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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.
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.
Heritability
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
- 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 0.98 (# of ridges) head width 0.95 height 0.84 blood pressure 0.70 IQ 0.55 twinning 0.52 handedness 0.32 body weight 0.05
Heritability
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 B1B2 B2B2
A1A1
A1A2
A2A2
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 Midparent value Offspring value
F1 x M1 4.34 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
← Slope = h2
Regress offspring value on midparent value
Heritability estimates from other regression analyses
Comparison Slope
Heritability estimates from other regression analyses
Comparison Slope Midparent-offspring h2
Heritability estimates from other regression analyses
Comparison Slope Midparent-offspring h2
Parent-offspring 1/2h2
Heritability estimates from other regression analyses
Comparison Slope Midparent-offspring h2
Parent-offspring 1/2h2
Half-sibs 1/4h2
Heritability estimates from other regression analyses
Comparison Slope Midparent-offspring h2
Parent-offspring 1/2h2
Half-sibs 1/4h2
First cousins 1/8h2
Heritability estimates from other regression analyses
Comparison Slope Midparent-offspring h2
Parent-offspring 1/2h2
Half-sibs 1/4h2
First cousins 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 h2
Parent-offspring 1/2h2
Half-sibs 1/4h2
First cousins 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?
Medium Character Ground finch
Body weight 0.91 Wing length 0.84 Tarsus length 0.71 Bill length 0.65 Bill depth 0.79 Bill width 0.90
• data from Boag (1983)
What are heritability estimates in nature?
Medium Song Character Ground finch Sparrow
Body weight 0.91 0.04 Wing length 0.84 0.13 Tarsus length 0.71 0.32 Bill length 0.65 0.33 Bill depth 0.79 0.51 Bill width 0.90 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 Sample size Mean h2 Std. error
Life history 341 0.262 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)
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.
Natural selection at the phenotypic level
After selection
During selection N
umbe
r of i
ndiv
idua
ls
Before selection
Normal distribution
Directional selection changes the average value of a trait.
Value of a trait
Body size class
Perc
enta
ge o
f bird
s
40 35
30
25
20
15
10
5
0
40
35
30
25
20
15
10
5
0
Difference in average
1 2 3 4 5 7 8 9 10 11 12 6
Survivors N = 1027
Nonsurvivors N = 1853
For example, directional selection caused overall body size to increase in a cliff swallow population
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.
Natural selection at the phenotypic level
Normal distribution
High fitness
Value of a trait
Num
ber o
f ind
ivid
uals
After selection
During selection
Before selection
Stabilizing selection reduces the amount of variation in a trait.
20
15
10
5
0 1 2 3 4 5 6 7 8 9 10 11
2
3
5
7
10
20
30
50
70
100
Birthweight (pounds)
Percentage of mortality
Perc
enta
ge o
f Pop
ulat
ion
Heavy mortality on extremes
Mortality
For example, very small and very large babies are most likely to die, leaving a narrower distribution of birthweights.
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.
Natural selection at the phenotypic level
Value of a trait
Low fitness
Normal distribution
Before selection
During selection
After selection
Num
ber o
f ind
ivid
uals
Disruptive selection increases the amount of variation in a trait.
6 7 11 10 8 9
Beak length (mm)
10
0
20
30
Num
ber o
f ind
ivid
uals
For example, only juvenile blackbellied seedcrackers with very long or very short beaks survived long enough to breed.
- 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.
Selection on quantitative traits
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