Lecture 13
Selection on quantitative characters
Selection on quantitative characters
What is a quantitative (continuous) character?
Selection on quantitative characters
What is a quantitative character?
• quantitative characters exhibit continuous
variation among individuals.
Selection on quantitative characters
What is a quantitative character?
• quantitative characters exhibit continuous
variation among individuals.
• unlike discrete characters, it is not possible to
assign phenotypes to discrete groups.
Examples of discrete characters
Example of a continuous character
Height
Two characteristics of quantitative traits:
Two characteristics of quantitative traits:
1. Controlled by many genetic loci
Two characteristics of quantitative traits:
1. Controlled by many genetic loci
2. Exhibit variation due to both genetic and
environmental effects
Two characteristics of quantitative traits:
1. Controlled by many genetic loci
2. Exhibit variation due to both genetic and
environmental effects
• the genes that influence quantitative traits are now
called quantitative trait loci or QTLs.
Quantitative characters can be controlled by
small numbers of genes
What are QTLs?
What are QTLs?
• QTLs possess possess multiple alleles, exhibit varying
degrees of dominance, and experience selection and
drift.
What are QTLs?
• QTLs possess multiple alleles, exhibit varying degrees
of dominance, and experience selection and drift.
• some QTLs exhibit stronger effects than others – these
are called major effect and minor effect genes,
respectively.
What are QTLs?
• QTLs possess multiple alleles, exhibit varying degrees
of dominance, and experience selection and drift.
• some QTLs exhibit stronger effects than others – these
are called major effect and minor effect genes,
respectively.
• the number and relative contributions of major effect
and minor effect genes underlies the genetic
architecture of the trait.
What are QTLs?
• QTLs possess multiple alleles, exhibit varying degrees
of dominance, and experience selection and drift.
• some QTLs exhibit stronger effects than others – these
are called major effect and minor effect genes,
respectively.
• the number and relative contributions of major effect
and minor effect genes underlies the genetic
architecture of the trait.
• mapping QTLs is expensive, labor intensive, and
fraught with statistical problems!
Mimulus phylogeny
F2 progeny from Mimulus cardinalis x
M. lewisii F1 hybrids
Heritability
-
heritability does not mean “heritable” or “inherited”!!
-
heritability represents the degree to which the trait is
determined by genetic and not by environmental effects.
Heritability
Beans:
Average is 404 mg.
Select the top 10% of the population for next years crop (new mean 692 mg).
- the mean of the crop from the selected group is 609 mg.
- the average seed size has thus increased by 51% over one generation.
1. What would have occurred if the variation in bean size was entirely due to
environmental effects?
the mean bean size would have remained unchanged (at about 404 mg).
2. What if all of the variation was controlled by genetic factors?
the mean bean size in generation 1 would have been about 692 mg.
Heritability
Selection differential, S = the “strength” of selection
= mean (selected) - mean (whole pop.) = 692 - 404 = 288
Response differential, R = the change in average phenotype due
to selection
= mean (whole pop. in gen. 1) - mean (whole pop. in gen. 0)
= 609 - 404 = 205
Realized heritability, h^2 = R/S
= 205/288 = 0.71
- a heritability of 0.71 means that 71% of the variation in bean size
in the starting population was due to genetic factors and 29% was
caused by the environmental factors
Heritability
- knowing the heritability of a trait allows us to predict its
response to selection.
- (Realized heritability, h^2 = R/S)
- the equation above can be rearranged to:
Response differential, R = h^2 . S
- this means that the response of the trait to selection is
determined by its heritability and by the intensity of selection.
- strong selection acting on a trait with a low heritability will be
ineffective!
Heritability
trait
h^2
fingerprint
(# of ridges)
head width
height
blood pressure
IQ
twinning
handedness
body weight
0.98
0.95
0.84
0.70
0.55
0.52
0.32
0.05
What is heritability?
What is heritability?
• heritability is the proportion of the total phenotypic
variation controlled by genetic rather than
environmental factors.
What is heritability?
• heritability is the proportion of the total phenotypic
variation controlled by genetic rather than
environmental factors.
The total phenotypic variance may be decomposed:
VP = total phenotypic variance
The total phenotypic variance may be decomposed:
VP = total phenotypic variance
VG = total genetic variance
The total phenotypic variance may be decomposed:
VP = total phenotypic variance
VG = total genetic variance
VE = environmental variance
The total phenotypic variance may be decomposed:
VP = total phenotypic variance
VG = total genetic variance
VE = environmental variance
VP = VG + VE
The total phenotypic variance may be decomposed:
VP = total phenotypic variance
VG = total genetic variance
VE = environmental variance
heritability = VG/VP (broad-sense)
The total genetic variance (VG) may be
decomposed:
The total genetic variance (VG) may be
decomposed:
VA = additive genetic variance
The total genetic variance (VG) may be
decomposed:
VA = additive genetic variance
VD = dominance genetic variance
The total genetic variance (VG) may be
decomposed:
VA = additive genetic variance
VD = dominance genetic variance
VI = epistatic (interactive) genetic variance
The total genetic variance (VG) may be
decomposed:
VA = additive genetic variance
VD = dominance genetic variance
VI = epistatic (interactive) genetic variance
VG = VA + VD + VI
The total genetic variance (VG) may be
decomposed:
VA = additive genetic variance
VD = dominance genetic variance
VI = epistatic (interactive) genetic variance
heritability = h2 = VA/VP (narrow sense)
What is additive gene action?
What is additive gene action?
Consider 2 genes:
B1B1
A1A1
A1A2
A2A2
B1B2
B2B2
What is additive gene action?
Consider 2 genes:
B1B1
B1B2
B2B2
A1A1
0
1
2
A1A2
2
3
4
A2A2
4
5
6
Estimating heritability
Estimating heritability
• one common approach is to compare phenotypic
scores of parents and their offspring:
Estimating heritability
• one common approach is to compare phenotypic
scores of parents and their offspring:
Junco tarsus length (cm)
Cross
Midparent value
Offspring value
Estimating heritability
• one common approach is to compare phenotypic
scores of parents and their offspring:
Junco tarsus length (cm)
Cross
F1 x M1
Midparent value
4.34
Offspring value
4.73
Estimating heritability
• one common approach is to compare phenotypic
scores of parents and their offspring:
Junco tarsus length (cm)
Cross
Midparent value
Offspring value
F1 x M1
4.34
4.73
F2 x M2
5.56
5.31
Estimating heritability
• one common approach is to compare phenotypic
scores of parents and their offspring:
Junco tarsus length (cm)
Cross
Midparent value
Offspring value
F1 x M1
4.34
4.73
F2 x M2
5.56
5.31
F3 x M3
3.88
4.02
Regress offspring value on midparent value
← Slope = h2
Heritability estimates from other
regression analyses
Comparison
Slope
Heritability estimates from other
regression analyses
Comparison
Midparent-offspring
Slope
h2
Heritability estimates from other
regression analyses
Comparison
Slope
Midparent-offspring
Parent-offspring
h2
1/2h2
Heritability estimates from other
regression analyses
Comparison
Slope
Midparent-offspring
Parent-offspring
Half-sibs
h2
1/2h2
1/4h2
Heritability estimates from other
regression analyses
Comparison
Slope
Midparent-offspring
Parent-offspring
Half-sibs
First cousins
h2
1/2h2
1/4h2
1/8h2
Heritability estimates from other
regression analyses
Comparison
Slope
Midparent-offspring
Parent-offspring
Half-sibs
First cousins
h2
1/2h2
1/4h2
1/8h2
• as the groups become less related, the
precision of the h2 estimate is reduced.
Heritabilities vary between 0 and 1
Heritability estimates from other
regression analyses
Comparison
Slope
Midparent-offspring
Parent-offspring
Half-sibs
First cousins
h2
1/2h2
1/4h2
1/8h2
• as the groups become less related, the
precision of the h2 estimate is reduced.
Cross-fostering is a common approach
Q: Why is knowing heritability important?
Q: Why is knowing heritability important?
A: Because it allows us to predict a trait’s
response to selection
Q: Why is knowing heritability important?
A: Because it allows us to predict a trait’s
response to selection
Let S = selection differential
Predicting the response to selection
Example: the large ground
finch, Geospiza magnirostris
Predicting the response to selection
Example: the large ground
finch, Geospiza magnirostris
Mean beak depth of survivors = 10.11 mm
Predicting the response to selection
Example: the large ground
finch, Geospiza magnirostris
Mean beak depth of survivors = 10.11 mm
Mean beak depth of initial pop = 8.82 mm
Predicting the response to selection
Example: the large ground
finch, Geospiza magnirostris
Mean beak depth of survivors = 10.11 mm
Mean beak depth of initial pop = 8.82 mm
S = 10.11 – 8.82 = 1.29 mm
Q: Why is knowing heritability important?
A: Because it allows us to predict a trait’s
response to selection
Let S = selection differential
Let h2 = heritability
Q: Why is knowing heritability important?
A: Because it allows us to predict a trait’s
response to selection
Let S = selection differential
Let h2 = heritability
Let R = response to selection
Q: Why is knowing heritability important?
A: Because it allows us to predict a trait’s
response to selection
Let S = selection differential
Let h2 = heritability
Let R = response to selection
R = h2S
Predicting the response to selection
Example: the large ground
finch, Geospiza magnirostris
Predicting the response to selection
Example: the large ground
finch, Geospiza magnirostris
Mean beak depth of survivors = 10.11 mm
Predicting the response to selection
Example: the large ground
finch, Geospiza magnirostris
Mean beak depth of survivors = 10.11 mm
Mean beak depth of initial pop = 8.82 mm
Predicting the response to selection
Example: the large ground
finch, Geospiza magnirostris
Mean beak depth of survivors = 10.11 mm
Mean beak depth of initial pop = 8.82 mm
S = 10.11 – 8.82 = 1.29 mm
Predicting the response to selection
Example: the large ground
finch, Geospiza magnirostris
Mean beak depth of survivors = 10.11 mm
Mean beak depth of initial pop = 8.82 mm
S = 10.11 – 8.82 = 1.29 mm
h2 = 0.72
Predicting the response to selection
Example: the large ground
finch, Geospiza magnirostris
Mean beak depth of survivors = 10.11 mm
Mean beak depth of initial pop = 8.82 mm
S = 10.11 – 8.82 = 1.29 mm
h2 = 0.72
R = h2S = (1.29)(0.72) = 0.93 mm
Predicting the response to selection
Example: the large ground
finch, Geospiza magnirostris
Mean beak depth of survivors = 10.11 mm
Mean beak depth of initial pop = 8.82 mm
S = 10.11 – 8.82 = 1.29
h2 = 0.72
R = h2S = (1.29)(0.72) = 0.93
Beak depth next generation = 8.82 + 0.93 = 9.75 mm
The selective differential and the selective
gradient
The selective differential and the selective
gradient
The selective differential and the selective
gradient
Selective gradient = β = Selective differential (S)
Variance
What are heritability estimates in nature?
What are heritability estimates in nature?
Character
Body weight
Wing length
Tarsus length
Bill length
Bill depth
Bill width
Medium
Ground finch
0.91
0.84
0.71
0.65
0.79
0.90
• data from Boag (1983)
What are heritability estimates in nature?
Character
Body weight
Wing length
Tarsus length
Bill length
Bill depth
Bill width
Medium
Ground finch
0.91
0.84
0.71
0.65
0.79
0.90
Song
Sparrow
0.04
0.13
0.32
0.33
0.51
0.50
• data from Boag (1983) and Smith & Zach (1979)
What are heritability estimates in nature?
What are heritability estimates in nature?
Trait
Sample size
Mean h2
Std. Error
What are heritability estimates in nature?
Trait
Life history
Sample size
341
Mean h2
0.262
Std. error
0.012
What are heritability estimates in nature?
Trait
Sample size
Mean h2
Std. error
Life history
341
0.262
0.012
Physiological
104
0.330
0.027
What are heritability estimates in nature?
Trait
Sample size
Mean h2
Std. error
Life history
341
0.262
0.012
Physiological
104
0.330
0.027
Behavioral
105
0.302
0.023
What are heritability estimates in nature?
Trait
Sample size
Mean h2
Std. error
Life history
341
0.262
0.012
Physiological
104
0.330
0.027
Behavioral
105
0.302
0.023
Morphological
570
0.461
0.004
• data from Mousseau and Roff (1983)
Natural selection at the phenotypic level
1.  Directional selection
2. Stabilizing selection
3. Disruptive selection
Natural selection at the phenotypic level
1.  Directional selection
a form of selection favoring individuals at above or below
the mean.
-
this type of selection causes the trait to either increase or
decrease in magnitude and, as a result, reduces the
population variance.
- example: cranial capacity in early hominid evolution.
Directional selection changes the average value of a trait.
Normal distribution
During selection
Number of individuals
Before selection
After selection
Value of a trait
For example, directional selection caused overall
body size to increase in a cliff swallow population
40
35
30
25
Percentage of birds
20
Nonsurvivors
N = 1853
15
10
5
Difference in
average
0
40
Survivors
N = 1027
35
30
25
20
15
10
5
0
1
2
3
4
5
6
7
8
Body size class
9
10
11 12
Natural selection at the phenotypic level
2. Stabilizing selection
a form of selection favoring intermediate phenotypes.
-
this form of selection reduces variation but does not change
the trait’s mean.
-
example: birth weight in humans.
Stabilizing selection reduces the amount of variation in a trait.
Normal distribution
During selection
Number of individuals
Before selection
High fitness
After selection
Value of a trait
For example, very small and very large babies are most
likely to die, leaving a narrower distribution of birthweights.
100
20
50
Mortality
15
30
20
10
Heavy
mortality
on
extremes
10
7
5
5
3
2
0
1
2
3
4
5
7
6
8
Birthweight (pounds)
9
10
11
Percentage of mortality
Percentage of Population
70
Natural selection at the phenotypic level
3.  Disruptive selection
a form of selection favoring both extremes of the phenotypic
distribution.
-
this causes the variation of the trait to increase in the population.
-
example: beak length in African seedcracker finches.
Disruptive selection increases the amount of variation in a trait.
Normal distribution
During selection
Number of individuals
Before selection
Low fitness
After selection
Value of a trait
For example, only juvenile blackbellied seedcrackers with very long
or very short beaks survived long enough to breed.
Number of individuals
30
20
10
0
6
7
8
Beak length (mm)
9
10
11
Selection on quantitative traits
- the three forms of selection outlined above occur on what
are called quantitative or polygenic traits.
- quantitative traits differ from discrete traits in that it is
not possible to assign individuals into distinct classes.
Selection on quantitative traits
1.  vary in a continuous fashion among individuals
2. are controlled by many genetic loci.
3. are affected by both genetic and environmental factors.
-
to understand and predict the evolution of quantitative
characters, we must define an important
parameter called heritability.
Modes of selection on quantitative traits
Modes of selection on quantitative traits
Directional selection on oil content in corn
Modes of selection on quantitative traits
Stabilizing selection on gall size
Modes of selection on quantitative traits
Disruptive selection in black-bellied
seedcracker finches