Punnett Squares

Punnett squares are nifty tools in genetics that help us to easily visualize allelic combinations and genotype outcomes in the offspring of a cross. From these genotypes, with the knowledge of dominant and recessive traits, Mendelian genetics, and any relevant exceptions to its principles, we can discover the phenotypes of offspring as well. Punnett squares also provide an easy method to help us see genotype and phenotype ratios.

Punnett square explained

Punnett squares help us to demonstrate the range of genotypes that are possible for the progeny of any particular cross (a mating event). Two parent organisms, usually called P1 and P2, create their gametes that contribute alleles for these crosses. Punnett squares are best used for straightforward crosses, where a single gene is analyzed, and the alleles of that gene obey the principles of Mendelian genetics.

Punnett square definition

A Punnett square is a diagram in the shape of a square, that has smaller squares encased within it. Each of those small squares contains a genotype that is possible from a cross of two parent organisms, whose genotypes are usually visible adjacent to the Punnett square. These squares are used by geneticists to determine the probability of any given offspring having certain phenotypes.

Punnett square labeled

Let's look at a labeled Punnett square for a greater understanding of both what it is capable of, and its limitations.

We will start with a monohybrid cross, which is a cross where we are only examining one trait or one gene, and both parents are heterozygous for these traits. In this case, the gene is the presence of freckles in human beings, a mendelian trait where the presence of freckles is dominant over lack of freckles.

We have labeled the parental generations with their two types of gametes (eggs in a female, and sperm in a male), concerning the freckles gene. For both parents: F is the allele for freckles (dominant, hence the capital F), and f is the allele for a lack of freckles. We see that both parents have one of each type of gamete.

When a Punnett square is performed, we can receive a lot of information from this simple set of squares.

Figure 1. Labelled monohybrid cross for the inheritance of freckles.

• First, we can determine possible genotypes of offspring.

  • According to the Punnett square, there are three possible genotypes; FF, Ff, and ff.

• Next, we can determine possible phenotypes of offspring.

  • Following Mendel's law of dominance, we know there are two possible phenotypes: freckled (FF and Ff) and freckle-free (ff)

• We can also use Punnett squares to determine the probability of any one child ending up with a certain genotype.

  • For example, what would be the probability that a child has the Ff genotype?

    • We can see that 2 out of 4 of the Punnett square boxes are Ff. This means a 2/4 (simplified, 1/2 or 50%) chance that a child has an Ff genotype.

      • Translating this fraction to percentages, we would assume that anyone's offspring of this cross has a 50% chance of having freckles

• We can determine the genotypic ratio of this cross.

  • 1/4 of children will be FF, 1/2 will be Ff, and 1/4 will be ff

  • Thus, the genotypic ratio is 1:2:1, FF to Ff to ff.

• We can determine the phenotypic ratio of this cross.

  • 1/4 of children will be FF, 1/2 will be Ff, and 1/4 will be ff

    • 1/4 + 1/2 children will be either FF or Ff

      • Thus, (1/4 + 1/2) = 3/4 freckled

      • Thus, (1 - 3/4) = 1/4 not freckled

  • Thus, the phenotypic ratio is 3:1 freckled to not freckled.

Let's say we didn't know the genes of the parents, but we do know the nature of the freckles gene (i.e. we know that freckles are a dominant trait).

• If one parent has freckles and the other also has freckles, and one of their children does not, can we know the parent's genotypes? Yes! But how?

  • In order for two parents expressing a dominant phenotype to have a child expressing a recessive phenotype, both parents must be heterozygotes. If even one has a homozygous dominant genotype, no child could have a recessive phenotype because they would receive a maximum of one recessive allele.

  • Both parents must be heterozygotes and therefore we can know their genotypes.

• This is an example of working backward in genetic analysis to establish parental genotype and potentially a Punnett square.

Let's say these two people produce offspring. If our freckled parents are the parental generation, the offspring they produce would be the F1 generation, or the first filial generation, of this monohybrid cross.

Say we wish to add another layer of complexity to this family's genetic analysis: it turns out that, not only is this couple heterozygous for the freckle gene, but they are also heterozygous for another gene as well: the widow's peak gene.

A widow's peak is a dominant trait that leads to a V-shaped hairline, as opposed to a straighter or more rounded hairline that is recessive. If these parents are heterozygous for these two genes, they are considered dihybrids, which are organisms that are heterozygous for two traits at two different gene loci.

Different Punnett squares

What would a Punnett square of this kind of cross, a dihybrid cross, look like? For dihybrid crosses, there are 16 small boxes within the larger square diagram that makes up the Punnett square. This is in contrast to the 4 small boxes that make up a Punnett square for a monohybrid cross (or any cross between two parent organisms where a single gene with two alleles is being analyzed).

Punnett squares example: a dihybrid cross

Figure 2. Labelled dihybrid cross for the inheritance of freckles and hairline.

We can also determine genotypic and phenotypic ratios with this large Punnett square. They are 1:2:1:2:4:2:1:2:1 and 9:3:3:1, respectively. (Yes, there are 9 possible genotypes in a dihybrid cross.)

Alongside this more complex Punnett square, we should determine more complex probabilities. To do that, there are two basic rules we should keep in mind, the sum law and the product law.

The sum law is best used when you see the word or in a question or analysis, while the product law is used when you see the words both or and. Even if you don't see these words, if you reason as to whether you are ultimately being asked an AND or an OR question, you can solve such problems with ease.

With the help of the Punnett square, let's analyze one such problem.

That's quite the figure, demonstrating how unlikely it is for such a couple to have three children with this specific genotype exclusively.

Another thing to note from the specificity of this probability is that we achieved it using the product and sum rule. Because it was a more complex assessment (three different offspring, with two different traits being analyzed for each), a Punnett square alone would ultimately be too tedious and confusing to perform this assessment of probability. This highlights to us the limitations of Punnett squares.

The Punnett square is best used for simple assessments of genes that obey the laws of Mendelian genetics. If a trait is polygenic, if we wish to examine the probability of multiple offspring exhibiting said trait, if we wish to analyze multiple traits and gene loci in tandem, and in other such considerations; we might find it better to use probability laws like the sum and product laws, or even pedigree analysis to look at inheritance patterns.