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Objectives

Students should be able to:

  1. Identify and define Mendel's law of segregation

  2. Identify and define Mendel's law of independent assortment

  3. Understand basic probability as it relates to Mendelian genetics

  4. Collect data from monohybrid and dihybrid crosses and analyze the results using the chi-square test of fitness.

  5. Define and work with examples of monohybrid, dihybrid and X-linked crosses involving different types of organisms.

  6. Define and utilize terms associated with Mendelian genetics.

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Introduction

Mendelian genetics is built on the work done by the "father of genetics", Gregor Johann Mendel (1822-1884). His contributions to the study of inheritance paved the way for our basic understanding of how traits are inherited from one generation to the next. He was also instrumental in applying statistical analysis to his experiments. Because of this he was able to predict outcomes of various genetic crosses and then test those predictions against actual crosses. 

Mendel did much of his work with easily obtained local organisms, especially members of the genus Pisum or garden peas. He also did genetic work with other plants and honey bees.

Mendel recognized from observations and early experiments that his experimental organisms had two alternate forms of a trait. We call these alternate forms alleles (genes). According to Mendel, an individual possesses two alleles for each trait. The individual can have two alleles that are the same or one of each form. If the individual possessed two alleles that were the same the individual would be homozygous (or pure) for the trait. Mendel would indicate this by using letters to represent the alleles. If an individual was homozygous then it would be AA or aa. If the offspring contained one of each allele then it was termed heterozygous or Aa. The uppercase form of the allele was used to indicate that the individual was dominant for the trait and lower case indicated that the individual was the contrasting opposite or recessive for the trait. For example, if the trait was color, and the dominant trait was red, the contrasting trait might be white. The terms dominant and recessive are used to signify when the trait appeared in the offspring of a cross between two homozygous individuals that represented alternate forms of the trait. If the trait appeared in the first generation (first filial or F1) then it was designated as dominant. If the trait "skipped" the F1 and appeared in the second generation (F2) then the trait was designated as recessive. The F2 generation was obtained by crossing two F1 individuals.

Mendel could not "see" the alleles for the trait but could see the outward appearance of the offspring. The outward appearance is called phenotype (color, size, etc.). The combination of alleles that caused the phenotype was called the genotype (AA, Aa, or aa). A homozygous dominant individual (AA) reflects the dominant trait. A heterozygous dominant individual (Aa) reflects the dominant trait also. A homozygous recessive individual (aa) reflects the recessive trait.

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The Monohybrid Cross

If a cross involves only one trait then it is called a monohybrid cross. A monohybrid cross is outlined in the following manner. The color name is the phenotype and the letters following it represent the genotype alleles. Uppercase letters represent the dominant trait, and lowercase letters represent the recessive trait.

Trait = Flower Color      
Dominant Trait = Red      
Recessive Trait = White      
       
P generation (Parental) Red (RR) X White (rr)
       
F1 generation   Red (Rr)  
       
F2 generation Red (Rr) X Red (Rr)
       
    Red (RR, Rr)  
    White (rr)  

In above cross between two homozygous individuals, one with the dominant trait (red flowering plant, RR) and one with the contrasting recessive trait (white flowering plant, rr), resulted in an F1 generation that is all heterozygous red flowering individuals. The F1 generation is crossed to produce the F2 generation and the results are homozygous and heterozygous red flowering plants (RR, Rr) and homozygous white flowering plants (rr). It is important to point out here that Mendel's experiment with this and his resultant statistical analysis and prediction showed that the total offspring of the F2 generation was 75% red flowering plants and 25% white flowering plants or a 3:1 ratio.

If two homozygous traits are crossed the phenotype of the F1 is called the dominant trait. When two F1's are crossed, the F2 phenotype will have representatives of the dominant trait and the recessive trait (the recessive trait was "hidden" in the F1 and reappears in the F2). The phenotypic ratio in the F2 will be 3:1, dominant to recessive.

In summary, the F2 generation of a monohybrid cross, with dominance, will result in a:

bulletPhenotypic ratio of 3:1
bulletGenotypic ratio of 1:2:1

This type of experimental monohybrid cross, led Mendel to develop his Law of Segregation, which is:

Each organism contains two alleles for each trait, and the alleles segregate during the formation of gametes. Each gamete then contains only one allele for each trait. When fertilization occurs, the new organism has two alleles for each trait, one from each parent.

Mendel stated it this way:

"Alternative versions of genes account for variations in inherited characters." "For each character, an organism inherits two genes, one from each parent". "If the two alleles differ, then one, the dominant allele, is fully expressed in the organism's appearance; the other, the recessive allele, has no noticeable effect on the organism's appearance." "The two genes for each character segregate during gamete production."

Gregor Mendel

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The Dihybrid Cross

If a cross involves two traits, then it is termed a dihybrid cross. A dihybrid cross is outlined in the following manner. The terms are similar to a monohybrid cross. There are some slight differences. In a dihybrid cross the recessive allele in the heterozygous condition does not effect the phenotype so it is generally signified by an underscore (i.e. A_)

Trait 1 = Flower Color Trait 1 Dominant  Red Trait 1 Recessive  White  
Trait 2 = Flower position Trait 2 Dominant Terminal Trait 2 Recessive Axial  
       
P Generation Red / Terminal (RRTT) X White / Axial (rrtt)
       
F1 Generation   Red / Terminal (RrTt)  
       
F2 Generation Red / Terminal (RrTt) X Red / Terminal (RrTt)
       
    Red / Terminal (R_T_)  
    Red / Axial (R_tt)  
    White / Terminal (rrT_)  
    White / Axial (rrtt)  

In the above cross of two homozygous individuals one with two dominant traits (red, terminal flowers, RRTT) and one with the contrasting recessive traits (white, axial flowers, rrtt), resulted in an F1 generation that is all heterozygous red terminal flowers. The F1 generation is crossed to produce the F2 generation and the results are a little different than in a monohybrid cross. In the monohybrid F2 there were only two phenotypes. In a dihybrid cross there are four phenotypes.  homozygous and heterozygous red, terminally flowered plants (R_T_), red, axially flowered plants (R_tt), white, terminally flowered plants (rrT_) and homozygous white axially flowered plants (rrtt).

Mendel's analysis of this type of cross showed that there was a ratio of 9 red, terminal to 3 red axial to 3 white terminal to 1 white axial or a 9:3:3:1 ratio

In summary, the F2 generation of a dihybrid cross, with dominance in the two traits will result in a:

bulletPhenotypic ratio of 9:3:3:1
bulletGenotypic ratio of 1:2:2:1:4:1:2:2:1

This type of experimental dihybrid cross led to the Law of Independent Assortment, which is:

"emergence of one trait will not effect the emergence of another"

Gregor Mendel

Or, the members of an allelic pair segregate independently of members of another allelic pair. All possible allelic combinations can occur in the reproductive cells.

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Probability

Mendel's contributions to the understanding of inheritance were numerous, but his application of the scientific method and the statistical analysis of his results were another important contribution to field of biology. This brings us in our study of genetics to your application of the statistics and probability to the lab results.

Probability allows you to predict outcomes of many genetic crosses that conform to Mendelian inheritance. One of the statistical applications that is used to analyze experimental results is the chi-square test of fitness (Х2 , Х = the Greek letter chi). This statistical test is used to determine if your experimental data is within acceptable parameters of the expected or theoretical data. For example, if you toss a coin 50 times you would expect it come up 25 heads and 25 tails. But if you observe 27 heads and 23 tails when you tossed the coin, is this an acceptable deviation due to chance or is it not acceptable and therefore not due to chance and chance alone. The chi-square test of fitness can determine if the deviations from the expected values are due to chance and therefore should be accepted. The chi-square test is as follows:

Х2 = Σ(d2 / e)

Where Σ = the sum of, d = the difference between the expected and the observed (deviation), and e = the expected outcome

The spreadsheets for the monohybrid and dihybrid crosses and the coin toss are set up to utilize the chi-square test. All you need to do is add your experimental data, and it will calculate Х2 . You will also need to employ a chi-square probability table which you will be asked to download so you can compare the calculated chi-square with the acceptable deviations.

Probabilities for chi-square range from 0.99 to 0.01. If your chi-square value is within the 0.80 to 0.99 probability then the deviations are insignificant. If they are within the 0.01 to 0.50 then the deviations are significant and they are not due to chance. However, the test does NOT tell you what caused the deviations.

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Pre-lab Activities

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Pre-Lab Activity #1 - Gregor Johann Mendel's Biography

Go to the Learning Resources Center (LRC) website, then to Access Science and find and print out a biography of Gregor Mendel. Make sure you read the biography and then attach it to your pre-lab questions.

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Pre-Lab Activity #2 - Thomas Hunt Morgan's Biography

Go to the Learning Resources Center (LRC) website, then to Access Science and find and print out a biography of Thomas Hunt Morgan. Make sure you read the biography and then attach it to your pre-lab questions.

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Pre-Lab Activity #3 - Downloading Chi-Square Spreadsheets

Download the following spreadsheets for data collection and Chi-square Analysis

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Monohybrid and Dihybrid Cross - On same spread sheet (Monohybrid is sheet 1 and dihybrid is sheet 1)

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Pre-Lab Activity #4 - Downloading Probability Analysis Spreadsheets and Data Collection Sheet

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Coin Toss - This lab Activity can be done before you come to lab.

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Chi-Square Probability Chart

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Data Collection Sheet - Genetics

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Pre-Lab Activity #5 - Virtual Monohybrid and Dihybrid Crosses; and Probability and Statistical Analysis

This is an optional way of doing Lab Activities #1, #2 and #3. Use the Monohybrid and Dihybrid Cross Probability Spreadsheets, Coin Toss, Chi-Square Probability Chart and the Data Collection Sheet - Genetics. (see above). You need to follow the same procedures for these three Lab Activities, except the corn kernel analysis will be as images.

Probability and Statistical Analysis
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Coin Toss and Chi Square Analysis- This lab Activity can be done outside of lab.

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Data Collection Sheet and Chi Square Analysis - this will assist you in analyzing the monohybrid and dihybrid genetic crosses

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Monohybrid Cross - Genetic Corn

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Dihybrid Cross - Genetic Corn

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Pre-lab Questions (html version)    Pre-Lab Questions (Word version)

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The Laboratory Activities and Data Collection

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Lab Activity #1 - Probability and Statistical Analysis (This lab activity can be done before the laboratory session)

Materials:

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Coin toss spreadsheet

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Penny

Procedures:

  1. Flip a penny 100 times and record the number of heads and the number of tails that occur in the Data Collection Sheet.

  2. Using an active spreadsheet enter your data from the Data Collection Sheet and let it calculate a value for chi-square.

  3. Using the Chi-square probability table determine if the results were due to chance or to some other factor. Your df = 1 (number of events minus 1)

  4. Print out the spreadsheet and attach it to your post-lab questions.

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Lab Activity #2 - Analysis of Monohybrid Cross

Materials:

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Corn kernels from an experimental cross (purple, yellow)

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Monohybrid cross spreadsheet.

Procedures:

  1. Obtain a bag containing the kernels from an experimental cross

  2. Separate out the kernels of the different phenotypes

  3. Count the total number of kernels of each phenotype

  4. Record your results on the Data Collection Sheet.

  5. Using an active spreadsheet, enter your data and let it calculate a value for chi-square.

  6. Using the chi-square probability table, and a df value of 1, find the value that is closest to your calculated value.

  7. Determine the probability and whether your result deviations are insignificant or significant.

  8. Graph the data as indicated on the spreadsheet.

  9. Print out the graph and attach it to your post-lab questions.

  10. Print out the spreadsheet and attach it to your post-lab questions.

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Lab Activity #3 - Analysis of Dihybrid Cross

Materials:

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Corn kernels from an experimental cross (purple smooth, purple wrinkled, yellow smooth, yellow wrinkled)

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Dihybrid cross spreadsheet.

Procedures:

  1. Obtain a bag containing the kernels from an experimental cross

  2. Separate out the kernels of the different phenotypes

  3. Count the total number of kernels of each phenotype

  4. Record your results on Data Collection Sheet.

  5. Using an active spreadsheet, enter your data and let it calculate a value for chi-square.

  6. Using the chi-square probability table, and a df value of 3, find the value that is closest to your calculated value.

  7. Determine the probability and whether your result deviations are insignificant or significant.

  8. Graph the data as indicated on the spreadsheet.

  9. Print out the graph and attach it to your post-lab questions.

  10. Print out the spreadsheet and attach it to your post-lab questions.

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Post-lab Activity and Data Analysis

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Results and Analysis:

  1. Use the chi-square calculations and graphs for answering your post-lab questions.

  2. Attach the spreadsheets and graphs to your post-lab questions.

  3. Answer the post-lab questions.

  4. Genetics Problems. Download and answer these genetics problems.

  5. Turn in all requested materials.

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Post-Lab Questions (html version)    Post-Lab Questions (Word version)

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