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.
What are the principles of Mendelian genetics? There are three laws that define them, namely the law of dominance, the law of segregation, and the law of independent assortment.
The law of dominance explains that there is a dominant allele and a recessive allele for a trait or gene, and the dominant allele will control the phenotype in a heterozygote. So a heterozygous organism will have the exact same phenotype as a homozygous dominant organism.
The law of segregation states that alleles are segregated or separated individually and equally into gametes. This law means that no allele has any preference over another when it comes to its heritability in future generations. All gametes have an equal chance of getting an allele, in proportion to the times that allele is present in the parent organism.
The law of independent assortment states that inheriting one allele on one gene won't influence or affect the ability to inherit a different allele on a different gene, or for that matter, a different allele on the same gene.
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.
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.
We can see here examples of how dominant traits are not necessarily the most common traits in a population. When dominant traits are things that offer fitness (increased chance of that organism to survive and reproduce) they tend to be the majority in a human population. We see that most genetic diseases are recessive, for example, and the wild-type or healthy alleles are dominant and the most common in humans.
Freckles and widow's peaks don't appear to confer much of an advantage or disadvantage as far as genetics or fitness are concerned, thus natural selection is not a major factor in their propagation. It's likely that they appeared as a random mutation in several initial individuals and then propagated in a standard manner, without being selected for or against.
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 states that to find the probability of one OR the other occurrence happening, we must add together the probabilities of each individual event happening.
The Product Law states that to find the probability of some occurrence AND another occurrence happening, we must multiply the probabilities of each event happening together.
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.
Q: What is the probability of having three offspring each with freckles and no widow's peak?
A: The probability of having three offspring with this phenotype is:
Pr (freckles, no widow's peak) x Pr (freckles, no widow's peak) x Pr (freckles, no widow's peak)
From the Punnett square and the standard phenotypic ratio of dihybrid crosses, we know that
Pr (freckles, no widow's peak) = 3/16
Therefore:
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.
Punnett Squares - Key takeaways
- Punnett squares are simple visual representations of genetic outcomes for offspring
- Punnett squares display the possible genotypes of future offspring in small squares encased in the larger diagram
- Punnett squares can help us to determine the probabilities of genetic outcomes in monohybrid or dihybrid crosses
- Punnett squares have their limitations, and the more complex or widespread a genetic analysis is, the less useful Punnett squares are
- The product and sum rule of genetic probability and pedigree analysis are good for assessing genetic outcomes when Punnett squares are no longer useful.
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