# Using Punnett Squares to Calculate Phenotypic Probabilities

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## Introduction: Using Punnett Squares to Calculate Phenotypic Probabilities

Introduction

Background

• Punnett Squares are a diagram which biologists use to determine the probability of an offspring having a particular trait. Creating a Punnett Square and using it to determine traits of offspring is called performing a cross. Punnett Square crosses are based on meiosis, a biological process where parents pass on alleles to sex cells, which they later transmit to their offspring. Each parent has two alleles for a trait and passes one along to its offspring. Each offspring ends up with a total of two alleles, one from each parent.
• Punnett Squares accomplish two things: They simplify and demonstrate meiosis and also provide scientists with information that they can go on to use in different ways. They use information from the crosses to study and draw conclusions about populations. An example of scientists using information they obtain from a cross is in calculating phenotypic probability. The crosses give predicted outcomes of traits, which can then be translated into numerical statistics about the appearance of those traits in a population.
• We are using the Punnett Squares in these instructions to study one trait, but they can also be expanded and used to study more complicated situations in genetics.

Purpose/Intended Audience

• These instructions are for anyone, commonly students and scientists, who is predicting the ratios of expected traits in one generation of an organism’s offspring.

Terminology

• Allele: one or more alternative forms of a gene that arise by mutation and are found at the same place on a chromosome.
• Dominant Allele: an allele that masks the effect of another allele.
• Note- It is represented with an UPPERCASE letter.
• Recessive Allele: an allele whose effect is masked by a dominant allele.
• Note- It is represented with a lowercase letter.
• F#: an uppercase “F” followed by a subscript number denotes a generation of offspring. As the number increases, the number of the generation increases.
• F1: the first generation of offspring from a P generation cross
• Generation: all of the offspring that are at the same stage of descent from a common ancestor.
• Genotype: an organism’s genetic constitution.
• Heterozygous: a genotype with two different alleles (one dominant and one recessive).
• Homozygous: a genotype with a pair of matching alleles (both dominant or both recessive).
• Offspring: the children produced by living organisms who reproduce by sexual reproduction.
• P: the parental generation
• Phenotype: an individual’s set of observable characteristics that results from the interaction of a genotype with the environment.
• Punnett Square: a diagram that is used to predict an outcome of a particular cross.
• Each box in the square represents one offspring.
• The letters in each box represent the organism's genotype.
• Trait: a genetically determined characteristic.

Materials Needed

• A writing utensil
• A piece of paper
• Background information about the parents' genotypes

Time needed to complete the task

• 1-5 minutes

Background Knowledge Needed

• None

Layout of the Instructions

• These instructions detail the process of calculating the probability of one trait using a basic Punnett Square. You will be given an initial problem, from which you will have to determine the parents’ genotype. Then you will use the parents’ genotypes to set up and do the Punnett Square cross. Lastly, you will use the results of the cross to calculate probabilities of phenotypes.

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## Step 1: Determining Parental Genotypes

1. You will need to be given information about the P generation before conducting a Punnett Square cross. The problem either needs to describe the parents’ genotype (either heterozygous or homozygous dominant/recessive) or give it to you explicitly (in letter notation).
2. Determine the genotypes of each parent and write them out in the appropriate letter notation

a. The genotypes in this problem mean that the mother has black eyes and the father has green eyes.

• Note- If necessary, use a chart to separate the information from the problem into genotypes (See Figures 1.4 & 1.5)

## Step 2: Set Up the Punnett Square

1. Draw a square with four boxes within it. (See Figure 3.1)
2. Write the mother’s genotype on top of the square. Each letter will be above one box.
3. Write the father’s genotype on the left side of the square. Each letter will be next to one box.

a. Note- See Figure 3.2

## Step 3: Cross the P Generation

1. Find the first column in the square. (See the red dashed line in Figure 4.1)
2. Write the first allele of the mother’s genotype in each of the two boxes in that column.
3. Repeat steps one and two for the second column. However, use the second allele from the mother’s genotype in the boxes.
4. Find the first row in the square. (See the blue solid line in Figure 4.1)
5. Write the first allele of the father’s genotype in each of the two boxes in that row.
6. Repeat steps four and five for the second row. However, use the second allele from the father’s genotype in the boxes.
7. Each box should end up with two letters in it. These two letters make up the genotype for one offspring. (See Figure 4.2)

a. Note- This process represents each parent passing alleles, and therefore traits, onto their offspring.

b. Note- Extra colors are not necessary, they are only used to help clarify where each allele is coming from

## Step 4: Determine the Phenotypes of the F1 Generation

1. Under your Punnett Square, list each genotype from each box.
2. Next, using the chart in Figure 5.1, write the expected phenotype next to each genotype on your paper. (See Figure 5.2)

## Step 5: Calculate Phenotypic Probabilities

1. Determine the trait you are interested in. (in this problem, you have 2 options)
2. Count the total number of boxes in your Punnett Square. This gives you the total number of predicted offspring.
3. Count the number of times the phenotype you are interested in occurs. (Example: the number of offspring (boxes) with green eyes (ee))
4. Divide the (number of occurrences of the phenotype) by (the total number of offspring).
5. Multiply the number from step 4 by 100 to get your percent.

a. See Figure 6.1 for an example.

Note- Your final percentage is the probability of the specific trait to occur in an F1 offspring from this specific cross.

## Step 6: Conclusion

Summary

• You were given a description about the P generation.
• You determined the genotypes of both parents in the P generation.
• You set up your Punnett Square.
• You performed the cross.
• You determined the phenotypes of the F1 generation.
• You calculated the phenotypic probability for the trait you are interested in.
• Following this procedure gave you a completed Punnett Square and predicted ratios (in a percentage format) of possible phenotypes.

Outside Information

• http://www.hobart.k12.in.us/jkousen/Biology/psquar...

• This link goes to another set of instructions for completing a Punnett Square

• http://www.dnaftb.org/5/animation.html
• This link goes to an animation that gives a short background of Punnett Squares, explains the process of a cross, and also explains the information resulting from the cross. The main website also provides information about other genetic concepts.
• This video demonstrates how to do various types of Punnett Squares

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