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BIO 184
Fall 2006
LECTURE 9
Lecture 9:
Mendelian Inheritance
Drawing of Pisum sativum, the common garden pea. This plant was cultivated by
Gregor Mendel and used to determine the rules governing the inheritance of
biological traits. http://www.mendelweb.org/images/pisum2.GIF
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BIO 184
Fall 2006
LECTURE 9
I. Early Theories of Inheritance
Many theories of inheritance have been proposed to explain the transmission of
hereditary traits:
a. Theory of pangenesis
 Proposed by Hippocrates (ca. 400 BC)
 “Seeds” are produced by all parts of the body
o Collected in reproductive organs
o Then transmitted to offspring at moment of conception
b. Theory of preformationism
 The organism is contained in one of the sex cells as a fully
formed homunculus, or miniature human being
 With proper nourishment the homunculus unfolds into its
adult proportions
 Drawing from http://en.wikipedia.org/wiki/Homunculus
c. Blending



Theory of Inheritance
Factors that control hereditary traits are meleable
They can blend together generation after generation
Much like mixing food coloring: red + yellow blends to
make orange, a completely different color, and the red
and yellow colors are forever lost
II. Gregor Mendel
Gregor Mendel’s pioneering experiments with garden peas refuted all of the above!
Mendel lived from 1822-1884 and is considered to be the “father” of genetics.
Mendel’s success can be attributed, in part, to
 His boyhood experience in grafting trees
o This taught him the importance of precision and attention to detail
 His university experience in physics and natural history
o This taught him to view the world as an orderly place governed by
natural laws that can be stated mathematically
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BIO 184
Fall 2006
LECTURE 9
Mendel was an Austrian monk and conducted his landmark studies in a small 115 by
23 foot plot in the garden of his monastery. From 1856-1864, he performed
thousands of crosses. He also kept meticulously accurate records that included
quantitative analysis.
His work, entitled “Experiments on Plant Hybrids” was published in 1866.
However, it was ignored for 34 years, probably because it was published in an
obscure journal and there was no understanding yet of chromosome transmission.
The behavior of chromosomes in cell nuclei was first observed in the 1880s and, in
1900, Mendel’s work was rediscovered by three botanists working independently.
Mendel’s work helped explain chromosome behavior during meiosis.
Mendel chose pea plants as his experimental organism to study the natural laws
governing the transmission of heritable traits. He performed hybridization
experiments, in which he mated two individuals with different characteristics (e.g.
white flowers x purple flowers). Such crosses produce offspring called hybrids.
The garden pea was advantageous to Mendel because:
 It exists in several varieties with easily distinguishable characteristics
 Its flower structure allows for easy crosses
 It is possible to self-fertilize the plants as well as to cross-fertilize them.
Mendel studied seven traits in the garden pea that “bred true.” Such plants
produce the same trait over and over again when they are selfed or bred to plants
like themselves. Note that each trait has two easily distinguishable alternative
forms (e.g. purple vs. white flowers).
See Figure 2.4 in Brooker text.
Mendel did not start out with a hypothesis to explain the inheritance of these
traits through the generations. Rather, he hoped that a quantitative analysis of
crosses might provide a hypothesis that could be rigorously tested.
III. Mendel’s First Law (Law of Segregation)
In his first set of experiments, Mendel crossed two variants that differed in only
one trait (e.g. flower color). This is termed a monohybrid cross.
 Mono = one trait is followed in the cross
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BIO 184

Fall 2006
LECTURE 9
Hybrid = the offspring of the cross are hybrids
See Figure 2.5 in Brooker text.
When the pure-breeding parent plants were crossed, they produced a generation
of offspring which Mendel called the first filial, or F1 generation. However, for
the traits Mendel chose, only one form of the trait was expressed in these F1
plants. For example, when Mendel crossed a pure-breeding purple-flowered pea
plant with a pure-breeding white-flowered plant, all of the offspring had purple
flowers. This clearly showed that “blending inheritance” was not taking place, but it
also confused Mendel at first. Had the other trait disappeared altogether?
To further explore what was happening, Mendel then selfed the F1 generation to
produce an F2 generation of plants. To his surprise, both traits reappeared in
their original forms among the F2s. Moreover, the traits appeared in a predictable
ratio of 3 to 1.
These results suggested a particulate inheritance and Mendel postulated the
following Law of Segregation to explain what he had seen:
1.
2.
3.
4.
A pea plant contains two discrete hereditary factors, one from each parent.
The two factors may be identical or different.
When different factors of a single trait are present in the same individual:
 One is “dominant” and its effect can be seen
 One is “recessive” and is not expressed
During gamete formation in a plant with both factors, the paired factors
segregate randomly so that half of the gametes receive one factor and half
receive the other
Today, Mendel’s “factors” are called “genes”, and the alternative forms of genes
(e.g. purple vs. white) are called “alleles.”
An individual with two identical alleles is termed homozygous (eg. AA or aa) and an
individual with two different alleles is termed heterozygous (eg. Aa).
The genotype of an individual refers to the specific allelic combination that it
carries, while its phenotype refers to the traits that the individual actually
expresses.
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BIO 184
Fall 2006
LECTURE 9
See Figure 2.6 in Brooker text
Mendel performed the monohybrid crosses for all seven of the traits he chose,
with the results shown on p. 23 of your text (“Data from Monohybrid Crosses”).
IV. Punnett Squares
One excellent way of visualizing Mendel’s crosses is to draw Punnett Squares. A
Punnett Square is a grid that enables one to predict the outcome of simple genetic
crosses.
As an example, suppose that we were following a cross between a pure-breeding
tall pea plant (TT) and a pure-breeding dwarf pea plant (tt). To set up the Punnett
Square, we must first determine what types of gametes each parent can produce.
In this case, each parent can only contribute one type of gamete to the cross, and
each gamte will contain only one factor, so the Punnett Square predicts that only
one type of offspring (Tt) will result:
T
Tt
t
The gametes from one parent are placed across the top of the square, and the
gametes of the other parent are placed along the left side of the square. The
gametes are then combined (fertilized) to produce the offspring (unshaded
square).
In a slightly more complicated cross, let’s see what happens if two Tt plants are
crossed to one another. In this case, Mendel’s Law of Segregation predicts that
each plant will produce two gamete types (T and t) in equal proportions. Thus, the
Punnett Square would be drawn as follows:
T
t
T
TT
Tt
t
Tt
tt
The Punnett Square now predicts a 1:2:1 genotypic ratio among the offspring (1 TT:
2 Tt: 1 tt) and a 3:1 phenotypic ratio (3 tall: 1 dwarf).
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BIO 184
Fall 2006
LECTURE 9
V. Mendel’s Second Law (Law of Independent Assortment)
After completing his monohybrid crosses, Mendel extended his experiments by
performing a series of dihybrid crosses. In a dihybrid cross, the hereditary
behavior of two different traits (e.g. seed shape and seed color) is followed
simultaneously in the same cross.
 For example, trait 1 = seed texture (round vs. wrinkled) and trait 2 is seed
color (yellow vs. green)
Again, Mendel started with pure-breeding plants, produced a generation of F1
plants, and then crossed the F1s to one another to produce an F2 generation.
Mendel postulated that there were two possible patterns he might observe. In the
first, the two dominant traits would always enter the same gametes and the two
recessive traits would enter the other gametes. Thus, a plant that was YyRr would
only produce gametes that were YR or yr. This is called linked assortment because
the traits are linked together through the cross.
The other alternative is called independent assortment, and was what Mendel
actually observed. In this pattern, the dominant forms of each trait have no
particular affinity for each other and the plant produces equal numbers of four
gamete types: YR, yr, Yr, and yR.
See Figure 2.7 in Brooker text.
For example, Mendel mated plants that were pure-breeding for round, yellow seeds
with plants that were pure-breeding for wrinkled, green seeds. As expected, all of
the F1 generation plants were round and yellow.
Then, he crossed (or selfed) the F1 plants and examined the F2 generation. When
he did so, he discovered that the F2s appeared in phenotypic ratios of 9:3:3:1, as
follows:
9
3
3
1
round, yellow
round, green
wrinkled, yellow
wrinkled, green
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BIO 184
Fall 2006
LECTURE 9
The round, yellow and wrinkled, green offspring are called parentals, or
nonrecombinants, because they have the same phenotypic combinations as the two
parents. The others are called nonparentals, or recombinants, because they look
different from either parent.
Figure 2.8 in Brooker illustrates Mendel’s dihybrid crosses and how he
interpreted his results.
Mendel performed dihybrid crosses for all possible combinations of the 7 traits he
had chosen. For all combinations but one, he got close to a 9:3:3:1 ratio in the F2
generation, supporting his model (we will discuss the one exception later).
VI. The Rules of Probability
Sometimes, it is easier to use the product rule than Punnett Squares to determine
the results of a cross. This is especially true when more than two traits are being
followed in the cross or when the relative frequency of a particular genotype or
phenotype is being sought.
The use of this rule is possible because of Mendel’s Law of Independent
Assortment – that is, the segregation of the factors for each trait in a cross is an
independent event from the segregation of the factors of all other traits in the
cross.
Consider the following example: A cross is made between the two plants with the
genotypes (Aa, Yy, rr) and (Aa, Yy, Rr), where A = purple flowers, a = white flowers;
Y = yellow seeds, y = green seeds; and R = round seeds and r = wrinkled seeds.
What fraction of the offspring would you expect to have the genotype (Aa,yy,rr) ?
To use the product rule to answer this question, you would first analyze each trait
separately. Then you would simply multiply the individual probabilities together to
arrive at a final answer.
A/a x A/a
½ A/a
Y/y x Y/y
¼ y/y
r/r x R/r
½ r/r
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½ x ¼ x ½ = 1/16
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BIO 184
Fall 2006
LECTURE 9
The product rule can also be used to predict the phenotypes of the offspring of a
genetic cross.
For example, using the same cross as above, what fraction of the offspring would
you expect to have purple flowers and yellow, wrinkled seeds?
The easiest way to solve this type of problem is to express the phenotype as a
genotype and then proceed as in part a.
purple flowers = A__
yellow seeds = Y__
wrinkled seeds = rr
Aa x Aa
¾ A__
Yy x Yy
¾ Y__
rr x Rr
½ rr
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¾ x ¾ x ½ = 9/32