A Punnett square is a diagram that was devised by an English geneticist named Reginald Punnett in the first half of the 20th century in order to determine the statistical likelihood of each possible genotype of the offspring of two parents. He was applying the laws of probability to work pioneered by Gregor Mendel in the mid-1800s. Mendel’s research focused on pea plants, but it is generalizable to all complex life forms. Punnett squares are a common sight in research and education when examining heritable traits. For predicting a single trait, which is known as a monohybrid cross, there will be a square with two perpendicular lines bisecting it like a windowpane, creating four smaller squares within it. When predicting two traits together, known as a dihybrid cross, there will usually be two vertical and two horizontal lines within the larger square instead of one of each, creating 16 smaller squares instead of four. In a trihybrid cross, the Punnett square will be eight squares by eight squares. (See Resources for examples)
TL;DR (Too Long; Didn't Read)
A Punnett square is a diagram used to determine the statistical likelihood of each possible genotype of the offspring of two parents for a given trait or traits. Reginald Punnett was applying the laws of probability to work pioneered by Gregor Mendel in the mid-1800s.
Punnett squares are broadly applicable, from predicting the likelihood that a plant’s offspring will have white or red flowers, to determining how likely it is that a human couple’s baby will have brown or blue eyes. That said, Punnett squares are only useful tools under certain conditions. It is especially important that the genes in question control what are known as Mendelian traits. When Mendel studied his pea plants in the 1850s and 1860s, he did not know about the existence of genes, although his innovative research allowed him to infer their existence. He chose to focus on the pea plants’ traits – or phenotypes – that had only two variants, which is known as a dimorphic trait. In other words, the pea plants only produced yellow or green seeds. There were never exceptions in which they had orange seeds, or seeds that were a color somewhere between yellow and green. He studied seven traits that behaved like this, in which each trait had two variants, without any instances of a plant’s offspring showing an in-between variant or a third, alternative variant.
This is typical of a Mendelian trait. In humans, most inherited traits are not Mendelian, although there are many that are, such as albinism, Huntington’s disease and blood type. Mendel discovered, without the knowledge of DNA or access to microscopes that scientists have today, that each parent plant had two “factors,” and one from each was copied and transferred to their offspring. By “factors,” Mendel was referring to what are now known as chromosomes. The traits he studied in the pea plants belonged to corresponding alleles on each chromosome.
Pure Line Breeding
Mendel developed “pure lines” of pea plants for each trait, which meant that each pure plant was homozygous for its variant. Unlike a heterozygous organism, a homozygous organism has the same allele (for whichever trait is being observed) on both chromosomes, although of course, Mendel did not think of it this way, since he did not know about the field of genetics he was fathering. For example, over several generations, he bred pea plants that had two yellow seed alleles: YY, as well as pea plants that had two green seed alleles: yy. From Mendel’s perspective, this simply meant that he bred plants that consistently had offspring with the same exact trait variant repeatedly, enough times that he was confident they were “pure.” The homozygous, YY pure line pea plants consistently had only yellow seed offspring, and the homozygous, yy pure line pea plants consistently had only green seed offspring. With these pure line plants, he was able to experiment with heredity and dominance.
Consistent Ratio of 3 to 1
Mendel observed that if he bred a pea plant with yellow seeds with a pea plant with green seeds together, all of their offspring had yellow seeds. When he crossbred the offspring, however, 25 percent of the next generation had green seeds. He realized that the information to produce green seeds must have been contained somewhere in the plants through the first, all-yellow generation. Somehow, the first generation of offspring had not been as pure as the parent generation. He was especially interested in why there was a consistent ratio of three to one in his experiments of one trait variant to the other in the second generation of offspring, regardless of which of the seven traits he was studying, whether it was seed color, flower color, stem length or the others.
Traits Hiding in Recessive Alleles
Through repeated experimentation, Mendel developed his principle of segregation. This rule asserted that the two “factors” in each parent become separated during the process of sexual reproduction. He also developed his principle of independent assortment, which posited that random chance determined which single factor from each parental pair were copied and transferred to the offspring, so that each offspring ended up with only two factors, instead of four. Geneticists now understand that independent assortment happens during anaphase I of meiosis. These two laws became founding principles of the field of genetics, and as such, they are fundamental guidelines for using Punnett squares.
Mendel’s understanding of statistical probability led him to determine that certain trait variants in the pea plants were dominant, while their counterparts were recessive. In the seven dimorphic traits he was studying, such as seed color, one of the two variants was always dominant. Dominance resulted in a greater probability of offspring with that variant of the trait in question. This statistical pattern of inheritance is also the case with human Mendelian traits. When the two homozygous pea plants – YY and yy – were bred together, all of the offspring in the first generation had the genotype Yy and Yy, in alignment with Mendel’s principles of segregation and independent assortment. Because the yellow allele was dominant, all of the seeds were yellow. Because the green seed allele was recessive, however, the information about the green phenotype was still stored in the genetic blueprint, even if it wasn’t showing itself in the plants’ morphologies.
In the next generation, when Mendel crossbred all of the Yy plants, there were a few possible genotypes that could result, In order to determine what those are and calculate the likelihood of each, a simple Punnett square with four smaller squares inside of it is the most useful tool.
How a Punnett Square Works
Begin by writing the genotypes of the parents along the outer horizontal and vertical axes of the Punnett square. Since one of the parent genotypes is a Yy, write a “Y” over the top line of the top left square and a “y” over the top line of the square to its right. Since the second parent genotype also happens to be a Yy, also write a “Y” to the left of the outer line of the top left square, and a “y” to the left of the outer line of the square below it.
In each square, combine the alleles that meet at its respective top and side. For the top left, write YY inside the square, for the top right write Yy, for the bottom left write Yy, and for the bottom right square write yy. Each square represents the probability of that genotype being inherited by the offspring of the parents. The genotypes are:
- One YY (yellow homozygous)
- Two Yy (yellow heterozygous)
- One yy (green homozygous)
Therefore, there is a three in four chance of the second generation of pea plant offspring having yellow seeds, and a one in four chance of the offspring having green seeds. The laws of probability support Mendel’s observations about a consistent three to one ratio of the trait variants in the second offspring generation, as well as his inferences about alleles.
Fortunately for Mendel and scientific progress, he chose to perform his research on the pea plant: an organism whose traits are clearly dimorphic and easily distinguishable, and where one of each trait’s variants is distinct in its dominance over the other. This is not the norm; he easily enough could have chosen another garden plant with traits that do not follow what are now known as Mendelian traits. Many allele pairs, for example, exhibit different types of dominance than the simple dominant and recessive kind encountered in the pea plant. With Mendelian traits, when there are both a dominant and recessive allele present as a heterozygous pair, the dominant allele has complete control over the phenotype. With the pea plants, for example, a Yy genotype meant that the plant would have yellow seeds, not green, even though the “y” was the allele for green seeds.
One alternative is incomplete dominance, in which the recessive allele is still partially expressed in the phenotype, even when combined with the dominant allele in a heterozygous pair. Incomplete dominance exists in many species, including humans. A well known example of incomplete dominance exists in a flowering plant called the snapdragon. Using a Punnett Square, you could determine that the homozygous red (CRCR) and the homozygous white (CWCW) crossed with each other would produce 100 percent chance of offspring with the heterozygous genotype CRCW. This genotype has pink flowers for the snapdragon, because the allele CR has only incomplete dominance over CW. Interestingly, Mendel’s discoveries were groundbreaking for their debunking of long-held beliefs that traits were blended by parents into offspring. All the while, Mendel missed the fact that many forms of dominance do in fact involve some blending.
Another alternative is codominance, in which both alleles are simultaneously dominant, and equally expressed in the offspring’s phenotype. The most well-known example is a form of human blood type called MN. The MN blood type is different than the ABO blood type; instead, it reflects an M or an N marker that sits on the surface of red blood cells. A Punnett square for two parents who are each heterozygous for their blood type (each with an MN type) would result in the following offspring:
- 25 percent chance of a homozygous MM type
- 50 percent chance of a heterozygous MN type
- 25 percent chance of a homozygous NN type
With Mendelian traits, this would suggest that there is a 75 percent chance of their offspring having a phenotype of an M blood type, if M were dominant. But because this is not a Mendelian trait and M and N are codominant, the phenotype probabilities look different. With the MN blood type, there is a 25 percent chance of an M blood type, a 50 percent chance of an MN blood type and a 25 percent chance of an NN blood type.
When a Punnett Square Will Not Be Useful
Punnett squares are helpful much of the time, even when comparing multiple traits or ones with complex dominance relationships. But sometimes predicting phenotypic outcomes can be a difficult practice. For example, most traits among complex life forms involve more than two alleles. Humans, like most other animals, are diploid, which means that they have two chromosomes in each set. There are usually a large number of alleles among the entire population of the species, despite the fact that any individual only has two, or only one in some cases involving sex chromosomes. The vast possibility of phenotypic outcomes makes it especially difficult to calculate probabilities for certain traits, while for others, such as eye color in humans, the options are limited, and therefore easier to enter into a Punnett square.