IV. Selection and Other Factors A. Mutation

IV. Selection and Other Factors

A. Mutation


A. Mutation

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


A. Mutation


q(eq) = √(m/s)


A. Mutation


q(eq) = √(m/s)

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


A. Mutation

B. Drift and "Adaptive Landscapes"

1. Single Loci

- consider a locus with selection against the heterozygote

p = 0.4, q = 0.6 AA Aa aa

Parental "zygotes" 0.16 0.48 0.36 = 1.00

prob. of survival (fitness) 0.8 0.4 0.6

Relative Fitness 1 0.5 0.75

Corrected Fitness 1 + 0.5 1.0 1 + 0.25

formulae 1 + s 1 + t

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


A. Mutation


1. Single Loci


p = 0.4, q = 0.6 AA Aa aa

Parental "zygotes" 0.16 0.48 0.36 = 1.00

prob. of survival (fitness) 0.8 0.4 0.6

Relative Fitness 1 0.5 0.75

Corrected Fitness 1 + 0.5 1.0 1 + 0.25

formulae 1 + s 1 + t

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


A. Mutation


1. Single Loci


mea

n f

itn

ess

0 0.33 1.0

1.0

0.75


A. Mutation


1. Single Loci

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

mea

n f

itn

ess

0 0.33 1.0

1.0

0.75


A. Mutation


1. Single Loci

mea

n f

itn

ess

0 0.33 1.0

1.0

0.75

- 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).


A. Mutation


1. Single Loci

mea

n f

itn

ess

0 0.33 1.0

1.0

0.75

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


A. Mutation


1. Single Loci

mea

n f

itn

ess

0 0.33 1.0

1.0

0.75

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


A. Mutation


1. Single Loci

mea

n f

itn

ess

0 0.33 1.0

1.0

0.75

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


A. Mutation


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.

f(A)

1.0

1.0f(B)


A. Mutation



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

f(A)

1.0

1.0f(B)


A. Mutation



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

f(A)

1.0

1.0f(B)


A. Mutation


- 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...

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



- 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.



- 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).



- 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.



- 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".


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




- Suppose: f(A) = p1 and f(a) = q1 f(B) = p2 and f(b) = q2 - Expected frequency of AB haplotype (gamete) = a = p1*p2




- 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




- 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….




- 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.




- 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).



1. A two-Locus Equilibrium Model2. Deviations from "Linkage" Equilibrium



1. A two-Locus Equilibrium Model2. 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" Equilibrium1. A two-Locus Equilibrium Model2. Deviations from "Linkage" Equilibrium3. Causes of Linkage Disequilibrium


- Linkage!! without sufficient time to equilibrate haplotype frequencies


- 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.


- Linkage!!! without sufficient time to equilibrate haplotype frequencies. - Selection: Some haplotypes occur more frequently than random because these combos confer a selective advantage.



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.





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.





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.

Toxic Models On Left

Papilio memnon (palatable) females

ttcc

TTCC

ttcc

Papilio memnon male

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 = .5f(t) = q1 = .5f(C) = p2 = .5f(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




If allelic effects are multiplicative or additive (like the size example), then the system will proceed to equilibrium.




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:

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(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


- Linkage!!! without sufficient time to equilibrate haplotype frequencies. - Selection: Some haplotypes occur more frequently than random because these combos confer a selective advantage. - Drift:


- 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.


- 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:


- 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" Equilibrium1. A two-Locus Equilibrium Model2. Deviations from "Linkage" Equilibrium3. Causes of Linkage Disequilibrium4. 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.


- 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" Equilibrium1. A two-Locus Equilibrium Model2. Deviations from "Linkage" Equilibrium3. Causes of Linkage Disequilibrium4. Effects5. The Utility of Linkage Disequilibrium

B. "Linkage" Equilibrium1. A two-Locus Equilibrium Model2. Deviations from "Linkage" Equilibrium3. Causes of Linkage Disequilibrium4. Effects5. 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!!!

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IV. Selection and Other Factors A. Mutation