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Punnett Squares Intro

Intro to this lesson has been adapted from Biology (Macaw edition, Miller and Levine, section 11.2)

Main idea:  We start off looking at Mendelian inheritance, the simplest, way that traits are inherited. (It is a real way but not the only way. See non-Mendelian inheritance at the end of this lesson.)

If a parent carries two versions for a gene we can’t be sure which of those will be inherited by any one of the parent’s offspring.  Yet though we can’t predict the exact future, probability – a field of math – explains the results.

Punnett square Mendel Wikipedia

parents that are heterozygous for the purple/white color alleles. From commons.wikimedia.org Punnett_square_mendel_flowers.svg, by Madeleine Price Ball.

Key Questions: How can we use probability to predict traits? How do alleles segregate when more than one gene is involved?

Key vocabulary:

* Punnett square
* Gene
* Allele
* homozygous and heterozygous genes
* dominant and recessive alleles
* phenotype and genotype


Alleles are different versions of the same gene

All humans have hair, and thus hair genes. But hair varies in color and texture. So we must have different versions of these genes.

All humans have eye color – and that too varies. So we must have different versions of these genes.

Different versions of the same gene are called alleles.

We’ll use middle-school math – punnet squares – to show how different combinations of these alleles leads to different results. This branch of math is called probability.

Alleles are not “ideas” or “social constructs”. They are physical objects located in the chromosomes, in our cell nucleus.

Here we see a pair of chromosomes, roughly showing where the alleles for certain genes are located.

Here is an actual photograph of chromosomes in onion root cells, during mitosis.


from the archive of Josef Reischig and is part of the 384 pictures kindly donated by the authorship heirs under CC BY SA 3.0 license as a part of Wikimedia Czech Republic’s GLAM initiative.


Dominant and Recessive genes

What happens if you get a gene with one instruction from mom, yet a different instruction from dad? How do these 2 different versions interact? In the simplest case, one will have an effect that you see, and the other gene has no effect.

Dominant means that the gene always has a visible effect.

Recessive means that the gene doesn’t have a visible effect, even though it exists alongside a dominant gene.

and finally: Recessive genes only have visible effects if no dominant genes are around. We need 2 copies of a recessive gene to see it have an effect.

Warning: These terms only have meaning in the simplest case. Sometimes the two genes combine to make an intermediate effect. When that happens we consider non-mendelian inheritance.

What is probability?

It is the likelihood that a particular event will occur.  Consider flipping a coin. There are two possible outcomes: Heads up or tails up. The probability of either is equal, 1 in 2 (50 percent)

If you flip a coin 3 times in a row, what is the probability it will land heads every time? Each flip is an independent event. Therefore, the probability of flipping three heads in a row is:  1/2  x  1/2  x  1/2 =  1/8

Note: Past outcomes do not affect future ones. Just because you’ve flipped 3 heads in a row doesn’t mean you’re more likely to have a coin land tails up the next time. The probability for that flip is still 1/2.

Applying probability to biology

During meiosis – the creation of eggs or sperm – genes are copied, shuffled a bit, and then segregated (moved apart from each other, into new daughter cells.)

Different versions of a gene (black hair vs red hair, 5 fingers vs 4 fingers) are called alleles.

Well, the way that alleles segregate is random, like a coin flip. So the principles of prob-ability can be used to predict the outcomes of genetic crosses. Lets examine this figure:

The “tallness” gene comes in two alleles (forms)

T = taller    t = shorter

When the plant makes pollen (sperm cells) the genes are segregated (separated into different cells)

segregation and probability Mendel

Notice how there are three possible combinations, when we mate the 2 plants.

TT  (two genes for being taller genes)

Tt  (one gene for taller & 1 for shorter)

tt (two genes for shorter)

What are the real-world results from these gene combinations?

TT  – plant is tall

Tt  – plant is also tall?!

tt – plant is short

TT and tt make sense. But shouldn’t the Tt combination make a medium-height plant? apparently not. We’ll have to think about this. There’s obviously a difference between what genes are inside an organism (genotype) and the way that organism grows and shows traits (phenotype)

genotype – what the actual genes inside the cells are

phenotype – how the genes are expressed when the organism grows

Homo- or Hetero- zygous

2 identical alleles for a particular gene – homozygous

2 different alleles for the same gene – heterozygous

End of section adapted from Biology/Macaw edition.

How to use Punnet Squares

From Ask-A-Biologist, askabiologist.asu.edu/punnett-squares

Punnett squares predict what the offspring will look like, when mating plants or animals.

Reginald Punnett, a mathematician, came up with these in 1905, long after Mendel’s experiments.

Parent Generation

Mendel began his experiments with true breeding strains – something simple to observe, where both alleles are the same for a gene. (homozygous)

Since there is only one kind of allele present, mating two plants from the same strain will produce offspring that have the same phenotype and genotype as their parents.

First Generation

Mendel first crossed two different true breeding strains together:
One that produced yellow peas and one that produced green peas.

“A” – yellow pea allele
“a” – green pea allele.

AA x aa

Result: all of the offspring had yellow seeds. How?

Create a Punnet Square. Write the parents’ genotypes along the top and side of the square.

Punnett Square, aa x AA

Next, fill in each cell with two alleles:

one from the parent along the top and one from the parent along the side.

The letters in the middle show you all possible combinations of alleles that can happen from mating these two genotypes.

Punnett Square, Aa all yellow

The order of the letters doesn’t make a difference in the phenotype: aA is the same as Aa

The capital letter is usually written before the lowercase.

These offspring are heterozygous, – have two different alleles for pea color.

Despite the fact that both alleles are present in the offspring, the traits did not blend together to result in yellowish-green peas.

Instead, only one phenotype was visible and all peas were yellow.

Because of this, the yellow pea phenotype is said to be dominant, meaning that it is visible in the heterozygous individual.

Aa Yellow

Second Generation

For the second generation, Mendel mated the heterozygous offspring from the first generation together.

Aa x Aa = 3/4 yellow, 1/4 green

Mendel looked at the offspring from this mating:
He noticed that 1/4 of the children plants had green seeds.
Why did this happen? How was it possible for some of the offspring to have green seeds when both of the parent plants had yellow seeds?

Use a Punnet square to find out:

Punnett Square, crossing 2 heterozygotes

We see that there are three possible genotypes that could result from this crossing:
AA, Aa, aa.

The genotypes AA and Aa will result in the yellow pea phenotype because A is dominant. Only aa will produce the green pea phenotype.

Punnett Square, results of heterozygous cross

Now we see how it was possible for the green pea phenotype to skip a generation.
The green pea allele was present in the F1 generation, but the phenotype was hidden by the yellow pea allele.
The green pea phenotype is said to be recessive: it is only visible in the homozygous individual when the yellow allele is not present.


In the F2 generation, only 1 of the 4 boxes produced green peas.
In other words, 25% of the offspring had green peas.

We can use the probability to predict how many offspring are likely to have certain phenotype when mating plants or animals with different traits. Just take the probability of a phenotype and multiply it by the total number of offspring.

Let’s imagine there were 160 total offspring in Mendel’s F2 generation.
How many peas are likely to be green?

25% green peas x 160 total offspring = 40 green pea offspring


What have been our hidden assumptions?

All of the above is based on certain assumptions. They are usually valid – but not always!  When they are valid we call the situation “Mendelian inheritance”. When these assumptions aren’t valid then it gets a bit more complicated, and we’d need to look at non-Mendelian inheritance.

So let’s look at the assumptions of mendelian inheritance:

Segregation of genes (Mendel’s first Law)

1. In most cells, genes exist in pairs. They exist more than one form (allele).

2. These genes segregate – physically separate – during meiosis.

So each gamete (sperm or egg) ends up with only one (instead of a pair.)

3. An offspring inherits a pair of alleles for a trait by inheriting homologous chromosomes from the parent organisms. One allele for each trait from each parent.

Independent assortment (Mendel’s second law)

Alleles for separate traits are passed independently from parents to offspring.

The selection of an allele for one trait has nothing to do with the selection of an allele for any other trait.

This assumption, it turns out, isn’t always true. There are many violations of this due to genetic linkage.

Dominance (Mendel’s third law)

When you have 2 different versions of a gene (heterozygous), we see that one allele is dominant and the other is recessive. (“complete dominance:)

Here is an illustration of how Mendelian inheritance, assuming these three laws, works:


“The maternal chromosome 1 lines up on either the left or right by chance and the maternal chromosome 2 lines up on the left or right by chance. Half the cells undergoing meiosis produce M1M2: P1 P2 products and half produce M1P2: P1M2 products. The result is independence of chromosome during segregation.”

Here is another illustration of how Mendelian inheritance works.

Law of Segregation Law of Independent Assortment

When these assumptions aren’t valid then it gets a bit more complicated, and we’d need to look at non-Mendelian inheritance.

Sample questions

People may be Rh-positive or Rh-negative for their blood types. Rh-positive individuals have Rh factors, or markers, on the surface of their red blood cells. Rh-negative individuals do not have these markers. Several genes code for Rh factors. The D allele, which codes for one type of Rh marker, is responsible for the majority of Rh-positive phenotypes. Because of this, the D and d alleles are often used to describe Rh blood type inheritance. Determining Rh blood type inheritance is especially important when an Rh-negative woman is pregnant. If the baby is Rh-positive, the woman is treated with a special medicine so she does not produce antibodies that attack the baby’s red blood cells.

a. Using the given allele symbols, identify the genotype of an Rh-negative woman.

b. Draw Punnett squares to represent all the different crosses in which an Rh-negative woman could have an Rh-positive baby.

c. For each Punnett square you drew in part (b), determine the percent chance that the baby will be Rh-positive.

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