. That brings me to the multiplication and addition rule. Let’s talk about that. 

The Multiplication Rule

The multiplication rule applies to independent events. That means the occurrence of one event does not affect the occurrence of another. For example, when you flip a coin you can get a head or a tail. If you flip it again you have an equal chance of getting a head or a tail again. What you got in the first toss does not affect what you will get in the second toss. This is different from dependent events where one event depends on another. For example, the time you get to work depends on what time you leave home or how bad the traffic is. During metaphase I in meiosis, genes assort themselves randomly and independently of each other as illustrated in the figure below. This is the law of random assortment. After that they segregate (or separate from each other) in anaphase I. Thus, alleles from each parent have an equal chance of ending up in the gamete. 

Using the multiplication rule we can determine the probability of one event by multiplying it by the probability of another simultaneous event. For example,

What is the probability of flipping five coins and getting 5 heads?

The probability is ½ x ½ x ½ x ½ x ½ = 1/32.

Let’s apply this to genetics.

In a simple monohybrid cross between pea plants that are heterogenous for purple flowers (Pp), what is the probability that the offspring will be homozygous recessive.

To solve this the Punnett square way, you would do the following.

To apply the multiplication rule you would multiply the probability of each parent contributing a p. That is, ½ x ½ = ¼ 

The multiplication rule becomes even more handy when working with trihybrid crosses. Constructing Punnett squares for these crosses is quite a bit of work as you saw earlier. So an easier alternative is awesome. Consider this problem –

What is the probability of getting a ppyyRr genotype in a cross between PpYyRr and Ppyyrr?

Using a Punnett square that we have already constructed, the answer is 1/16.

Using the alternate multiplication rule, you can multiply the probability of each allele pair to get the answer.

Fractions above indicate the probability of contributing the respective alleles. 

Therefore, the probability of getting an offspring that is exactly ppyyRr is ¼ x ½ x ½ = 1/16.

As you can see, we can use the multiplication rule because the events are independent and occurring simultaneously. But, what if the events are mutually exclusive (can’t happen at the same time). For example, what is the probability of getting an offspring that is either ppyyRr, or ppYrr? To solve this, we use the addition rule.

The Addition Rule

Here, all you need to do is add the probability of the events. We have already determined the probability of ppyyRr which is 1/16. Now find the probability of getting ppYyrr.

The probability of getting either ppyyRr, or ppYrr = 1/16 + 1/16 = 1/8.

Checking the Punnett square you can see that your answer of 1/8 is correct.

Deviations From Simple Mendelian Genetics

So far, our attention has been on simple Mendelian genetics where one allele affects phenotype in a very predictable way. However, this relationship is not always so straightforward. Here are some examples.

Incomplete Dominance: When there is incomplete dominance, you end up with a phenotype that is a blend of the two rather than one or the other. For example, instead of red or white flower, you may observe pink. When constructing a Punnett square for incomplete dominance, use letter superscript instead of capital and common letters. For example,

Notice the color ratio of 1:2:1.

Codominance: In this situation both phenotypes are expressed if present on both alleles.

Pleiotropy: This is when one gene has multiple phenotype effects (true of most genes). An example of this is the A, B and O blood types. One version of the gene produces an A protein, one version produces a B protein and a third version is a “null allele” producing no protein.

Epistasis (“standing upon”): This occurs when the expression of one gene alters the expression of another. That means, even if you have a dominant gene, it will not be expressed unless another specific gene is present.

Polygenic Inheritance: This type of inheritance occurs when a single trait is delivered by multiple genes. For example, each gene may contribute different concentrations of a red pigment resulting in the phenotype being different shades of pink instead of just red or white.   

Textbook: Textbook: Reece, J. B., & Campbell, N. A. (2011). Campbell biology. Boston: Benjamin Cummings / Pearson.

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Courtney Simons
Courtney Simons
Dr. Simons is a food science educator. He earned his bachelor’s degree in food science, and Ph.D. in cereal science at North Dakota State University.