The Punnett quadrilateral is a visual device used in the science of genetics to determine which combinations of genes may occur at conception. A Punnett square is made of a simple square grid divided into a 2x2 (or larger) grid. With this grid, and knowledge of the genotypes of both parents, scientists can discover potential gene combinations for offspring and possibly even know some inherited traits.
Step
Before You Begin: Some Important Definitions
“If you want to skip the "basics" section and get straight to the discussion about the Punnett quadrilateral, click here."
Step 1. Understand the concept of genes
Before learning about how to create and use a Punnett quadrilateral, you should know some important basics. The first is the idea that all living things (from tiny microbes to giant blue whales) have "genes." Genes are extremely complex microscopic sequences of instructions that are encoded into almost every cell in the body of all organisms. Genes are responsible for all aspects of an organism's life, including appearance, behavior, and more.
One of the important concepts to understand when working with Punnett quadrilaterals is that "all living things get their genes from their parents." Subconsciously, you may already be aware of this yourself. Think about it - don't most people you know look like their parents in looks and behavior?
Step 2. Understand the concept of sexual reproduction
Most of the organisms (not all) that you know about in this world produce offspring through "sexual reproduction." A condition when male and female parents donate their respective genes to produce offspring. In this case, half of the child's genes come from both parents. The Punnett quadrilateral is basically a way of showing the various possibilities of this half-half gene swap in graphical form.
Sexual reproduction is not the only form of reproduction that exists. Some organisms, (such as bacteria) reproduce by "asexual reproduction", a condition in which parents produce their own children, without the help of a partner. In asexual reproduction, all of a child's genes come from only one parent, making them more or less exact copies of the parent
Step 3. Understand the concept of allele in genetics
As mentioned above, the genes in an organism are basically a series of instructions that govern every cell in the body on how to survive. In fact, unlike a manual, genes are also divided into chapters, sections, and subsections, with different sections of the gene regulating separate functions individually. If any of these "subsections" differ between two organisms, the two will look and behave differently - for example, genetic differences make one person black and the other blonde. These different forms in the same gene (human gene) are called "alleles".
Since each child gets two sets of genes - each male and female parent - the child will get two copies for each allele
Step 4. Understand the concept of dominant and recessive alleles
A child's allele does not always "share" the power of the gene. Some alleles, referred to as dominant alleles, will manifest in the physical appearance and behavior of the child (we call them "expressed") by default. Other alleles, called “recessive” alleles, can only be expressed if they are not paired with a dominant allele, which is capable of “overrunning” them. The Punnett square is often used to help determine how likely a child is to receive a dominant or recessive allele.
Because these genes can be "overrun" by dominant ales, recessive alleles tend to be expressed less frequently. In general, a child must inherit the recessive allele from both parents for the allele to be expressed. Blood disease conditions are a frequently used example of a recessive trait - but please note that a recessive allele does not mean "bad"
Method 1 of 2: Showing Monohybrid (Single Gene) Crosses
Step 1. Create a 2x2 grid
The most basic Punnett squares are fairly easy to make. Start by drawing an equilateral rectangle, then divide the interior into four equal grids. When you're done, there should be two grids in each column and two grids in each row.
Step 2. Use letters to represent the parent or source allele in each row and column
In a Punnett quadrilateral, columns are assigned to mothers, and rows to fathers, or vice versa. Write the letters next to each row and column that represent each of the paternal and maternal alleles. Use capital letters for dominant alleles and lowercase letters for recessive alleles.
It will be much easier to understand with an example. For example, let's say you want to determine the probability that the children of a particular couple will be able to roll their tongues. We represent this with the letters "R" and "r" - a capital letter for the dominant gene and a lowercase letter for the recessive. If both parents were heterozygous (having one copy of each allele), we would write an "R" and an "r" along the top of the grid grid and an "R" and an "r" along the left side of the grid.
Step 3. Write the letters for each grid in the rows and columns
After filling in the alleles given from each parent, filling in the Punnett square becomes easy. On each grid, write the two-letter gene combinations of the paternal and maternal alleles. In other words, take the letters from the grid in the column and row, and then write them both in the connecting blank box.
- In this example, fill in our Punnett quadrilateral grid as follows:
- The box on the top left: “RR”
- The box at the top right: “Rr”
- Box at bottom left: “Rr”
- The box at the bottom right: “rr”
- Note that usually the dominant allele (capital letter) is written first.
Step 4. Determine the genotype of each potential offspring
Each box filled in in the Punnett square represents the offspring that the parents may have. Each square (and therefore each offspring) is equally likely - in other words, in a 2x2 grid, there is a 1/4 chance for every four possibilities. The different combinations of alleles represented in the Punnett quadrilateral are called "genotypes". While genotypes represent genetic differences, offspring do not necessarily differ for each lattice (see steps below).
- In our example Punnett quadrilateral, the possible genotypes for offspring from these two parents are:
- “Two dominant alleles” (two R's)
- “One dominant and one recessive allele” (R and r)
- “One dominant and one recessive allele” (R and r) - note that there are two grids with this genotype.
- “Two recessive alleles” (two r's)
Step 5. Determine the phenotype of each potential offspring
The phenotype in an organism is the actual physical trait shown based on its genotype. Some examples of phenotypes such as eye color, hair color, and the presence of blood disease cells - these are physical traits "determined" by genes, but not actual combinations of genes themselves. The phenotype that a potential offspring will have is determined by the characteristics of the gene. Different genes will have different rules in terms of their manifestation as a phenotype.
- In our example, let's say that the gene that allows a person to roll their tongue is the dominant gene. This means that each offspring will be able to roll their tongue, even if only one allele is dominant. In this case, the phenotypes of the potential offspring are:
- Top left: “Able to roll tongue (two R's)”
- Top right: “Able to roll tongue (one R)”
- Bottom left: “Able to roll tongue (one R)”
- Bottom right: “Unable to roll tongue (no R)”
Step 6. Use the grid to determine the probability of the different phenotypes appearing
One of the most common uses of the Punnett quadrilateral is to determine how likely an offspring is to have a specific phenotype. Since each grid represents an equivalent possible genotype, you can find the possible phenotypes by "divide the number of grids containing that phenotype by the total number of lattices present."
- The Punnett quadrilateral in our example states that there are four possible combinations of genes for any offspring, from these two parents. Three of these combinations create offspring capable of tongue-rolling. Therefore, the probabilities for our phenotype are:
- Offspring able to roll tongue: 3/4 = “0.75 = 75%”
- Offspring unable to roll tongue: 1/4 = “0.25 = 25%”
Method 2 of 2: Showing a Dihybrid Cross (Two Genes)
Step 1. Duplicate each side of the basic 2x2 grid for each additional gene
Not all gene combinations are as easy as the basic monohybrid (single-gene) crosses from the section above. Some phenotypes are determined by more than one gene. In this case, you have to account for every possible combination, which means drawing a bigger grid.
- The basic rule of the Punnett quadrilateral when there is more than one gene is: “multiply each side of the grid for every gene other than the first”. In other words, since the one-gene grid is 2x2, the two-gene grid is 4x4, the three-gene grid is 8x8, and so on.
- To make this concept easier to understand, let's follow the example problem of two-genes. This means we have to draw a “4x4” grid. The concepts in this section also apply to three or more genes - this problem simply requires a larger grid and additional work.
Step 2. Assign contributing parental genes
Next, find the genes that both parents share for the characteristic being studied. Because of the many genes involved, each parent's genotype will get two extra letters for each gene in addition to the first - with the word cloth, four letters for two genes, six letters for three genes, and so on. It can be helpful to write the genotype of the mother on the top of the grid, and the genotype of the father on the left (or vice versa) as a visual reminder.
Let's use a classic example to illustrate this conflict. A pea plant can have smooth or wrinkled beans, yellow or green in color. Smooth and yellow are dominant traits. In this case, use M and m to represent dominant and recessive for smoothness and K and k for yellowness. Let's say the mother has a genotype of "MmKk" and the father's gene has a genotype of "MmKK"
Step 3. Write the various gene combinations along the top and left sides
Now, above the top row of the grid and to the left of the far left column, write down the different alleles that each parent might contribute. As when dealing with a single gene, each allele is equally likely to be inherited. However, because there are so many genes, each column and row will get more than one letter: two letters for two genes, three letters for three genes, and so on.
- In this example, we must list the different combinations of genes that parents may inherit from their MmKk genotype. If we have the MmKk gene from the mother along the top lattice and the father's MmKK gene in the left lattice, then the alleles for each gene are:
- Along the top grid: “MK, Mk, mK, mk”
- Down on the left side: “MK, MK, mK, mK”
Step 4. Fill in each grid with each allele combination
Fill in the grid as when dealing with a single gene. This time, however, each grid will have two additional letters for each gene in addition to the first: four letters for two genes, six letters for three genes. In general, the number of letters in each grid should equal the number of letters in each parent's genotype.
- In this example, we will populate the existing grid as follows:
- Top row: “MMKK, MMKk, MmKK, MmKk”
- Second line: “MMKK, MMKk, MmKK, MmKk”
- Third line: “MmKK, MmKk, mmKK, mmKk”
- Bottom row: “MmKK, MmKk, mmKK, mmKk”
Step 5. Find the phenotype for each potential offspring
When dealing with multiple genes, each lattice in the Punnett quadrilateral still represents the genotype for each potential offspring - there are more choices than a single gene. The phenotype for each lattice, again, depends on the exact gene being handled. However, in general, dominant traits need only one allele to be expressed, while recessive traits require "all" recessive alleles.
- In this example, because smoothness (M) and yellowness (K) are the dominant traits or traits for the pea plant in the example, each grid containing at least one capital M represents a plant with the smooth phenotype, and each grid containing at least one large K represents a crop. yellow phenotype. Wrinkled plants need two lowercase s alleles, and green plants need two lowercase k alleles. From this condition, we get:
- Top row: “Seamless/yellow, Seamless/yellow, Smooth/yellow, Seamless/yellow”
- Second line: “Seamless/yellow, Smooth/yellow, Smooth/yellow, Smooth/yellow”
- Third row: “Smooth/yellow, Smooth/yellow, wrinkled/yellow, wrinkled/yellow”
- Bottom row: “Smooth/yellow, Smooth/yellow, wrinkled/yellow, wrinkled/yellow”
Step 6. Use the grid to determine the probability of each phenotype
Use the same technique as when dealing with a single gene to find the probability that each offspring from both parents can have a different phenotype. In other words, the number of grids containing the phenotype divided by the total number of grids is equal to the probability for each phenotype.
- In this example, the probabilities for each phenotype are:
- Offspring are smooth and yellow: 12/16 = “3/4 = 0.75 = 75%”
- Offspring are wrinkled and yellow: 4/16 = “1/4 = 0.25 = 25%”
- Offspring are smooth and green: 0/16 = “0%”
- Offspring characterized by wrinkles and green: 0/16 = “0%”
- Note that since it is impossible for every offspring to have two recessive k alleles, neither of the offspring is green (0%).
Tips
- In a hurry? Try using the Punnett quadrilateral online calculator (for example in this one), which is able to create and populate a Punnett quadrilateral grid based on the parental genes you have specified.
- In general, recessive traits are not as common as dominant traits. However, there are situations where this rare trait can increase the fitness of an organism and thus become more prevalent through natural selection. For example, the recessive trait that causes hereditary blood disease conditions also confer immunity to malaria, making it necessary in tropical climates.
- Not all genes have only two phenotypes. For example, several genes exist that have separate phenotypes for heterozygous combinations (one dominant, one recessive).
