- Define probability.
- Explain how probability is related to inheritance.
- Describe how to use a Punnett square.
- Explain how Mendel interpreted the results of his experiments.
- Describe complex patterns of inheritance.
Chapter 6.2 workbook pages
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- relationship between two alleles for the same gene in which both alleles are expressed equally in the phenotype of the heterozygote
- incomplete dominance
- relationship between the alleles for a gene in which one allele is only partly dominant to the other allele so an intermediate phenotype results
- polygenic characteristic
- characteristic, or trait, controlled by more than one gene, each of which may have two or more alleles
- the likelihood, or chance, than a certain event will occur
- Punnett square
- chart for determining the expected percentages of different genotypes in the offspring of two parents
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.
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.
18 Casting lots causes contentions to cease,
And keeps the mighty apart.
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.
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.
An explanation of Punnett squares can be viewed in the video below:
Punnett Squares by Bozeman Science:
An example of the use of a Punnett square can be viewed at http://www.youtube.com/watch?v=nsHZbgOmVwg&feature=related (5:40), just in case you are totally not getting this yet. If you get it, move along and feel free to skip it!!
Predicting Offspring Genotypes
In the cross shown in Figure above (skip up past the 3 videos), 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.
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).
How Mendel Worked Backward to Get Ahead
Mendel used hundreds or even thousands of pea plants in each experiment he did. Therefore, his results were very close to those you would expect based on the rules of probability. For example, in one of his first experiments with flower color, there were 929 plants in the F2 generation. Of these, 705 (76 percent) had purple flowers and 224 (24 percent) had white flowers. Thus, Mendel’s results were very close to the 75 percent purple and 25 percent white you would expect by the laws of probability for this type of cross. Of course, Mendel had only phenotypes to work with. He knew nothing about genes and genotypes. Instead, he had to work backward from phenotypes and their percents in offspring to understand inheritance. From the results of his first set of experiments, Mendel realized that there must be two factors controlling each of the characteristics he studied, with one of the factors being dominant to the other. He also realized that the two factors separate and go to different gametes and later recombine in the offspring. This is an example of Mendel’s good luck. All of the characteristics he studied happened to be inherited in this way. Mendel also was lucky when he did his second set of experiments. He happened to pick characteristics that are inherited independently of one another. We now know that these characteristics are controlled by genes on nonhomologous chromosomes. What if Mendel had studied characteristics controlled by genes on homologous chromosomes? Would they be inherited together? If so, how do you think this would have affected Mendel’s conclusions? Would he have been able to develop his second law of inheritance? To better understand how Mendel interpreted his findings and developed his laws of inheritance, you can visit the following link. It provides an animation in which Mendel explains how he came to understand heredity from his experimental results.
The inheritance of characteristics is not always as simple as it is for the characteristics that Mendel studied in pea plants. Each characteristic Mendel investigated was controlled by one gene that had two possible alleles, one of which was completely dominant to the other. This resulted in just two possible phenotypes for each characteristic. Each characteristic Mendel studied was also controlled by a gene on a different (nonhomologous) chromosome. As a result, each characteristic was inherited independently of the other characteristics. Geneticists now know that inheritance is often more complex than this.
Codominance and Incomplete Dominance
A characteristic may be controlled by one gene with two alleles, but the two alleles may have a different relationship than the simple dominant-recessive relationship that you have read about so far. For example, the two alleles may have a codominant or incompletely dominant relationship. The former is illustrated by the flower in Figure below, and the latter in Figure below.
Codominance occurs when both alleles are expressed equally in the phenotype of the heterozygote. The red and white flower in the figure has codominant alleles for red petals and white petals.
Incomplete dominance occurs when the dominant allele is not completely dominant. Expression of the dominant allele is influenced by the recessive allele and an intermediate phenotype results. The pink flower in the figure has an incompletely dominant allele for red petals and a recessive allele for white petals.
Codominance. The flower has red and white petals because of codominance of red-petal and white-petal alleles.
Incomplete Dominance. The flower has pink petals because of incomplete dominance of a red-petal allele and a recessive white-petal allele.
Many genes have multiple (more than two) alleles. An example is ABO blood type in humans. There are three common alleles for the gene that controls this characteristic. The allele for type A is codominant with the allele for type B, and both alleles are dominant to the allele for type O. Therefore, the possible phenotypes are type A, B, AB, and O. Do you know what genotypes produce these phenotypes?
Try out this worksheet to help you understand Mendelian inheritance:
Polygenic characteristics are controlled by more than one gene, and each gene may have two or more alleles. The genes may be on the same chromosome or on nonhomologous chromosomes.
- If the genes are located close together on the same chromosome, they are likely to be inherited together. However, it is possible that they will be separated by crossing-over during meiosis, in which case they may be inherited independently of one another.
- If the genes are on nonhomologous chromosomes, they may be recombined in various ways because of independent assortment.
For these reasons, the inheritance of polygenic characteristics is very complicated. Such characteristics may have many possible phenotypes. Skin color and adult height are examples of polygenic characteristics in humans. Do you have any idea how many phenotypes each characteristic has?
Effects of Environment on Phenotype
Genes play an important role in determining an organism’s characteristics. However, for many characteristics, the individual’s phenotype is influenced by other factors as well. Environmental factors, such as sunlight and food availability, can affect how genes are expressed in the phenotype of individuals. Here are just two examples:
- Genes play an important part in determining our adult height. However, factors such as poor nutrition can prevent us from achieving our full genetic potential.
- Genes are a major determinant of human skin color. However, exposure to ultraviolet radiation can increase the amount of pigment in the skin and make it appear darker.
- Probability is the chance that a certain event will occur. For example, the probability of a head turning up on any given coin toss is 50 percent.
- Probability can be used to predict the chance of gametes and offspring having certain alleles.
- A Punnett square is a chart for determining the expected percents of different genotypes and phenotypes in the offspring of two parents.
- Mendel used the percents of phenotypes in offspring to understand how characteristics are inherited.
- Many characteristics have more complex inheritance patterns than those studied by Mendel. They are complicated by factors such as codominance, incomplete dominance, multiple alleles, and environmental influences.
Lesson Review Questions
1. Define probability. Apply the term to a coin toss.
2. How is gamete formation like tossing a coin?
3. What is a Punnett square? How is it used?
4. What information must you know to determine the phenotypes of different genotypes for a gene with two alleles?
5. Based on the results of his experiments, what did Mendel conclude about the factors that control characteristics such as flower color?
6. Draw a Punnett square of an Ss x ss cross. The S allele codes for long stems in pea plants and the s allele codes for short stems. If S is dominant to s, what percent of offspring would you expect to have each phenotype?
7. What letter should replace the question marks (?) in this Punnett square? Explain how you know.
8. Explain how Mendel used math and probability to understand the results of his experiments.
9. Compare and contrast codominance and incomplete dominance.
10. Mendel investigated stem length, or height, in pea plants. What if he had investigated human height instead? Why would his results have been harder to interpret?
Points to Consider
Like most of the characteristics of living things, the characteristics Mendel studied in pea plants are controlled by genes. All the cells of an organism contain the same genes, because all organisms begin as a single cell. Most of the genes code for proteins.
- How is the information encoded in a gene translated into a protein? Where does this occur, and what processes are involved?
- If cells have the same genes, how do you think different cells arise in an organism? For example, how did you come to have different skin, bone, and blood cells if all of your cells contain the same genes?
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