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Mendelian Genetics
Objectives
1. To understand the Principles of Segregation and Independent Assortment.
2. To understand how Mendel’s principles can explain transmission of
characters from one generation to the next.
3. To understand and use the 2 goodness-of-fit statistical test to evaluate
hypotheses about mechanisms of inheritance.
I. Background
Much of our understanding of genetics today is taken for granted, as the
use of DNA has become common in forensics and medicine. However,
compared to many fields in biology, genetics is relatively young. Mendel’s
“Laws” of inheritance were rediscovered in the early 1900s, and Watson and
Crick described the structure of DNA only about fifty years ago (if you are
interested in exploring the history of genetics, you can find a list of good
web sites at http://dmoz.org/Science/Biology/Genetics/History/)
People have always been interested in explaining how traits were passed
from one generation to the next. In the 19th century, the leading hypothesis
of heritability was that offspring resembled their parents because parental
traits blended. A prediction of this hypothesis is that offspring of a cross
of purple-flowered and white-flowered peas will have pale purple flowers.
We can sum up their position and the outcome of Mendel’s experiments in
the following table:
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OBSERVATION
The characters of the offspring appear to be a blend of
the parental traits.
QUESTION
HYPOTHESIS /
PREDICTION
EXPERIMENT(S)
How are traits inherited?
EVALUATION/
DRAW INFERENCES
Blending of heritable information from both parents
produces offspring with intermediate traits.
Mendel’s pea experiments.
Data: The offspring from certain crosses, such as purple
x white-flowered peas, resemble only one parent, not a
blend.
The data do not support the hypothesis. Mendel
proposed alternative models.
Mendel conducted these breeding experiments over and over again, with
different traits, all of them with two phenotypes, and from his results
developed his “laws” of segregation and independent assortment. We place
Mendel’s experiments into our structure for the scientific method in the
following table:
OBSERVATION
Pea flower color is either white or purple, but never a
blend.
QUESTION
If blending does not explain how traits are inherited, then
how are traits inherited?
HYPOTHESIS /
PREDICTION
Some “particle” determining flower color is inherited
intact from parent to offspring (Mendel did not coin the
term “gene”). Prediction: the “particle” determining white
color is still present in the offspring.
EXPERIMENT
Cross the offspring resulting from purple x white crosses,
and see if some “grand-offspring” (F2) are white.
Data: about 25% of the F2 are white, the remainder are
purple
The data support the hypothesis. Mendel predicted that
about 2/3 of the purple F2 would carry the “white”
particle, and that other characteristics such as pea color
and plant height would show similar patterns of
inheritance.
EVALUATE/DRAW
INFERENCES
We can put this experiment into the context of modern genetics by using
modern terminology. In the parental generation (P), plants are true-
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breeding: for the trait of interest such as flower color, crosses within the
true-breeding group always produce offspring that resemble the parents.
This is because the parents are homozygous (identical alleles) for either the
purple or white color. When Mendel crossed the true-breeding purple and
white flowers, he always obtained plants, the F1 generation, with purple
flowers, but the allele for “white” is not lost: we refer to these individuals
as heterozygous. When he then crossed two F1 heterozygotes and
determined the flower color of the F2, he found 705 individuals with purple
flowers and 224 individuals with white flowers. He referred to this as
“Segregation” because he stated that the particle for white color
segregated from the particle for purple color. He further proposed that
these two genes are alternative states (alleles) for the same particle. We
now know that these two states are two different alleles for the same gene,
where we define a gene (or genetic locus) as a specific section of a
chromosome coding for a particular protein. Different alleles of one genetic
locus code for different versions of the same protein.
II. The monohybrid cross
The experiment described above is a monohybrid cross: the true-breeding
parents are homozygous for different flower colors, and the F1 are hybrids
for that one trait. Our understanding of meiosis provides a mechanistic
explanation for the pattern of segregation in monohybrid crosses. In
meiosis, when the gametes are being formed, each gamete only gets one copy
of each chromosome. In the F1 plants, each gamete will either get the allele
for purple or the allele for white flower color: no gametes can have both
alleles because they are on homologous chromosomes. One gamete from one
parent combines with one gamete from the other parent, but which gamete
combines with which (i.e., purple with purple or with white) is random. For
each gamete type (purple or white) from one parent, there is a 50:50 chance
it will combine with either white or purple from the other parent. This will
produce, in the F2 generation, purple/purple: purple/white: white/white
genotypes in a 1:2:1 ratio. Since the purple allele “masks” or is dominant to
the white allele, the phenotypes of the F2 generation will be 3 purple:1
white.
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Male
(genotype
Ww)
Female (genotype Ww)
gamete
genotypes
P
p
P
PP
Pp
p
Pp
pp
This is represented here in a
Punnett Square. P represents
the allele for the dominant
purple flower trait and p
represents the allele for the
recessive white flower trait.
III. Dihybrid cross.
Mendel also conducted experiments where he crossed true-breed plants
that differed in two different traits, producing F2 offspring that were
hybrids at two genetic loci, or dihybrids. Now it can be imagined that two
traits affecting the same structure, pea color and shape for instance, might
move jointly to the next generation: if the original homozygous parents have
smooth, yellow peas then all descendents with smooth peas will have yellow
peas. The alternative hypothesis is that the traits are separate, and that
the inheritance of pea color will be independent of the inheritance of pea
shape. These two alternative hypotheses can be put into our table of the
scientific method, and a single experiment can test both of them:
Observation
Question
Hypothesis 1,
Prediction 1
Hypothesis 2,
Prediction 2
Experiment
Evaluation,
Inferences
Peas display four different phenotypes: (1) yellow and
smooth, (2) yellow and wrinkled, (3) green and smooth,
(4) green and wrinkled.
Does the inheritance of one trait influence the
inheritance of another trait?
Yes: if the original pea parents have either smooth and
yellow peas or green and wrinkled peas, all the F2
offspring will have one of these combinations.
No: no matter what combination of traits the original
parents have, all possible combinations will be found in
the F2 generation.
Cross true-breeding plants then cross the F1 offspring.
Rear the resultant F2 plants and determine the
frequencies of the different combinations of traits.
Data: in the F2, all possible combinations of traits are
found.
Hypothesis 1 is rejected; there is no “linkage” of the
two different traits as they are passed from
generation to generation.
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Male:
WwYy
In modern terminology, the inference drawn from this result is that the two
genetic loci, pea color and pea shape, are not “linked”. The predicted
genotype and phenotype distribution in offspring of a dihybrid cross using
unlinked genetic loci can be calculated in two fashions. First, you can do a 4
x 4 Punnett square (you should finish filling in all possible genotypes):
gametes:
WY
Wy
wY
wy
WY
WWYY
WWYy
WwYY
WwYy
Female: WwYy
Wy
wY
WWYy
WwYY
wy
WwYy
Since W- is always round and Y- is always green, we can determine the
phenotypes of these offspring, and find a 9:3:3:1 ratio for W-Y- : wwY- : Wyy : wwyy.
A second, and much quicker, way to predict phenotype frequencies is to
recall that in a monohybrid cross, 3/4 of the offspring will have the
dominant phenotype and 1/4 will have the recessive phenotype. To estimate
how many offspring from a dihybrid cross will have, for instance, the
phenotype “round green” (W-Y-) you simply multiply the proportion of W- by
the proportion of Y-, or 3/4 x 3/4 = 9/16. Similarly, 1/4 x 3/4 = 3/16 will
have the phenotype “wrinkled green” (wwY-). This approach has the benefit
that it is easily expanded to many more genetic loci, when Punnett’s squares
become awkward or impossible to draw (one needs an additional dimension
for every additional genetic locus!)
It is important to note that not all genetic loci assort independently. If two
genetic loci are relatively close together on the same chromosome, they will
not move independently into the gametes and hence will appear linked in
experimental crosses.
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Again, we can look to our understanding of meiosis for
a mechanistic explanation of independent assortment.
Remember that during meiosis, homologous
chromosomes pair along the center of the cell during
metaphase I. When they are lined up, however, the
orientation of each pair of chromosomes is
independent of the orientation of every other pair.
In other words, there is equal chance that the wcarrying chromosome will be aligned with the ycarrying chromosome or with the Y-carrying
chromosome. Assigning letters to each allele (W:round,
w:wrinkled, Y: green, y: yellow), we can diagram these
possibilities in a drawing of metaphase I.
IV.
Today’s Lab with Corn.
For your experiments today, you will use what you have learned about the
principles of independent assortment and segregation to test hypotheses
concerning the mechanisms of inheritance for color and sugar content in
corn.
Corn Genetics: Kernel color and sugar content
Ears of corn are good study systems for learning about genetics, because
each kernel represents an independent union of gametes, and thus a cob has
a population of genetically unique kernels. The cobs you will be studying are
variable for two traits of interest, color and sugar content. You can detect
sugar content differences because high-sugar kernels are wrinkled and lowsugar kernels are smooth. Each of these characteristics is determined by a
single gene with two alleles.
For your experiments today, you will use what you have learned about the
principles of independent assortment and segregation to infer the
mechanisms of inheritance for color and sugar content in corn. You will pose
questions concerning these traits, reformulate them as testable hypotheses,
and collect data to test three of them by sampling kernels on the cob.
Finally, you will evaluate your hypotheses by comparing your data with your
predicted results using the 2 statistical test.
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Forming Testable Hypotheses
Observation: Individual kernels of corn on a cob vary in color and shape.
Questions: What are four questions Mendel might have posed, had he been
working with corn rather than garden peas?
1.
2.
3.
4.
Hypotheses: Working with your partner and the teaching fellow, reformulate
three of your questions into hypotheses concerning the
mechanisms of inheritance of these characteristics (color and
shape). Then make predictions of what you would observe in the
population of corn kernels if the hypothesis is correct. These will
be the “working hypotheses” guiding your experiments.
hypotheses
predictions
1.
2.
3.
Results: You will use the 2 goodness-of-fit test if your observed results are
consistent with the predictions made based on Mendel’s principles.
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The 2 test allows you to determine whether your results could have
happened by chance alone. Typically, the null hypothesis being tested is that
the observed results (O) and the expected results (E) are not different (Ho:
O = E). The alternative hypothesis is that the observed counts and the
expected counts are different (Ha: O ≠ E).
The general method for calculating the 2 value for a goodness-of-fit test is
to fill in a table, shown as an example for a monohybrid cross:
class
A–
aa
total
observed
65
35
100
expected*
75
25
100
(O-E)
-10
+10
(O-E)2/E
1.333
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2 = 5.333
df=2-1 =1
The general equation for the chi=square value for a particular experiment is:
2
O  E

2

 E
The last ingredient for the test is the “degrees of freedom”, d.f., which is
calculated as the number of
classes, less one (in this example, df= 2-1 =1).
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The observed  value (calculated with the above equation) is compared to
those in a statistical table (see section V, page 12) containing values from a
2 distribution for each number of degrees of freedom, and their associated
probability of occurring at random. A 2 value of 0 (zero) indicates no
deviation from the expected values. Therefore, any 2 value greater than 0
represents some deviation from the expected values. The statistical table
provides a basis for evaluating the probability that the deviation from 0 has
occurred by chance. The results are expressed as a range of probability (p)
values. In our example, 0.05>0> 0.01, or the probability of finding these
results purely by chance is less than 5% but greater than 1%.
Experimental Procedures
Methods: Obtain a cob of corn. These cobs are the results of F1 dihybrid
crosses, in other words the kernels are the F2 generation. Before you
start, determine a protocol that you will follow to test each of your
hypotheses. For each hypothesis, decide how many kernels you will
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count (sample size), where on the cob you will start (we recommend a
new start point for each sample), and how you will classify each kernel.
Fill in your protocol for each experiment in the section below.
Experiment 1
Your question:
Your hypothesis:
Protocol: Number of kernels to be counted__________
Kernel characteristics (categories)______________
Predicted results: if your hypothesis is correct, what numerical results do
you expect (how many kernels in each category)? These will be your
Expected values for your 2 test.
Results:
Evaluation: do the 2 test.
Conclusion; do your results cause you to reject your hypothesis?
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Experiment 2
Your question:
Your hypothesis:
Protocol: Number of kernels to be counted__________
Kernel characteristics (categories)______________
Predicted results: if your hypothesis is correct, what numerical results to
you expect (how many kernels in each category)? These will be your
Expected values for your 2 test.
Results:
Evaluation: do the 2 test.
Conclusion; do your results cause you to reject your hypothesis?
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Experiment 3
Your question:
Your hypothesis:
Protocol: Number of kernels to be counted__________
Kernel characteristics (categories)______________
Predicted results: if your hypothesis is correct, what numerical results to
you expect (how many kernels in each category)? These will be your
Expected values for your 2 test.
Results:
Evaluation: do the 2 test.
Conclusion; do your results cause you to reject your hypothesis?
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V.
VI. Questions and Interpretation of Data
1. Based on your results, what is the relationship between kernel color
alleles? Support your answer.
2. Based on your results, what is the relationship between kernel sugar
content alleles? Support your answer.
3. Do the genes for kernel color and sugar content assort independently
among gametes? Support your answer.
4. You explored both monohybrid and dihybrid crosses, and the resultant
phenotypic patterns exhibited by their offspring. How would you perform a
trihybrid cross? If both parents breed true, what phenotypic patterns
would be exhibited in the F1 offspring from this cross? What about the F2?
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