Data Samples
Count the visible beans by color. You are looking at the F2 generation.
For the coin toss data, toss the coin 20 times.
Monohybrid Cross Dihybrid Cross
Purple is dominant, yellow is recessive
Smooth is dominant, wrinkled is recessive (disregard small dents)
You are looking at the F2 generations.
PCB3063L – Intro Genetics Lab – Heredity and The Chi-Square
Objectives: Upon investigation
1. Explain Mendel’s principle of segregation and independent assortment.
2. Understand all pattern of inheritance: complete dominance, incomplete dominance, co-
dominance, multiple alleles, sex-linked inheritance.
3. Recognize and interpret maize F2 data for monohybrid cross that illustrated Mendel’s
Law of Segregation.
4. Recognize and interpret maize F2 data for dihybrid cross that illustrated Mendel’s Law of
Independent Assortment.
5. Know how to calculate 2 to determine whether experimentally obtained data constitute
a good fit to expected ratio.
6. Interpret a calculate Χ2 value, given the appropriate number of degrees of freedom, and
a table of Χ2 value.
Key Concepts
Mendel’s Study of Pea Plants
Mendel Followed the Outcome of a Single Character for Two Generations
1. Mendel conducted experiments to determine the mathematical relationship between
hereditary traits. This process is called the empirical approach
2. In a single-factor cross the parental generation (P generation) is a true-breeding line for the
variant of the trait being studied (purple flower color, tall height, etc.)
a. The offspring of the parental generation are called the first filial (F1) generation.
b. The offspring of the F1 generation are called the second filial (F2) generation.
3. Mendel’s single-factor cross followed the following steps (Figure 2.5):
a. Two true-breeding lines were crosses that differed only for one trait.
b. The F1 generation are allowed to self-fertilize, producing an F2 generation.
4. The data (pg. 22) from these experiments yielded the following information regarding
inheritance:
a. The F1 generation did not exhibit blending. Rather, it showed that one of the traits was
dominant over the other (recessive) trait.
b. The dominant trait was always displayed in the F1 generation. In the F2 generation the
dominant trait was present in the majority (75%) of the plants, while the recessive trait
was present in the minority (25%) of the plants.
c. The genetic information is passed on from one generation to the next as “unit factors,”
which are now called genes. This supported the particulate theory of inheritance which
suggests that the units governing traits remain unchanged (unblended) from generation
to generation.
d. The 3:1 ratio of dominant to recessive offspring in the F2 generation suggested that
each parent possesses two traits, which segregate during the formation of gametes.
e. Mendel was the first to apply quantitative analyses to the study of inheritance.
Mendel’s 3:1 Phenotypic Ratio Is Consistent with the Law of Segregation
1. Mendel was unaware of the concept of DNA or genes.
a. the term gene was first introduced by Wilhelm Johannsen
b. genes reside on chromosomes
c. the variants in the traits are due to versions of the gene called an allele
2. Mendel’s law of segregation: The two copies of a gene segregate from each other during
transmission from parent to offspring.
3. Alleles for a gene are typically represented using uppercase (for the dominant trait) and
lowercase (for the recessive trait) letters (Figure 2.6).
4. The genotype is the genetic combination of an individual.
a. homozygous indicates individuals with two identical alleles
b. heterozygous indicates individuals with two different alleles
5. The observable characteristics of an organism are called the phenotype.
A Punnett Square Can Be Used to Predict the Outcome of Crosses
1. Allows you to predict the types of offspring the parents will produce and the proportion of
the trait in the offspring.
2. Steps for preparing a Punnett Square
a. write down the genotypes of both parents
b. write down the possible gametes that each parent can make
c. create an empty Punnett square in which the number of columns equals the number of
male gametes and the number of rows equals the number of female gametes
d. fill in the possible genotypes of the offspring by combining the alleles of the gametes in
the empty boxes
e. determine the relative proportions of genotypes and phenotypes of the offspring
Law of Independent Assortment
Mendel Also Analyzed Crosses Involving Two Different Characters
1. Mendel conducted crosses using two-factors to see if additional information regarding
patterns of inheritance could be determined. These are now known as dihybrid crosses.
2. In a two-factor cross there are two possibilities of how the traits can be inherited (Figure
2.7)
a. They may be linked to one another and inherited as a single unit.
b. They may be unlinked and assort themselves independently during inheritance.
3. Mendel’s experimental system followed the same pattern as the single-factor cross (Figure
2.8).
a. Two true-breeding lines were selected that were different with regards to two different
traits (seed shape, seed color).
b. The F1 plants were allowed to self-fertilize.
c. The phenotypic ratio of the F2 generation was determined.
4. Mendel’s experimental data (page 26) indicated the following:
a. The F2 generation of seeds possessed a 9:3:3:1 phenotypic ratio, not the 1:2:1 ratio
expected by a linked model.
b. Some seeds of the F2 generation were nonparentals, thus further disproving that the
traits were linked.
5. Mendel’s law of independent assortment states that two different genes will randomly
assort their alleles during the formation of haploid reproductive cells.
6. Independent assortment means that a single individual can produce a vast array of
genetically different gametes (Figure 2.9).
7. An offspring receiving a different combination of alleles than are seen in the parental
generation is known as genetic recombination.
A Punnett Square Can Also Be Used to Solve Independent Assortment Problems
1. For a two-factor cross, each parent can produce four types of gametes. Thus the Punnett
square would have 16 cells (4 rows x 4 columns) (Figure 2.10).
2. Process is the same as the single-factor Punnett square.
3. Punnett squares are not practical for more than two traits. The forked-line method or
multiplication method are more useful for larger crosses.
4. The dihybrid test cross involves using an individual who is homozygous recessive for both
traits in the cross.
Modern Geneticists Are Often Interested in the Relationship Between the Molecular
Expression of Genes and the Outcome of Traits
1. Genes encode proteins that perform the majority of cellular functions. Proteins influence an
individual’s expressed traits.
2. The study of loss-of-function alleles can assist geneticists in understanding the relationship
between a gene and a phenotype.
a. The white flower color in Mendel’s pea plants is an example of a loss-of-function allele
(unknown to Mendel).
The Chi-Square Test Can Be Used to Test the Validity of a Genetic Hypothesis
1. Involved in hypothesis testing, such as determining if the data from a given genetic cross is
consistent with a certain pattern of inheritance.
a. Tests the goodness of fit between the observed data and that predicted by the
hypothesis
b. This is sometimes called a null hypothesis because it assumes there is no real
difference between the observed and expected values.
c. Does not prove that a hypothesis is correct or incorrect
2. Formula (pg. 34)
Χ2 = ∑ (O – E)2
E
O = observed data in each category
E = expected data in each category
∑ = sum of each category
3. Steps of a Chi square test.
a. Propose a hypothesis that allows us to calculate the expected values based on
Mendel’s laws.
b. Calculate the expected values for each phenotype.
c. Apply the Chi square formula, using the data for the observed and expected values as
calculated in step 2.
d. Interpret the results using a Chi square table.
4. P values (Table 2.1) allow us to determine the likelihood that the variation indicated by the
Chi square calculation is due to random chance alone. Hypotheses are usually rejected if
the chi-square value results in a P value less than 0.05
5. Degrees of freedom (df) is the measure of the number of categories in the experiment that
are independent of one another. Represented as n-1, where n equals the number of
categories
Work on the following:
1. Study how to calculate and interpret Χ2 value.
2. Obtain a mixture of beans, segregate and count the beans of different colors. Record
your data in Table 1. Calculate Χ2 value and interpret the result whether you accept or
reject the hypothesis (expected ratio 1:1.)
3. Calculate chi-square using 20 tosses of a coin in table 2.
4. Obtain an ear of monohybrid corn, observe phenotypes, record the number of kernels
observed in Table 3.
5. Obtain an ear of dihybrid corn, observe phenotypes, record the number of kernels
observed in Table 4.
6. Work on practice and assigned problems individually as homework assignment.
a. Recommended Practice: See “Problem Sets & Insights” number 5 at the end of
Chapter 2 in the lecture textbook.
Table 1. Calculation of X2 for a sample removed from a large population consisting of
equal numbers of colored and white beans
Class
(Phenotypes)
Observed
(O)
Expected
(E)
Deviations
(O-E)
(O-E)2 (O-E)2/E
Colored
White
Totals X2 = ___________
How many degrees of freedom?
What is the p-value?
Do you accept or reject the hypothesis?
Table 2. Calculation of X2 on data from tossing 1 coin
Class
(Phenotypes)
Observed
(O)
Expected
(E)
Deviations
(O-E)
(O-E)2 (O-E)2/E
Heads
Tails
Totals X2 = ___________
How many degrees of freedom?
What is the p-value?
Do you accept or reject the hypothesis?
Table 3. Calculation of X2 on data from monohybrid corn
Class
(Phenotypes)
Observed
(O)
Expected
(E)
Deviations
(O-E)
(O-E)2 (O-E)2/E
Purple
Yellow
Totals X2 = ___________
How many degrees of freedom?
What is the p-value?
Do you accept or reject the hypothesis?
Table 4. Calculation of X2 on data from dihybrid corn
Class
(Phenotypes)
Observed
(O)
Expected
(E)
Deviations
(O-E)
(O-E)2 (O-E)2/E
Purple/Smooth
Purple/Wrinkle
Yellow/Smooth
Yellow/Wrinkle
Totals X2 = ___________
How many degrees of freedom?
What is the p-value?
Do you accept or reject the hypothesis?
Test Review: Upon investigation, you need to be able to
1. Solve genetics problem for all patterns of inheritance and pedigrees.
2. Perform chi-square analysis, degree of freedom, calculate the p-value, and determine
whether to accept or reject hypothesis.
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