III. Modelling Effects at Multiple Loci
III. Modelling Effects at Multiple Loci
A. The Complex Phenotype
- traits are often influenced by more than one locus, and their effects are not
necessarily independent. In other words, there are often epistatic interactions
between loci...the value of an allele may depend on the genotype at other loci
III. Modelling Effects at Multiple Loci
A. The Complex Phenotype
- traits are often influenced by more than one locus, and their effects are not
necessarily independent. In other words, there are often epistatic interactions
between loci...the value of an allele may depend on the genotype at other loci
- For example, suppose 'A' and 'B' each contribute a unit of growth, and
suppose there is selection for intermediate size.
III. Modelling Effects at Multiple Loci
A. The Complex Phenotype
- traits are often influenced by more than one locus, and their effects are not
necessarily independent. In other words, there are often epistatic interactions
between loci ...the value of an allele may depend on the genotype at other loci
- For example, suppose 'A' and 'B' each contribute a unit of growth, and
suppose there is selection for intermediate size.
- There will be three adaptive genotypes: AAbb, AaBb, and aaBB that each
have two alleles for growth (0,1,3, and 4 create larger and smaller organisms
that are at a selection disadvantage in this example).
III. Modelling Effects at Multiple Loci
A. The Complex Phenotype
- traits are often influenced by more than one locus, and their effects are not
necessarily independent. In other words, there are often epistatic interactions
between loci... the value of an allele may depend on the genotype at other loci
- For example, suppose 'A' and 'B' each contribute a unit of growth, and
suppose there is selection for intermediate size.
- There will be three adaptive genotypes: AAbb, AaBb, and aaBB that each
have two alleles for growth (0,1,3, and 4 create larger and smaller organisms
that are at a selection disadvantage in this example).
- However, a population full of heterozygotes is impossible, the population
will either move to "fixation" at AAbb OR aaBB.
III. Modelling Effects at Multiple Loci
A. The Complex Phenotype
- traits are often influenced by more than one locus, and their effects are not
necessarily independent. In other words, there are often epistatic interactions
between loci... the value of an allele may depend on the genotype at other loci
- For example, suppose 'A' and 'B' each contribute a unit of growth, and
suppose there is selection for intermediate size.
- There will be three adaptive genotypes: AAbb, AaBb, and aaBB that each
have two alleles for growth (0,1,3, and 4 create larger and smaller organisms
that are at a selection disadvantage in this example).
- However, a population full of heterozygotes is impossible, the population
will either move to "fixation" at AAbb OR aaBB.
- So, is an "aa" genotype good or bad? Well, it depends on what's happening
at "B".
III. Modelling Effects at Multiple Loci
A. The Complex Phenotype
B. "Linkage" Equilibrium
III. Modelling Effects at Multiple Loci
A. The Complex Phenotype
B. "Linkage" Equilibrium
1. A two-Locus Equilibrium Model
- Suppose: f(A) = p1 and f(a) = q1 f(B) = p2 and f(b) = q2
III. Modelling Effects at Multiple Loci
A. The Complex Phenotype
B. "Linkage" Equilibrium
1. A two-Locus Equilibrium Model
- Suppose: f(A) = p1 and f(a) = q1 f(B) = p2 and f(b) = q2
- Expected frequency of AB haplotype (gamete) = a = p1*p2
III. Modelling Effects at Multiple Loci
A. The Complex Phenotype
B. "Linkage" Equilibrium
1. A two-Locus Equilibrium Model
- Suppose: f(A) = p1 and f(a) = q1 f(B) = p2 and f(b) = q2
- Expected frequency of AB haplotype (gamete) = a = p1*p2
f(Ab) = b = p1q2
f(aB) = c = q1p2
f(ab) = d = q2q2
III. Modelling Effects at Multiple Loci
A. The Complex Phenotype
B. "Linkage" Equilibrium
1. A two-Locus Equilibrium Model
- In essence, this becomes the equilibrium model for two loci; when a
population reaches linkage equilibrium, the frequency of haplotypes will be
equal to the product of the independent gene frequencies….
III. Modelling Effects at Multiple Loci
A. The Complex Phenotype
B. "Linkage" Equilibrium
1. A two-Locus Equilibrium Model
- In essence, this becomes our equilibrium model for two loci.
- TWO LOCI, EVEN IF THEY ARE CLOSELY LINKED, WILL CROSS-OVER
OCCASIONALLY. OVER TIME, EVEN WITH CLOSELY LINKED GENES, THE
FREQUENCIES OF HAPLOTYPES WILL REACH THE ‘EQUILIBRIUM’ VALUES
(ACTING LIKE THEY ASSORT INDEPENDENTLY) IF PANMIXIA OCCURS.
III. Modelling Effects at Multiple Loci
A. The Complex Phenotype
B. "Linkage" Equilibrium
1. A two-Locus Equilibrium Model
- In essence, this becomes our HWE model for two loci.
- TWO LOCI, EVEN IF THEY ARE CLOSELY LINKED, WILL CROSS-OVER
OCCASIONALLY. OVER TIME, EVEN WITH CLOSELY LINKED GENES, THE
FREQUENCIES OF HAPLOTYPES WILL REACH EQUILIBRIUM IF PANMIXIA
OCCURS.
- So, recombination drives a population towards equilibrium. The rate
depends on the distance between loci. (Neighboring loci take longer to
equilibrate because less crossing over occurs each generation).
III. Modelling Effects at Multiple Loci
A. The Complex Phenotype
B. "Linkage" Equilibrium
1. A two-Locus Equilibrium Model
2. Deviations from "Linkage" Equilibrium
III. Modelling Effects at Multiple Loci
A. The Complex Phenotype
B. "Linkage" Equilibrium
1. A two-Locus Equilibrium Model
2. Deviations from "Linkage" Equilibrium
- Linkage DISequilibrium is measured as "D"
D = ad - bc.
If D = 0, the pop is in equilibrium.
If D is not zero, then D becomes a measure of deviation from the equilibrium.
B. "Linkage" Equilibrium
1. A two-Locus Equilibrium Model
2. Deviations from "Linkage" Equilibrium
3. Causes of Linkage Disequilibrium
B. "Linkage" Equilibrium
1. A two-Locus Equilibrium Model
2. Deviations from "Linkage" Equilibrium
3. Causes of Linkage Disequilibrium
- Linkage!! without sufficient time to equilibrate haplotype frequencies
B. "Linkage" Equilibrium
1. A two-Locus Equilibrium Model
2. Deviations from "Linkage" Equilibrium
3. Causes of Linkage Disequilibrium
- Linkage!!! without sufficient time to equilibrate haplotype frequencies.
- Selection: Some haplotypes occur more frequently than random because
these combos confer a selective advantage.
B. "Linkage" Equilibrium
1. A two-Locus Equilibrium Model
2. Deviations from "Linkage" Equilibrium
3. Causes of Linkage Disequilibrium
- Linkage!!! without sufficient time to equilibrate haplotype frequencies.
- Selection: Some haplotypes occur more frequently than random because
these combos confer a selective advantage.
Curiously, selection will only create linkage disequilibrium if the alleles act
"epistatically".
B. "Linkage" Equilibrium
1. A two-Locus Equilibrium Model
2. Deviations from "Linkage" Equilibrium
3. Causes of Linkage Disequilibrium
- Linkage!!! without sufficient time to equilibrate haplotype frequencies.
- Selection: Some haplotypes occur more frequently than random because
these combos confer a selective advantage.
Curiously, selection will only create linkage disequilibrium if the alleles act
"epistatically".
Papilio memnon - females mimic different model species.
B. "Linkage" Equilibrium
1. A two-Locus Equilibrium Model
2. Deviations from "Linkage" Equilibrium
3. Causes of Linkage Disequilibrium
- Linkage!!! without sufficient time to equilibrate haplotype frequencies.
- Selection: Some haplotypes occur more frequently than random because
these combos confer a selective advantage.
Curiously, selection will only create linkage disequilibrium if the alleles act
"epistatically".
Papilio memnon - females mimic different model species.
In the simplest terms:
T (swallowTAIL) > t (no tail) and
C >c, where CC, Cc is coloration for a tailed model and
cc is coloration for a tailess model.
B. "Linkage" Equilibrium
1. A two-Locus Equilibrium Model
2. Deviations from "Linkage" Equilibrium
3. Causes of Linkage Disequilibrium
- Linkage!!! without sufficient time to equilibrate haplotype frequencies.
- Selection: Some haplotypes occur more frequently than random because
these combos confer a selective advantage.
Curiously, selection will only create linkage disequilibrium if the alleles act
"epistatically".
Papilio memnon - females mimic different model species.
In the simplest terms:
T (swallowTAIL) > t (no tail) and
C >c, where CC, Cc is coloration for a tailed model and
cc is coloration for a tailess model.
So, fitness at t locus depends on the fitness at the C locus. If CC is
advantageous, then TT is, too. If cc is advantageous, then TT is NOT. So,
fitness at T depends on fitness at C.
B. "Linkage" Equilibrium
1. A two-Locus Equilibrium Model
2. Deviations from "Linkage" Equilibrium
3. Causes of Linkage Disequilibrium
- Linkage!!! without sufficient time to equilibrate haplotype frequencies.
- Selection: Some haplotypes occur more frequently than random because
these combos confer a selective advantage.
Curiously, selection will only create linkage disequilibrium if the alleles act
"epistatically".
Papilio memnon - females mimic different model species.
In the simplest terms:
T (swallowTAIL) > t (no tail) and
C >c, where CC, Cc is coloration for a tailed model and
cc is coloration for a tailess model.
So, fitness at t locus depends on the fitness at the C locus. If CC is
advantageous, then TT is, too. If cc is advantageous, then TT is NOT. So,
fitness at T depends on fitness at C.
So, TC haplotype and tc haplotypes will dominate in a constant
disequilibrium.
In the simplest terms:
T (swallowTAIL) > t (no tail) and
C >c, where CC, Cc is coloration for a tailed model and
cc is coloration for a tailless model.
So, fitness at t locus depends on the fitness at the C locus. If CC is
advantageous, then TT is, too. If cc is advantageous, then TT is NOT. So,
fitness at T depends on fitness at C.
So, TC haplotype and tc haplotypes will dominate in a constant
disequilibrium.
f(T) = p1 = .5
f(t) = q1 = .5
f(C) = p2 = .5
f(c) = q2 = .5
Expected
Observed
a = p1*p2
.25
.5
b = p1*q2
.25
0
c = q1*p2
.25
0
d = q1*q2
.25
.5
D = ad - bc = .25 - 0 = 0.25.... not in equilibrium
B. "Linkage" Equilibrium
1. A two-Locus Equilibrium Model
2. Deviations from "Linkage" Equilibrium
3. Causes of Linkage Disequilibrium
- Linkage!!! without sufficient time to equilibrate haplotype frequencies.
- Selection: Some haplotypes occur more frequently than random because
these combos confer a selective advantage.
Curiously, selection will only create linkage disequilibrium if the alleles act
"epistatically".
If allelic effects are multiplicative or additive (like the size example), then the
system will proceed to equilibrium.
B. "Linkage" Equilibrium
1. A two-Locus Equilibrium Model
2. Deviations from "Linkage" Equilibrium
3. Causes of Linkage Disequilibrium
- Linkage!!! without sufficient time to equilibrate haplotype frequencies.
- Selection: Some haplotypes occur more frequently than random because
these combos confer a selective advantage.
Curiously, selection will only create linkage disequilibrium if the alleles act
"epistatically".
If allelic effects are multiplicative or additive (like the size example), then the
system will proceed to equilibrium.
In the case of size, it goes to fixation for AAbb or aaBB, each of which is ad bc = 0 = linkage equilibrium. So selection, in this case, does NOT create a
disequilibrium.
In the case of size, if goes to fixation for AAbb or aaBB, each of which is ad bc = 0 = linkage equilibrium. So selection, in this case, does NOT create a
disequilibrium.
For example, if the population fixes at AAbb:
f(A) = p1 = 1.0
f(a) = q1 = 0.0
f(B) = p2 = 0.0
Expected
Observed
a = p1*p2
0.0
0
b = p1*q2
1.0
1.0
c = q1*p2
0.0
0
d = q1*q2
0.0
0
f(b) = q2 = 1.0
D = ad - bc = 0 - 0 = 0.... in equilibrium
B. "Linkage" Equilibrium
1. A two-Locus Equilibrium Model
2. Deviations from "Linkage" Equilibrium
3. Causes of Linkage Disequilibrium
- Linkage!!! without sufficient time to equilibrate haplotype frequencies.
- Selection: Some haplotypes occur more frequently than random because
these combos confer a selective advantage.
- Drift:
B. "Linkage" Equilibrium
1. A two-Locus Equilibrium Model
2. Deviations from "Linkage" Equilibrium
3. Causes of Linkage Disequilibrium
- Linkage!!! without sufficient time to equilibrate haplotype frequencies.
- Selection: Some haplotypes occur more frequently than random because
these combos confer a selective advantage.
- Drift: Random fluctuation in the relative frequencies of haplotypes can cause
disequilibrium.
B. "Linkage" Equilibrium
1. A two-Locus Equilibrium Model
2. Deviations from "Linkage" Equilibrium
3. Causes of Linkage Disequilibrium
- Linkage!!! without sufficient time to equilibrate haplotype frequencies.
- Selection: Some haplotypes occur more frequently than random because
these combos confer a selective advantage.
- Drift: Random fluctuation in the relative frequencies of haplotypes can cause
disequilibrium.
- Non-random mating:
B. "Linkage" Equilibrium
1. A two-Locus Equilibrium Model
2. Deviations from "Linkage" Equilibrium
3. Causes of Linkage Disequilibrium
- Linkage!!! without sufficient time to equilibrate haplotype frequencies.
- Selection: Some haplotypes occur more frequently than random because
these combos confer a selective advantage.
- Drift: Random fluctuation in the relative frequencies of haplotypes can cause
disequilibrium.
- Non-random mating: If A individuals preferentially mate with B individuals,
then AB will be more frequent than expected by chance.
B. "Linkage" Equilibrium
1. A two-Locus Equilibrium Model
2. Deviations from "Linkage" Equilibrium
3. Causes of Linkage Disequilibrium
4. Effects
B. "Linkage" Equilibrium
1. A two-Locus Equilibrium Model
2. Deviations from "Linkage" Equilibrium
3. Causes of Linkage Disequilibrium
4. Effects
- Hitchhiking - selection at one locus can drive changes in linked genes
before recombination eliminates disequilibrium. This can work to prevent the
acquisition of advantageous alleles at a locus if it is closely linked to a
deleterious allele at a second locus. However, this effect declines as the
distance between genes (and thus the rate of recombination) increases.
B. "Linkage" Equilibrium
1. A two-Locus Equilibrium Model
2. Deviations from "Linkage" Equilibrium
3. Causes of Linkage Disequilibrium
4. Effects
- Hitchhiking - selection at one locus can drive changes in linked genes
before recombination eliminates disequilibrium. This can work to prevent the
acquisition of advantageous alleles at a locus if it is closely linked to a
deleterious allele at a second locus. However, this effect declines as the
distance between genes (and thus the rate of recombination) increases.
B. "Linkage" Equilibrium
1. A two-Locus Equilibrium Model
2. Deviations from "Linkage" Equilibrium
3. Causes of Linkage Disequilibrium
4. Effects
5. The Utility of Linkage Disequilibrium
B. "Linkage" Equilibrium
1. A two-Locus Equilibrium Model
2. Deviations from "Linkage" Equilibrium
3. Causes of Linkage Disequilibrium
4. Effects
5. The Utility of Linkage Disequilibrium
- By examining whether an allele is in disequ with a neutral marker, we can
draw inferences about its selective value. For example, if an allele is in
disequ, we can infer it is relatively new (or recombination would have reduced
the disequ), or it is probably of selective value.
OK!!!