Thursday, March 4, 2021

What is a Punnett square?


Biologists who study inheritance patterns, genetic counselors, and you (apparently) need to bridge the gap between DNA and some of life’s questions, like “What crop will produce the greatest yield?” or “Which dog has the shiniest coat?” I don’t know: there are millions of questions different people ask from one day to the next that have to do with inheritance.

For example, if you run a pet store, where bunnies with black fur sell better than bunnies with brown fur, you might want to know the chances of getting bunnies with black fur if you cross a black female with a brown male. We’ll use this example to explain how pet store owners and others can use Punnett squares to answer these questions.

First, you should understand that Punnett squares are a way to represent genes and a way to represent theoretical probability. They are not real, but they are just a tool we made up so that we could understand DNA, inheritance, and mathematical probability a little better, as it relates to the study of life on Earth.

The comments to this post will explain, step by step, how to make or draw Punnett squares, how they are used, and some different varieties of Punnett squares.

Paul Katula
Paul Katula is the executive editor of the Voxitatis Research Foundation, which publishes this blog. For more information, see the About page.


  1. Autosomal traits involving only one locus

    In our bunny example above, let’s just say we know that the allele for black fur (B) is dominant to the allele for brown fur (b). I don’t know for sure that this is true in any species of rabbit, but we are just using this as an example to show how to use Punnett squares in the study of inheritance.

    It is important to use a capital letter to represent the dominant allele (capital B for black fur in our example) and a lowercase letter to represent the recessive allele (lowercase b for brown fur).

    It doesn’t matter what letter you use, but on tests, it can matter which letter you choose. For example, the letters C, P, S, and V don’t make good choices for alleles, because the capital letter looks very similar to the lowercase letter. If your teacher can’t tell whether you’re writing a capital or lowercase letter, how can he or she tell whether you mean the dominant or recessive allele? On the other hand, the letters B, G, and H make good choices, because it’s easy to tell the capital letters from the lowercase ones when those are your choices.

    from, an adoption network for home rabbits in Massachusetts, New Hampshire, and Connecticut

    Back to our example: If the allele for black fur is dominant, we know the rabbit with the brown fur is homozygous recessive (bb). Here we are going to assume that the rabbit with black fur is heterozygous (Bb), since we don’t know.

    In a typical Punnett square, we write each allele of one individual as the header of a column and each allele of the other individual as the header of a row in a table that looks like a matrix. For our rabbits, we would write “b b” across the top and “B b” down the side, representing the genotypes of the individuals we are mating in this cross:

          b b

    Now that we have written the parents in our Punnett square, we have to figure out what the offspring are, which will be written in the squares in our matrix. First for the upper left offspring square, take the “B” from the parent on the left and pair it up with the “b” from the parent on the top. Write the result in the box that is across from the allele on the left and below the allele on the top (shown in red):

          b b
    B Bb      

    In this case, one dominant allele (B) from the parent on the left pairs up with one recessive allele (b) from the parent on the top, resulting in a heterozygote, or a bunny with a heterozygous genotype for the black fur trait.

    For each offspring square, we pair up the allele on the left and the allele on the top, resulting in a two-allele zygote for each offspring square. Continuing with our table, B x b produces Bb in the upper right square; b x b produces bb in the lower left square; and again in the lower right square:

          b b
    B Bb Bb
    b bb bb

    There are some conventions when writing Punnett squares, but since these are just something we made up, you are free to disregard any or all of the conventions. First, most people put the female across the top and the male down the side. The results of the Punnett square are not affected by the sex of the individual on top or on the side.

    Second, for homozygous individuals, it is not necessary to write both alleles. This means the above Punnett square could have been abbreviated by using the shortcut Punnett square below:

    B Bb
    b bb

    Third, heterozygotes are usually written with the capital letter first, such as Bb in our case. You can write them as bB (it’s still heterozygous, and the phenotype would be the same), but why would you? It is much easier to read with the capital letter first, which is probably why the convention developed in the first place.

    What this Punnett square means

    The offspring squares in a completed Punnett square represent the probability that a certain zygote will be formed when a sperm from the male parent fertilizes an egg from the female parent. In our example, there are two Bb offspring and two bb offspring.

    This leads to a Bb:bb ratio of 2:2, which equals 1:1 and results in a 50 percent chance that these rabbits will produce bunnies with the Bb genotype (black fur is the phenotype for these) and a 50 percent chance that these rabbits will produce bunnies with the bb genotype (these will have brown fur).

    In other words, if these two rabbits had 200 bunnies (and they might — given how rabbits reproduce these days), we would expect about 100 of those bunnies to have black fur with the heterozygous (Bb) genotype and about 100 bunnies to have brown fur with the homozygous recessive (bb) genotype. It could be 110 to 90, or even 200 to 0, for that matter. Punnett squares are just probabilities. Each bunny has a 50 percent chance of having the Bb genotype and a 50 percent chance of having the bb genotype. But our prediction is that 100 bunnies would have black fur and 100 bunnies would have brown fur.

    Nature doesn’t always work as the mathematical probabilities would predict, though, so be careful what you tell the pet store owner.

  2. The six basic Punnett squares

    Because there are only three genotypes (homozygous dominant, heterozygous, and homozygous recessive), there are only six Punnett squares that can result from a cross of two individuals for a one-locus gene that is not sex-linked, meaning that it is an autosomal gene. The six Punnett squares are as follows:

    (1) Homozygous dominant x homozygous dominant

          B B
    B BB BB
    B BB BB

    Genotypic ratio of offspring: BB:Bb:bb = 1:0:0
    Phenotypic ratio of offspring: Dominant:Recessive = 1:0

    (2) Homozygous dominant x heterozygous

          B B
    B BB BB
    b Bb Bb

    Genotypic ratio of offspring: BB:Bb:bb = 1:1:0
    Phenotypic ratio of offspring: Dominant:Recessive = 1:0

    (3) Homozygous dominant x homozygous recessive

          B B
    b Bb Bb
    b Bb Bb

    Genotypic ratio of offspring: BB:Bb:bb = 0:1:0
    Phenotypic ratio of offspring: Dominant:Recessive = 1:0

    (4) Heterozygous x heterozygous

          B b
    B BB Bb
    b Bb bb

    Genotypic ratio of offspring: BB:Bb:bb = 1:2:1
    Phenotypic ratio of offspring: Dominant:Recessive = 3:1

    (5) Heterozygous x homozygous recessive

          B b
    b Bb bb
    b Bb bb

    Genotypic ratio of offspring: BB:Bb:bb = 0:1:1
    Phenotypic ratio of offspring: Dominant:Recessive = 1:1

    (6) Homozygous recessive x homozygous recessive

          b b
    b bb bb
    b bb bb

    Genotypic ratio of offspring: BB:Bb:bb = 0:0:1
    Phenotypic ratio of offspring: Dominant:Recessive = 0:1

  3. Sex-linked Punnett squares

    We’ve presented information above on single-locus, autosomal traits. That means the trait (fur color, in our example) is the result of a single gene (called a locus) and that the gene is not located on the sex chromosomes, X and Y.

    The term “autosomal” is the opposite of “sex-linked.” A gene that is sex-linked means that it is on the sex-determining chromosomes, X and Y. A gene that is not on the sex chromosomes is called “autosomal” by definition.

    When the gene for a particular trait is found on the sex chromosomes, there is an added layer of complexity to how we do the Punnett squares. Before getting into that, though, please note that the sex chromosomes for a female are XX, whereas they are XY for a male offspring.

    For sex-linked traits, there is no allele for the gene on the Y chromosome; only the X chromosome has an allele for the gene that carries information about the trait involved.

    That means that for male offspring, who have only one X chromosome, whatever that chromosome is, becomes the phenotype of the male offspring.

    Let’s do an example at this point. Suppose the gene for a certain disorder is sex-linked. People who are dominant for this disorder express the disease. Thus we have the following possible genotypes for males:

    • xBy — dominant, will express the trait
    • xby — recessive, will not express the trait

    and these for females:

    • xBxB — homozygous dominant, will express the trait
    • xBxb — heterozygous, will express the trait
    • xbxb — homozygous recessive, will not express the trait

    In making a Punnett square for the inheritance of this trait, we do the same as we did for the autosomal case, except that the alleles now carry the sex-determining information along with the trait. First build a Punnett square with just the parents. Let’s say we are crossing a heterozygous female with a dominant male for the above disorder. We get this beginning:

          xB xb

    Notice: the female’s genotype is xBxb, and the male’s is xBy. There is no allele for this trait on the male’s y chromosome. See how we have written the alleles for the trait as a superscript to the X and Y chromosomes? That is generally how it’s done, but the important thing is to link the allele for the trait to the X chromosome and to have no allele for this trait on the Y chromosome.

    We do the cross just like we did in the autosomal case: take the column headings one allele at a time, pair it up with each row heading, and write the resulting genotype (one from the mom and one from the dad) in the offspring square that both headings share. I’ll do the first one here:

          xB xb
    xB xBxB      

    What I’m showing here is that one-fourth of the couple’s children are expected to be homozygous dominant girls. They will have the disorder if they get the dominant X allele from their mother and the dominant X allele from their father. Now, to complete the other offspring squares:

          xB xb
    xB xBxB xBxb
    y xBy xby

    What this Punnett square shows is that for this couple’s children, half are expected to be girls (XX) and half are expected to be boys (XY) — duh!

    But since this is a dominant sex-linked condition that we made up, all the girls this couple has will express the condition. Most sex-linked disorders are recessive, but we made this one up, and thus we got what we got.

    All girls in the Punnett square (all two of them) have at least one dominant X allele, which for the heterozygous case masks the recessive allele. This means that girls this couple has cannot escape having the disorder. There is a 100 percent chance that a female child will have the condition.

    As for the boys this couple has, half are expected to have the disorder (the dominant ones) and half are expected to be free of the condition (the recessive ones).

    The Punnett square does not predict that the couple will have four children, and this is a common misconception. It also doesn’t mean that if the couple has four children, two will be boys and two will be girls. It just gives you the odds and tells you what to expect.

  4. All of the above applies if only one gene controls a trait. For many physical properties, more than one gene plays a role.

    An easy example here is that height in humans is controlled by many traits. One of these is how long your thigh is, another is the shape of your skull, and so on.

    Traits controlled by two loci

    Let’s say the inheritance pattern for a two-loci, autosomal trait needs to be determined. If there are two genes involved, and each gene has two alleles (recessive and dominant), there are nine possible genotypes for an individual with regard to this trait:

    • AABB — homoz. dom. for both traits
    • AABb — homoz. dom. for trait A, heteroz. for trait B
    • AAbb — homoz. dom. for A, homoz. rec. for B
    • AaBB — heteroz. for A, homoz. dom. for B
    • AaBb — heteroz. for both traits
    • Aabb — hetero. for A, homoz. rec. for B
    • aaBB — homoz. rec. for A, homoz. dom. for B
    • aaBb — homoz. rec. for A, heteroz. for B
    • aabb — homoz. rec. for both traits

    For the A alleles (the two that the individual has), when the sex cell is made, there is an equal chance (usually) that it will be with each of the two B alleles the individual has. For example, if an individual has the genotype AaBb, the egg or sperm has a one-fourth probability of being AB, one-fourth of being Ab, one-fourth aB, and one-fourth ab.

    In other words, take each A allele and match it up with each B allele. The number of possibilities constitutes the number of columns or rows for that individual in the Punnett square:

          AB Ab aB ab

    Next, what if this individual is crossed with an individual who is homozygous dominant for the A gene and heterozygous for the B gene? We complete the left parent column on the Punnett square with the four possible combinations there.

          AB Ab aB ab

    Instead of starting with the upper left corner this time, let’s start with the lower right offspring possibility, just to change things up a bit.

    For this square (shown in red below), the left parent contributes a dominant A allele and a recessive b allele, and the top parent contributes a recessive a and a recessive b allele. The result is shown here:

            AB     Ab     aB     ab  
      Ab             Aabb

    Finally, we complete the remaining 15 squares, being careful to match up the alleles properly:

          AB Ab aB ab
      AB   AABB AABb AaBb AaBb
      Ab   AABb AAbb AaBb Aabb
      AB   AABB AABb AaBb AaBb
      Ab   AABb AAbb AaBb Aabb

    In this particular case, we can eliminate the two last rows, since they are repeats of the first two rows. This will make computing the probabilities a little easier, since they will be out of eight rather than sixteen.

          AB Ab aB ab
      AB   AABB AABb AaBb AaBb
      Ab   AABb AAbb AaBb Aabb
      AB   AABB AABb AaBb AaBb
      Ab   AABb AAbb AaBb Aabb

    Genotypic ratios

    For these two individuals, the genotypic ratio can be written as follows:

    AABB:AaBB:aaBB:AABb:AaBb:aaBb:AAbb:Aabb:aabb = 1:0:0:2:3:0:1:1:0

    And this can also be abbreviated, as long as the meaning is clear, to AABB:AABb:AaBb:AAbb:Aabb = 1:2:3:1:1.

    Let’s not worry too much about syntax, though. The probabilities that an offspring will have a given genotype are stated in the table below:

    • AABB — 12.5 percent
    • AaBB — 0
    • aaBB — 0
    • AABb — 25 percent
    • AaBb — 37.5 percent
    • aaBb — 0
    • AAbb — 12.5 percent
    • Aabb — 12.5 percent
    • aabb — 0

    As you can see, things get a little more mathematical as we include more loci. Just imagine if we didn’t have the opportunity to abbreviate the Punnett square!

    Phenotypic ratios

    What these genotypes look like — that is, the physical expression of these genotypes — makes all the difference in determining the phenotypic ratios. Obviously, once you have the genotypic ratios, you can simply add up the probabilities for those genotypes that produce an identical phenotype. That will give you the phenotypic ratios.

    For example, suppose A was a gene that coded for fur color in mice, and B was a gene that coded for the presence of a tip. The dominant allele, A, codes for gray fur, and the recessive allele, a, codes for white fur. The dominant allele, B, codes for a yellow tip on the fur, and the recessive allele, b, codes for no tip. But, if the fur is white, there is no yellow tip, regardless of the genotype at the B locus.

    This means that mice with a genotype of AABB, AaBB, AABb, or AaBb will have gray fur with a yellow tip. If we add those probabilities, we find a probability that mice born from these two parents have a 75 percent chance of having gray fur with a yellow tip.

    The other 25 percent of mice from the table above (AAbb and Aabb) will have gray fur as well, but they will not have a yellow tip on their fur. Note that no babies from these two parents will have white fur.

    Please note that this is not a real example. I don’t know what the genotype/phenotype combination looks like for any species of mouse. I just used it as an example to demonstrate how to use a two-loci Punnett square.

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