Transcript Data_Analysis

Lecture 4--Genetic Data Analysis
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Extra-credit question:
Name one dominant human
trait mentioned in Chapter 2
of your text.
Genetic Data Analysis
Does a genetic model fit the data?
Genetic Experiments
You have discovered a new mutation in a fruit fly
and have done a set of crosses to determine the
inheritance pattern.
What if the F2 generation of a monohybrid cross
has a phenotypic ratio of 3.5 to 1?
How do we tell if deviations from an expected result
is due to chance or due to the fact that our
genetic hypothesis is wrong?
Thought Experiment
Repeat a simple experiment many times.
Toss a fair coin 100 times and count how
many heads are thrown.
Repeat this experiment 100 times.
What is the most likely outcome of a
single experiment (if coin is fair)?
Will all 100 experiments have the
same outcome?
100 Experiments
Coin Toss Experiment
9
8
Number of Times/100
7
6
5
4
3
2
1
0
1
5
9
13
17
21
25
29
33
37
41
45
49
53
57
Number of Heads
61
65
69
73
77
81
85
89
93
97
Coin Toss Experiment
9
8
Number of Times/100
7
6
5
4
3
2
1
0
1
5
9
13
17
21
25
29
33
37
41
45
49
53
57
61
65
69
73
77
81
85
89
93
97
Number of Heads
What is the probability that you would get 55 or more heads
in a single experiment?
P = 0.184. So, 55 is different from expected, but close
enough that the differences is likely due to chance.
What is the probability that you would get 65 or more heads?
P = 0.0018. So, 65 is different from expected, and the
difference is unlikely to be due to chance.
Genetic example
Q: You cross two moths with different phenotypes,
then cross the F1 back to the parent that you think
has a recessive phenotype (testcross). Progeny:
65 of the “dominant” phenotype, and 35 of the
“recessive” phenotype. Can you reject your
hypothesis that the F1 individual was Aa and the
‘recessive’ parent was aa?
First, what is the expected result?
What is the observed result?
How could we measure the difference between the
expected and observed results?
Genetic Model
P:
F1:
Testcross:
AA x aa
Aa
Aa x aa
Expected result?
(100 offspring)
Observed result?
50 Aa: 50 aa
65 Aa: 35 aa
Hypothesis (null): observed results do not deviate
from expected results more than expected by chance.
2 Test
A way to tell if the difference between observed results
and expected results is too big to be due to chance.
Observed number (O) in each category is compared to
the expected number (E) under your genetic model:
(Obs - Exp).
Use the square of the difference between observed and
expected numbers : (O - E)2
Standardize by dividing by the expected number in a
category: (O - E)2 /E
2 Test
class
Aa
aa
O
65
35
E
50
50
(O-E)
15
-15
(O-E)2 = d2
225
225
(O-E)2/E
225/50 = 4.5
225/50 = 4.5
 = 9
d.f. = (#classes -1) = 1
= ∑ [(O-E)2]/E = ∑ (d2/E)
(O-E) is the “difference” (d).
 symbol means to sum the values over each
category or “class” of the data.
2

Table
Probabilities
df
0.90
0.50
0.20
0.05
0.01
0.001
1
0.02
0.46
1.64
3.84
6.64
10.83
2
0.21
1.39
3.22
5.99
9.21
13.82
3
0.58
2.37
4.64
7.82
11.35
16.27
4
1.06
3.36
5.99
9.49
13.28
18.47
Experiment
You have crossed two plants with purple flowers. Your
hypothesis is that both plants are heterozygous for a
dominant allele at a single locus controlling flower color.
H0: P: (Ww X Ww) H0 stands for ‘null hypothesis’
F1: 3/4 W- (purple) and 1/4 ww (white)
Expected: If H0 is true, you expect 3/4 purple and 1/4
white out of 166: 124.5 purple: 41.5 white.
Observed Data: 166 progeny: 110 purple & 56 white.
Q: Is the deviation from expected too big to be due to
chance?
 Test
Class
Purple
White
O
E
(O-E)
110 124.5
56 41.5
-14.5
14.5
(O-E)2 = d2
210.25
210.25
d2 /E
1.69
5.07
 = 6.76
df = 1
 Table
df
1
2
3
4
0.90
0.02
0.21
0.58
1.06
Probabilities
0.50
0.20
0.05
0.46
1.64
3.84
1.39
3.22
5.99
2.37
4.64
7.82
3.36
5.99
9.49
0.01
6.64
9.21
11.35
13.28
0.001
10.83
13.82
16.27
18.47
Problem: An ear of corn has a total of 381
grains, including 216 purple, smooth, 79
purple, shrunken, 65 yellow, smooth, and
21 yellow, shrunken.
Your Hypothesis: This ear of corn was
produced by a dihybrid cross (PpSs x
PpSs) involving two pairs of heterozygous
genes resulting in an expected ratio of
9:3:3:1. Purple dominant to yellow; smooth
dominant to shrunken.
(O-E)2/E
Class
Obs
Exp
O-E
Purple
Smooth
216
214
2
4/214 = 0.019
Purple
Shrunk
79
71
8
64/71 = 0.901
Yellow
Smooth
65
71
6
36/71 = 0.507
Yellow
Shrunk
21
24
3
9/24 = 0.375
d.f. = 3
2 = 1.80
2 = 1.80
d.f. = 3
Probabilities
df
1
2
3
4
0.90
0.02
0.21
0.58
1.06
0.50
0.46
1.39
2.37
3.36
0.20
1.64
3.22
4.64
5.99
0.05
3.84
5.99
7.82
9.49
0.01
6.64
9.21
11.35
13.28
0.001
10.83
13.82
16.27
18.47
Extra credit problem for next
class
An agouti mouse is crossed to a white mouse and all the F1
offspring are agouti.
An F1 female is crossed to an F1 male, and the offspring
are:
11 agouti: 5 white: 4 black
Q: Test the hypothesis that the original parental
genotypes were BBCC and bbcc. Give the 2 value,
the df, the P value, and state whether or not you reject
the hypothesis.
Pedigrees-Review
Not affected
Female
Male
Affected
Partly affected
Which is the pedigree of (1) autosomal
dominant; (2) autosomal recessive; (3) sexlinked recessive?
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