ANNOUNCEMENTS

1
ANNOUNCEMENTS

• HW3 is due on Wednesday (Feb. 18th) in lecture.
• Take-home Exam 1 will be available on the 18th
  and is due on the 25th.
• Discussion sections meet next week.

Happy 200th Birthday Darwin!!!
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TODAY...

• Probability and hypothesis testing
• - review product sum rules
• - conditional probabilities
• - hypothesis testing with ?2 test
• Linkage
• How do pairs of genes on the same chromosome
  segregate relative to each other?

3

• How many unique gametes can an individual of
  genotype AABbCcDdEE make?
• 4
• 8
• 16
• 32
• 64

4

• How many unique gametes can an individual of
  genotype AABbCcDdEE make?
• 4
• 8
• 16
• 32
• 64

possible gametes 2n, where n is the number
of heterozygous loci
5

• Assuming independent assortment, what is the
  probability that an offspring of the test-cross
  AABbCcDdEe x aabbccddee has only dominant traits?
• 0.5
• 0.25
• 0.125
• 0.0625
• 0.03125

6

• Assuming independent assortment, what is the
  probability that an offspring of the test-cross
  AABbCcDdEe x aabbccddee has only dominant traits?
• 0.5
• 0.25
• 0.125
• 0.0625
• 0.03125

P (ABCDE gamete) 1/2 x 1/2 x 1/2 x 1/2 1/16
.0625
7
Conditional Probability The probability of an
event occurring conditional upon a limited set of
possibilities. For example, what is the
probability of rolling a 3 with a dice given we
roll an odd number?
8
What is the conditional probability that a tall
plant from a cross between two heterozygotes (Tt
x Tt) will be heterozygous?
9
Hypothesis Testing Chi-square (?2) goodness of
fit test
Used throughout biology and other sciences to
test hypotheses about categorical data.
Do the observed data fit the distribution that we
would expect if our null hypothesis is true?
10
Chi-square goodness of fit test
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Null hypothesis (HO) Mendelian ratio of 121
Do these values fit this hypothesis?
We will conclude that these values fit Ho if the
observed deviation from 121 is no more than we
would expect by chance if our null hypothesis is
true.
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Degrees of freedom The number of classes minus
one. df n 1 3 1 2
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We use a chi-square table to determine the
critical value given the degrees of freedom.
df 2
14
The worse the fit between observed (O) and
expected (E), the greater the value of ?2.
increasingly worse fit
We will reject HO when the probability of the
observed distribution is less than 5.
15
If the null hypothesis is correct (HO 121), we
expect a ?2 value greater than 5.99 less than 5
of the time.
df 2
We will reject the null hypothesis only if the ?2
value is greater than 5.99 (df2).
In this case, the chi-sq value (0.776) is less
than 5.99 so we accept the null hypothesis.
16
Linkage and Genetic Mapping

• Today conceptual basis for studying linkage
  between genes on the same chromosome
• Goals
• Understand linkage
• Be able to use ?2 to test for independent
  assortment of loci
• Estimate the rate of recombination (r) between
  pairs of loci

Wednesday Genetic Genomic mapping
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Linkage

• In any eukaryotic genome, there are many
  thousands of genes located on a small number of
  chromosomes (in humans, 35,000 genes on 23
  chromosomes)
• Genes located on different (non-homologous)
  chromosomes assort independently gt equal
  probability of all possible gamete combinations
• What about genes on the same chromosome?

18
Linkage terms

• Genes on the same chromosome are syntenic.
• Genes on the same chromosome may be genetically
  linked as well.

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TRAIT
VARIANTS
White
Flower color
Purple
Terminal
Flower position
Axial
Green
Seed color
Yellow
Seed shape
Round
Wrinkled
Constricted
Inflated
Pod shape
Pod color
Green
Yellow
Tall
Dwarf
Height
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• Mendels Principles
• Dominance In a heterozygote, one allele may
  conceal another.
• Segregation In a heterozygote, two different
  alleles segregate from each other during the
  formation of gametes.
• Independent Assortment The alleles of different
  genes segregate (or assort) independently of each
  other.

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r
y
r
Y
y
Y
R
R
Meiosis I
y
Y
Y
y
or
r
R
r
R
Meiosis II
y
y
y
y
Y
Y
Y
Y
R
R
r
r
R
r
r
R
y
y
y
y
Y
Y
Y
Y
r
r
R
r
r
R
R
R
25 Ry
25 ry
25 rY
25 RY
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round, yellow wrinkled, green
RRYY
rryy
round, yellow
RrYy
RY Ry rY ry
Gametes
25 25 25 25
23
round, yellow wrinkled, yellow round,
green green, wrinkled
9 3 3
1
24
round, yellow wrinkled, green
RRYY
rryy
round, yellow
RrYy (self-fertilize)
round, yellow wrinkled, yellow round,
green wrinkled, green
315 101 108
32
(312.8) (104.2) (104.2)
(34.8)
25
315 101 108
32
(312.8) (104.2) (104.2)
(34.8)
0.02 0.10 0.14 0.23 0.48
How many degrees of freedom? (a) 1 (b) 2 (c)
3 (d) 4
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0.48 lt 7.82 Accept HO
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B
b
b
b
B
B
A
a
a
a
A
A
Meiosis
Meiosis
B
B
B
B
A
A
A
a
b
b
b
b
A
a
a
a
Possible haploid cells
Possible haploid cells
Without crossing over, linked alleles
segregate together.
Crossing over can reassort linked alleles.
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Bateson Punnett (1908)
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Null Hypothesis 9331 ratio
Exp (451.7) (150.1)
(150.1) (50.2)
9 3
3 1
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Exp (451.7) (150.1)
(150.1) (50.2)
(9/16) x 803 (451.7)
(1/16) x 803 (50.2)
(3/16) x 803 (150.1)
37.97 102.60 105.93 285.90
532.40
df 3
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If the null hypothesis is correct (HO 9331),
we expect a chi-square value greater than 7.82
(df3) less than 5 of the time.
The actual chi-square is 532.40 so . . .
We reject the null hypothesis because the
chi-square value is greater than 7.82.
532.4 gtgtgt 7.82