Download Dihybrid crosses

INDEPENDENT
ASSORTMENT
OF ALLELES
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Genetica per Scienze Naturali
a.a. 08-09 prof S. Presciuttini
Mendel’s dihybrid crosses
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Mendel went on to analyze the descendants of pure lines that differed
in two characters.
Here we need a general symbolism to represent genotypes including
two genes. If two genes are on different chromosomes, the gene pairs
are separated by a semicolon, for example, A /a ; B /b . If they are on
the same chromosome, the alleles on one chromosome are written
adjacently and are separated from those on the other chromosome by a
slash, for example, A B /a b or A b /a B.
An accepted symbolism does not exist for situations in which it is not
known whether the genes are on the same chromosome or on different
chromosomes. For this situation, we will separate the genes with a
dot, for example, A /a ·B /b . A double heterozygote, A /a · B /b , is
also known as a dihybrid. From studying dihybrid crosses (A /a · B /b
× A /a · B /b ), Mendel came up with another important principle of
heredity.
Genetica per Scienze Naturali
a.a. 08-09 prof S. Presciuttini
Yellow/green-round/wrikled seeds
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The two specific characters that he began working with were seed
shape and seed color.
To perform a dihybrid cross, Mendel started with two parental pure
lines. One line had yellow, wrinkled seeds; because Mendel had no
concept of the chromosomal location of genes, we must use the dot
representation to write this genotype as Y /Y · r /r . The other line had
green, round seeds, the genotype being y /y · R /R .
The cross between these two lines produced dihybrid F1 seeds of
genotype R /r · Y /y , which he discovered were round and yellow.
This result showed that the dominance of R over r and of Y over y
was unaffected by the presence of heterozygosity for either gene pair
in the R /r · Y /y dihybrid.
Genetica per Scienze Naturali
a.a. 08-09 prof S. Presciuttini
DiHybrid-cross F2 ratios

Next Mendel made the dihybrid cross by selfing the dihybrid F1 to
obtain the F2 generation. The F2 seeds were of four different types in
the following proportions:
What could be the explanation? Mendel added up
the numbers of individuals in certain F2 phenotypic
classes to determine if the monohybrid 3:1 F2
ratios were still present. He noted that, in regard to
seed shape, there were 423 round seeds (315+108)
and 133 wrinkled seeds (101+32). This result is
close to a 3:1 ratio. Next, in regard to seed color,
there were 416 yellow seeds (315+101) and 140
green (108+32), also very close to a 3:1 ratio. The
presence of these two 3:1 ratios hidden in the
9:3:3:1 ratio was undoubtedly a source of the
insight that Mendel needed to explain the 9:3:3:1
ratio, because he realized that it was nothing more
than two independent 3:1 ratios combined at
random.
Genetica per Scienze Naturali
a.a. 08-09 prof S. Presciuttini
Visualizing the 9:3:3:1 ratio
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One way of visualizing the random
combination of these two ratios is with a
branch diagram, as follows:

The combined proportions are
calculated by multiplying along the
branches in the diagram because, for
example, 3/4 of 3/4 is calculated as 3/4
× 3/4, which equals 9/16 These
multiplications give us the following
four proportions:
Genetica per Scienze Naturali
a.a. 08-09 prof S. Presciuttini
The Punnett square
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The four female gametic types will be fertilized
randomly by the four male gametic types to
obtain the F2 , and the best way of showing this
graphically is to use a 4×4 grid called a Punnett
square, which is depicted in Figure 2-10 . Grids
are useful in genetics because their proportions
can be drawn according to genetic proportions or
ratios being considered, and thereby a visual data
representation is obtained. In the Punnett square
in Figure 2-10 , for example, we see that the areas
of the 16 boxes representing the various gametic
fusions are each one-sixteenth of the total area of
the grid, simply because the rows and columns
were drawn to correspond to the gametic
proportions of each. As the Punnett square shows,
the F2 contains a variety of genotypes, but there
are only four phenotypes and their proportions
are in the 9:3:3:1 ratio.
Genetica per Scienze Naturali
a.a. 08-09 prof S. Presciuttini
Mendel’s trihybrid experiment
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Mendel submitted his principle of independent assortment to a further
test. He tested the segregation ratios of the F2 progeny from parental
plants that were simultaneously pure for three characters:
ABC seed parents:
A form round
B albumen yellow
C seed-coat gray-brown
abc pollen parents:
a form wrinkled
b albumen green
c seed-coat white
In Mendel’s own words:
“This experiment was made in precisely the same way as the previous
one. Among all the experiments it demanded the most time and trouble.
From 24 hybrids, 687 seeds were obtained in all. From these, 639 plants
fruited in the following year.
Genetica per Scienze Naturali
a.a. 08-09 prof S. Presciuttini
Mendel’s original results
These 639 plants were backcrossed with the triple-recessive parental line, so that
Mendel was able to classify them by genotype and not only by phenotype. He
presented the following table:
8 plants ABC
14
9
11
8
10
10
7
"
"
"
"
"
"
"
ABc
AbC
Abc
aBC
aBc
abC
abc
22 plants ABCc
45 plants
ABbCc
17
25
20
15
18
19
24
14
18
20
16
36
38
40
49
48
"
"
"
"
"
aBbCc
AaBCc
AabCc
AaBbC
AaBbc
78
"
AaBbCc
"
"
"
"
"
"
"
"
"
"
"
AbCc
aBCc
abCc
ABbC
ABbc
aBbC
aBbc
AaBC
AaBc
AabC
Aabc
“The whole expression contains 27 terms. Of these, 8 are constant in all characters, and
each appears on the average 10 times; 12 are constant in two characters, and hybrid in the
third; each appears on the average 19 times; 6 are constant in one character and hybrid in
the other two; each appears on the average 43 times. One form appears 78 times and is
hybrid in all of the characters. The ratios 10:19:43:78 agree so closely with the ratios
10:20:40:80, or 1:2:4:8 that this last undoubtedly represents the true value”.
Genetica per Scienze Naturali
a.a. 08-09 prof S. Presciuttini
Punnett’s square of Mendel’s trihybrid crosses
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We can easily interpret Mendel’s trihybrid experiment using the
Punnett square:
1/8
ABC
1/8
1/8
1/8
1/8
1/8
1/8
1/8
1/8
ABC
ABc
AbC
aBC
Abc
aBc
abC
abc
1/8
ABc
1/8
AbC
1/8
aBC
1/8
Abc
1/8
aBc
1/8
abC
1/8
abc
AA-BB-CC AA-BB-cC AA-bB-CC aA-BB-CC AA-bB-cC aA-BB-cC aA-bB-CC aA-bB-cC
AA-BB-Cc AA-BB-cc AA-bB-Cc aA-BB-Cc AA-bB-cc aA-BB-cc aA-bB-Cc aA-bB-cc
AA-Bb-CC AA-Bb-cC AA-bb-CC aA-Bb-CC AA-bb-cC aA-Bb-cC aA-bb-CC aA-bb-cC
Aa-BB-CC Aa-BB-cC Aa-bB-CC aa-BB-CC Aa-bB-cC aa-BB-cC aa-bB-CC aa-bB-cC
AA-Bb-Cc AA-Bb-cc AA-bb-Cc aA-Bb-Cc AA-bb-cc aA-Bb-cc aA-bb-Cc aA-bb-cc
Aa-BB-Cc Aa-BB-cc Aa-bB-Cc aa-BB-Cc Aa-bB-cc aa-BB-cc aa-bB-Cc aa-bB-cc
Aa-Bb-CC Aa-Bb-cC Aa-bb-CC aa-Bb-CC Aa-bb-cC aa-Bb-cC aa-bb-CC aa-bb-cC
Aa-Bb-Cc
Aa-Bb-cc
Aa-bb-Cc
aa-Bb-Cc
Aa-bb-cc
aa-Bb-cc
aa-bb-Cc aa-bb-cc
Colors distinguish the four classes of genotypes identified by Mendel:
1)
2)
3)
4)
Plants homozygous for all traits (red);
Plants homozygous for two traits and heterozygous for one (pale blue);
Plants heterozygous for two traits and homozygous for one (pink);
Plants heterozygous for all three traits (yellow).
Genetica per Scienze Naturali
a.a. 08-09 prof S. Presciuttini
Mendel’s series 1:2:4:8
Examining the Punnett square, we can see that:
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each of the 8 different red genotypes appears in the table only
once, so that each has a probability of 1/64;
each of the 12 different pale-blue genotypes appears in the table
twice, so that each occurs with probability 2/64 or 1/32;
each of the 6 pink genotypes appears in the table four times, so that
each occurs with probability 4/64 or 1/16;
the unique yellow genotype appears in the table eight times, so that
its probability is 8/64 or 1/8.
Summing these probabilities together for each class we find
the series 1:2:4:8 that Mendel correctly recognized and
allowed him to confirm the law of independent segregation.
Genetica per Scienze Naturali
a.a. 08-09 prof S. Presciuttini
Genotype Observed Expected
Chisq
AA-BB-CC
AA-BB-cc
AA-bb-CC
aa-BB-CC
AA-bb-cc
aa-BB-cc
aa-bb-CC
aa-bb-cc
AA-BB-Cc
AA-bb-Cc
aa-BB-Cc
aa-bb-Cc
AA-bB-CC
AA-Bb-cc
aa-Bb-CC
aa-Bb-cc
Aa-BB-CC
Aa-BB-cc
Aa-bb-CC
Aa-bb-cc
AA-Bb-Cc
aa-Bb-Cc
Aa-BB-Cc
Aa-bb-Cc
Aa-Bb-CC
Aa-Bb-cc
Aa-Bb-Cc
0.394
1.615
0.097
0.103
0.394
0.000
0.000
0.892
0.207
0.441
1.268
0.000
1.236
0.194
0.047
0.814
1.784
0.194
0.000
0.789
0.642
0.388
0.094
0.000
2.056
1.628
0.044
15.322
0.951
8
14
9
11
8
10
10
7
22
17
25
20
15
18
19
24
14
18
20
16
45
36
38
40
49
48
78
639
9.98
9.98
9.98
9.98
9.98
9.98
9.98
9.98
19.97
19.97
19.97
19.97
19.97
19.97
19.97
19.97
19.97
19.97
19.97
19.97
39.94
39.94
39.94
39.94
39.94
39.94
79.88
639.00
Probability =
Chi-square analysis of
Mendel’ tri-hybrid crosses
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Reasoning in modern terms, we
can test the independent
segregation of the three loci
investigated by Mendel by means
of chi-square analysis
Expected values of each
genotype is obtained by
mutiplying its probability (1/8,
1/16, 1/32, or 1/64) by the total
number of observation (639).
The final chi-square value of
15.3 is not significant of
deviation from the expected
values (P > 0.05).
Genetica per Scienze Naturali
a.a. 08-09 prof S. Presciuttini