Punnett Squares

1. Overview and Reading Guide

2. Introduction

Introduction

Assume you are a plant breeder trying to develop a new variety of plant that is more useful to humans. You plan to cross-pollinate an insect-resistant plant with a plant that grows rapidly. Your goal is to produce a variety of plant that is both insect resistant and fast growing. What percent of the offspring would you expect to have both characteristics? Mendel’s laws can be used to find out. However, to understand how Mendel’s laws can be used in this way, you first need to know about probability.

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3. Probability

Probability

Probability is the likelihood, or chance, that a certain event will occur. The easiest way to understand probability is with coin tosses (see Figure below). When you toss a coin, the chance of a head turning up is 50 percent. This is because a coin has only two sides, so there is an equal chance of a head or tail turning up on any given toss.

If you toss a coin twice, you might expect to get one head and one tail. But each time you toss the coin, the chance of a head is still 50 percent. Therefore, it’s quite likely that you will get two or even several heads (or tails) in a row. What if you tossed a coin ten times? You would probably get more or less than the expected five heads. For example, you might get seven heads (70 percent) and three tails (30 percent). The more times you toss the coin, however, the closer you will get to 50 percent heads. For example, if you tossed a coin 1000 times, you might get 510 heads and 490 tails.

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4. Probability and Inheritance

Probability and Inheritance

The same rules of probability in coin tossing apply to the main events that determine the genotypes of offspring. These events are the formation of gametes during meiosis and the union of gametes during fertilization.

Probability and Gamete Formation

How is gamete formation like tossing a coin? Consider Mendel’s purple-flowered pea plants again. Assume that a plant is heterozygous for the flower-color allele, so it has the genotype Bb (see Figure below). During meiosis, homologous chromosomes—and the alleles they carry—segregate and go to different gametes. Therefore, when the Bb pea plant forms gametes, the B and b alleles segregate and go to different gametes. As a result, half the gametes produced by the Bb parent will have the B allele and half will have the b allele. Based on the rules of probability, any given gamete of this parent has a 50 percent chance of having the B allele and a 50 percent chance of having the b allele.

Probability and Fertilization

Which of these gametes joins in fertilization with the gamete of another parent plant? This is a matter of chance, like tossing a coin. Thus, we can assume that either type of gamete—one with the B allele or one with the b allele—has an equal chance of uniting with any of the gametes produced by the other parent. Now assume that the other parent is also Bb. If gametes of two Bb parents unite, what is the chance of the offspring having one of each allele like the parents (Bb)? What is the chance of them having a different combination of alleles than the parents (either BB or bb)? To answer these questions, geneticists use a simple tool called a Punnett square.

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5. Using a Punnett Square

Using a Punnett Square

A Punnett square is a chart that allows you to easily determine the expected percents of different genotypes in the offspring of two parents. An example of a Punnett square for pea plants is shown in Figure below. In this example, both parents are heterozygous for flower color (Bb). The gametes produced by the male parent are at the top of the chart, and the gametes produced by the female parent are along the side. The different possible combinations of alleles in their offspring are determined by filling in the cells of the Punnett square with the correct letters (alleles).

At the link below, you can watch an animation in which Reginald Punnett, inventor of the Punnett square, explains the purpose of his invention and how to use it.

http://www.dnalc.org/view/16192-Animation-5-Genetic-inheritance-follows-rules-.html

Watch the following explanation of Punnett squares:

Wathc the following example of the use of a Punnett square.

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6. Genotype and Phenotype

Predicting Offspring Genotypes

Punnett Square.

This Punnett square shows a cross between two heterozygotes.

In the cross shown in Figure above, you can see that one out of four offspring (25 percent) has the genotype BB, one out of four (25 percent) has the genotype bb, and two out of four (50 percent) have the genotype Bb. These percents of genotypes are what you would expect in any cross between two heterozygous parents. Of course, when just four offspring are produced, the actual percents of genotypes may vary by chance from the expected percents. However, if you considered hundreds of such crosses and thousands of offspring, you would get very close to the expected results—just like tossing a coin.

Predicting Offspring Phenotypes

You can predict the percents of phenotypes in the offspring of this cross from their genotypes. B is dominant to b, so offspring with either the BB or Bb genotype will have the purple-flower phenotype. Only offspring with the bb genotype will have the white-flower phenotype. Therefore, in this cross, you would expect three out of four (75 percent) of the offspring to have purple flowers and one out of four (25 percent) to have white flowers. These are the same percents that Mendel got in his first experiment.

Determining Missing Genotypes

A Punnett square can also be used to determine a missing genotype based on the other genotypes involved in a cross. Suppose you have a parent plant with purple flowers and a parent plant with white flowers. Because the b allele is recessive, you know that the white-flowered parent must have the genotype bb. The purple-flowered parent, on the other hand, could have either the BB or the Bb genotype. The Punnett square in Figure below shows this cross. The question marks (?) in the chart could be either B or b alleles.

Can you tell what the genotype of the purple-flowered parent is from the information in the Punnett square? No; you also need to know the genotypes of the offspring in row 2. What if you found out that two of the four offspring have white flowers? Now you know that the offspring in the second row must have the bb genotype. One of their b alleles obviously comes from the white-flowered (bb) parent, because that’s the only allele this parent has. The other b allele must come from the purple-flowered parent. Therefore, the parent with purple flowers must have the genotype Bb.

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7. Punnett Squares for Two Traits

Punnett Square for Two Characteristics

When you consider more than one characteristic at a time, using a Punnett square is more complicated. This is because many more combinations of alleles are possible. For example, with two genes each having two alleles, an individual has four alleles, and these four alleles can occur in 16 different combinations. This is illustrated for pea plants in Figure below. In this cross, both parents are heterozygous for pod color (Gg) and seed color (Yy).