# What Is the Main Function of the Punnett Square?

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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.

## Mendelian Traits

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
• 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

• One YY (yellow homozygous)
• Two Yy (yellow heterozygous)
• One yy (green homozygous) :

## Non-Mendelian Traits

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.

## Incomplete Dominance

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.

## Codominant Alleles

• 25 percent chance of a homozygous MM type
• 50 percent chance of a heterozygous MN type
• 25 percent chance of a homozygous NN 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.