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IV. Selection and Other Factors A. Mutation. IV. Selection and Other Factors A. Mutation - Mutation can maintain a deleterious allele in the population against the effects of selection, such that:. IV. Selection and Other Factors A. Mutation

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slide2

IV. Selection and Other Factors

A. Mutation

- Mutation can maintain a deleterious allele in the population against the effects of selection, such that:

slide3

IV. Selection and Other Factors

A. Mutation

- Mutation can maintain a deleterious allele in the population against the effects of selection, such that:

q(eq) = √(m/s)

slide4

IV. Selection and Other Factors

A. Mutation

- Mutation can maintain a deleterious allele in the population against the effects of selection, such that:

q(eq) = √(m/s)

- more deleterious alleles are maintained if m increases, or if selection differential declines... this should make sense.

slide5

IV. Selection and Other Factors

A. Mutation

B. Drift and "Adaptive Landscapes"

1. Single Loci

- consider a locus with selection against the heterozygote

peq = t/(s + t) = .25/.75 = 0.33

slide6

IV. Selection and Other Factors

A. Mutation

B. Drift and "Adaptive Landscapes"

1. Single Loci

- consider a locus with selection against the heterozygote

peq = t/(s + t) = .25/.75 = 0.33

slide7

IV. Selection and Other Factors

A. Mutation

B. Drift and "Adaptive Landscapes"

1. Single Loci

- consider a locus with selection against the heterozygote

1.0

0.75

mean fitness

1.0

0

0.33

slide8

IV. Selection and Other Factors

A. Mutation

B. Drift and "Adaptive Landscapes"

1. Single Loci

- suppose there is random movement up the \'wrong\' slope?

1.0

0.75

mean fitness

1.0

0

0.33

slide9

IV. Selection and Other Factors

A. Mutation

B. Drift and "Adaptive Landscapes"

1. Single Loci

1.0

- if this is a large pop with no drift, the population will become fixed on the \'suboptimal\' peak, (p = 0, q = 1.0, w = 0.75).

0.75

mean fitness

1.0

0

0.33

slide10

IV. Selection and Other Factors

A. Mutation

B. Drift and "Adaptive Landscapes"

1. Single Loci

1.0

- BUT if it is small, then drift may be important... because only DRIFT can randomly BOUNCE the gene freq\'s to the other slope!

0.75

mean fitness

1.0

0

0.33

slide11

IV. Selection and Other Factors

A. Mutation

B. Drift and "Adaptive Landscapes"

1. Single Loci

1.0

- And then selection can push the pop up the most adaptive slope!

0.75

mean fitness

1.0

0

0.33

slide12

IV. Selection and Other Factors

A. Mutation

B. Drift and "Adaptive Landscapes"

1. Single Loci

1.0

- The more shallow the \'maladaptive valley\', (representing weaker selection differentials) the easier it is for drift to cross it...

0.75

mean fitness

1.0

0

0.33

slide13

IV. Selection and Other Factors

A. Mutation

B. Drift and "Adaptive Landscapes"

2. Two Loci - create a 3-D landscape, with "mean fitness" as the \'topographic relief"

Suppose AAbb and aaBB work well, but combinations of the other two do not.

1.0

f(A)

1.0

f(B)

slide14

IV. Selection and Other Factors

A. Mutation

B. Drift and "Adaptive Landscapes"

2. Two Loci - create a 3-D landscape, with "mean fitness" as the \'topographic relief"

Again, strong selection or weak drift will cause mean fitness to move up nearest slopes.

1.0

f(A)

1.0

f(B)

slide15

IV. Selection and Other Factors

A. Mutation

B. Drift and "Adaptive Landscapes"

2. Two Loci - create a 3-D landscape, with "mean fitness" as the \'topographic relief"

Only strong drift or weak selection and some drift (shallow valley) can cause the population to cross the maladaptive valley.

1.0

f(A)

1.0

f(B)

slide16

IV. Selection and Other Factors

A. Mutation

B. Drift and "Adaptive Landscapes"

- so, the interactions between drift and selection are necessary for a population to find the optimal adaptive peak... think about this in the context of peripatric speciation.... THINK HARD about this...

slide18

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

slide19

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.

slide20

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).

slide21

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.

slide22

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".

slide23

III. Modelling Effects at Multiple Loci

A. The Complex Phenotype

B. "Linkage" Equilibrium

slide24

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

slide25

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

slide26

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

slide27

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….

slide28

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.

slide29

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).

slide30

III. Modelling Effects at Multiple Loci

A. The Complex Phenotype

B. "Linkage" Equilibrium

1. A two-Locus Equilibrium Model

2. Deviations from "Linkage" Equilibrium

slide31

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.

slide32

B. "Linkage" Equilibrium

1. A two-Locus Equilibrium Model

2. Deviations from "Linkage" Equilibrium

3. Causes of Linkage Disequilibrium

slide33

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

slide34

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.

slide35

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".

slide36

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.

slide37

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 tailless model.

slide38

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.

slide39

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.

slide40

Papilio memnon (palatable) females

ttcc

TTCC

ttcc

Toxic Models On Left

Papilio memnon male

slide41

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

D = ad - bc = .25 - 0 = 0.25.... not in equilibrium

slide42

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.

slide43

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.

slide44

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

f(b) = q2 = 1.0

D = ad - bc = 0 - 0 = 0.... in equilibrium

slide45

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:

slide46

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.

slide47

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:

slide48

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.

slide49

B. "Linkage" Equilibrium

1. A two-Locus Equilibrium Model

2. Deviations from "Linkage" Equilibrium

3. Causes of Linkage Disequilibrium

4. Effects

slide50

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.

slide51

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.

slide52

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

slide53

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.

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