quantitative characters · 2015-10-21 · ab ab ab ab ab ab ab ab 4 3 3 3 3 2 2 2 2 2 1 1 1 1 0 2 a...
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Quantitative characters
Joe Felsenstein
GENOME 453, Autumn 2015
Quantitative characters – p.1/38
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ab
aB
Ab
AB
ab
aB
Ab
AB
4
3
3
3
3
2
2
2
2
2
1
1
1
1
0
2
A random−mating population with two genes having2 alleles each, at equal frequencies, symmetrically
affecting a quantitative character
Quantitative characters – p.2/38
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4
3
3
3
3
1
1
1
1
0
2
2
2
2
2
2
Quantitative characters – p.3/38
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4
3
3
3
3
1
1
1
1
0
2
2
2
2
2
2
Quantitative characters – p.4/38
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43210
aabb
Aabb
aAbb
aaBb
aabB
AaBb
aABb
AAbb
AabB
aAbB
aaBB
AABb
AAbB
AaBB
aABB AABB
The distribution of the genotypes and the quantitative
character before artificial selection
Quantitative characters – p.5/38
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An imaginary quantitative character with 4 loci
The character is a sum of effects including interaction and environmentaleffects:
AA
Aa
aa
−1
2
3
CC
Cc
cc
−2
0
3
+
+
BB
Bb
bb
DD Dd dd
0.85.24 −4.0
3.28 0.1 −3.08
0.56 −1.0 −2.2
+
startingvalue
two loci that add up
plus two that interact plus an environmental effect
12 +
0−4 4
What kind of distribution will this lead to when gene frequencies at the fourloci are pA = 0.4, pB = 0.5, pC = 0.3, and pD = 0.6 ?
Quantitative characters – p.6/38
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The resulting distribution
0 5 10 15 20 25 30 35
Phenotype
freq
uenc
y
Quantitative characters – p.7/38
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A similar distribution in a 5-locus character
0 1 2 3 4 5 6 7 8
Gene frequencies
A
BCDE
0.4
0.30.40.20.6
Phenotype:
Number of copiesof these alleles.No environmentaleffects
100 random
individuals:
Quantitative characters – p.8/38
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Distributions of quantitative characters
Quantitative characters – p.9/38
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Quantitative characters – p.10/38
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Quantitative characters – p.11/38
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Recall this distribution
Mean phenotype of
43210
aabb
Aabb
aAbb
aaBb
aabB
AaBb
aABb
AAbb
AabB
aAbB
aaBB
AABb
AAbB
AaBB
aABB AABB
The distribution of the genotypes and the quantitative
character before artificial selection
10
Before selection
frequency of A = 0.5
frequency of B = 0.5
population = 2.0
Quantitative characters – p.12/38
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Truncation selection
43210
AaBb
aABb
AAbb
AabB
aAbB
aaBB
AABb
AAbB
AaBB
aABB AABB
The distributions after artificial selection which
saves only those individuals at or above 2
After selection:
0.6364
Before selection
frequency of A = 0.5
frequency of B = 0.5
Mean phenotype of
survivors = 2.545
frequency of A = 14/22 =
frequency of B = 14/22 = 0.6364
Quantitative characters – p.13/38
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Offspring of truncation selection
43210
In fact, the offspring will have this distribution:
9
60
154
180
81
Mean phenotype
of offspring = 2.545
(484 copies in all)
Quantitative characters – p.14/38
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Effect of truncation selection on one locus
phenotype
With a larger number of loci, focusing just on one locus
Quantitative characters – p.15/38
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Effect of truncation selection on one locus
aa
Aa
AA
phenotype
With a larger number of loci, focusing just on one locus
Quantitative characters – p.16/38
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Effect of truncation selection on one locus
Aa AA
phenotype
aa
The distribution of offspring at this locus
Quantitative characters – p.17/38
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Heritability
V = V + V + V
Variance of a character = VT
T A D E
Total variance
Additive genetic variance
Dominance variance
Environmental variance
heritability = h = V
V
A
T
2
heritability in effect measures the fraction of
variations that are passed on to the next generation,
undisrupted by Mendelian segregation
assuming genes are additive and environments are independent)(
Quantitative characters – p.18/38
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Heritabilities in a real-life example
Quantitative characters – p.19/38
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Response to artificial selection
truncation point
breed from thesediscard these
mean of newborns mean of thosewho we breed from
S
mean of newborns
in next generation
Sh2
R = h S2
h = heritability2
Quantitative characters – p.20/38
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Response to artificial selection
1000 lbs 1100 lbs
weight
If heritability = 0.4
This is the expected gain in one generation
Mean of selected individuals#
of in
divi
dual
s
S = selection differential
= mean of selected individuals − population mean = 100 lbs
R = gain
= 40 lbs2 = h S
Population mean
Quantitative characters – p.21/38
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Some features of artificial selection experiments
replicate lines
relaxation of selection
reverse selection
a selection limit?
generations
mea
n ph
enot
ype
control line
selection up
selection down
Quantitative characters – p.22/38
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Body weight in mice
Quantitative characters – p.23/38
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Tooth decay in rats
Quantitative characters – p.24/38
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White blood cell counts
Quantitative characters – p.25/38
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Chicken legs
Quantitative characters – p.26/38
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Thorax bristles in Drosophila
Quantitative characters – p.27/38
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Abdominal bristles in Drisophila
Quantitative characters – p.28/38
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Dobzhansky’s glass maze
Quantitative characters – p.29/38
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Artificial selection on geotaxis
Quantitative characters – p.30/38
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Artifical selection on phototaxis
Quantitative characters – p.31/38
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Ken Weber’s “inebriometer”
diagram photograph
Quantitative characters – p.32/38
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The Illinois corn selection experiment (oil content)
Quantitative characters – p.33/38
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Quantitative characters – p.34/38
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The Illinois corn selection experiment (protein, oil)
Stephen P. Moose, John W. Dudley and Torbert R. Rocheford . 2004.Maize selection passes the century mark: a unique resource for 21stcentury genomics. Trends in Plant Science 9 (7): 358-364.
Quantitative characters – p.35/38
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Hermon Bumpus’s 1896 sparrows – lengths
length
Fre
quen
cy
150 155 160 165 1700
5
10
15
20
Histogram of female total lengths in millimeters
Quantitative characters – p.36/38
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Sparrow survival data
length
Fre
quen
cy
150 155 160 165 1700
5
10
15
20
Histogram of total lengths of females, and those that survived
Quantitative characters – p.37/38
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Least squares fit of estimated fitnesses
155 160 165
0.0
0.2
0.4
0.6
0.8
1.0
fitne
ss
total length of female (mm)
Fraction of surviving females, and estimate of (quadratic) fitness curve
Quantitative characters – p.38/38