Transcript modsel

Population Genetics
I. Basic Principles
II. X-linked Genes
III. Modeling Selection
A. Selection for a Dominant Allele
Population Genetics
I. Basic Principles
II. X-linked Genes
III. Modeling Selection
A. Selection for a Dominant Allele
p = 0.4, q = 0.6
AA
Aa
aa
Parental "zygotes"
0.16
0.48
0.36
= 1.00
Population Genetics
I. Basic Principles
II. X-linked Genes
III. Modeling Selection
A. Selection for a Dominant Allele
p = 0.4, q = 0.6
AA
Aa
aa
Parental "zygotes"
0.16
0.48
0.36
prob. of survival (fitness)
0.8
0.8
0.2
= 1.00
Population Genetics
I. Basic Principles
II. X-linked Genes
III. Modeling Selection
A. Selection for a Dominant Allele
p = 0.4, q = 0.6
AA
Aa
aa
Parental "zygotes"
0.16
0.48
0.36
prob. of survival (fitness)
0.8
0.8
0.2
Relative Fitness
1
1
0.25
= 1.00
Population Genetics
I. Basic Principles
II. X-linked Genes
III. Modeling Selection
A. Selection for a Dominant Allele
p = 0.4, q = 0.6
AA
Aa
aa
Parental "zygotes"
0.16
0.48
0.36
prob. of survival (fitness)
0.8
0.8
0.2
Relative Fitness
1
1
0.25
Survival to Reproduction
0.16
0.48
0.09
= 1.00
Population Genetics
I. Basic Principles
II. X-linked Genes
III. Modeling Selection
A. Selection for a Dominant Allele
p = 0.4, q = 0.6
AA
Aa
aa
Parental "zygotes"
0.16
0.48
0.36
prob. of survival (fitness)
0.8
0.8
0.2
Relative Fitness
1
1
0.25
Survival to Reproduction
0.16
0.48
0.09
= 1.00
= 0.73
Population Genetics
I. Basic Principles
II. X-linked Genes
III. Modeling Selection
A. Selection for a Dominant Allele
p = 0.4, q = 0.6
AA
Aa
aa
Parental "zygotes"
0.16
0.48
0.36
prob. of survival (fitness)
0.8
0.8
0.2
Relative Fitness
1
1
0.25
Survival to Reproduction
0.16
0.48
0.09
= 0.73
Geno. Freq., breeders
0.22
0.66
0.12
= 1.00
= 1.00
Population Genetics
I. Basic Principles
II. X-linked Genes
III. Modeling Selection
A. Selection for a Dominant Allele
p = 0.4, q = 0.6
AA
Aa
aa
Parental "zygotes"
0.16
0.48
0.36
prob. of survival (fitness)
0.8
0.8
0.2
Relative Fitness
1
1
0.25
Survival to Reproduction
0.16
0.48
0.09
= 0.73
Geno. Freq., breeders
0.22
0.66
0.12
= 1.00
Gene Freq's, gene pool
p = 0.55
q = 0.45
= 1.00
Population Genetics
I. Basic Principles
II. X-linked Genes
III. Modeling Selection
A. Selection for a Dominant Allele
p = 0.4, q = 0.6
AA
Aa
aa
Parental "zygotes"
0.16
0.48
0.36
prob. of survival (fitness)
0.8
0.8
0.2
Relative Fitness
1
1
0.25
Survival to Reproduction
0.16
0.48
0.09
= 0.73
Geno. Freq., breeders
0.22
0.66
0.12
= 1.00
Gene Freq's, gene pool
p = 0.55
Genotypes, F1
0.3025
= 1.00
q = 0.45
0.495
0.2025
= 100
III. Modeling Selection
A. Selection for a Dominant Allele
Δp = spq2/1-sq2
III. Modeling Selection
A. Selection for a Dominant Allele
Δp = spq2/1-sq2
- in our previous example, s = .75, p = 0.4, q = 0.6
III. Modeling Selection
A. Selection for a Dominant Allele
Δp = spq2/1-sq2
- in our previous example, s = .75, p = 0.4, q = 0.6
- Δp = (.75)(.4)(.36)/1-[(.75)(.36)] = . 108/.73 = 0.15
III. Modeling Selection
A. Selection for a Dominant Allele
Δp = spq2/1-sq2
- in our previous example, s = .75, p = 0.4, q = 0.6
- Δp = (.75)(.4)(.36)/1-[(.75)(.36)] = . 108/.73 = 0.15
p0 = 0.4, so p1 = 0.55 (check)
III. Modeling Selection
A. Selection for a Dominant Allele
Δp = spq2/1-sq2
III. Modeling Selection
A. Selection for a Dominant Allele
Δp = spq2/1-sq2
- next generation: (.75)(.55)(.2025)/1 - (.75)(.2025)
- = 0.084/0.85 = 0.1
III. Modeling Selection
A. Selection for a Dominant Allele
Δp = spq2/1-sq2
- next generation: (.75)(.55)(.2025)/1 - (.75)(.2025)
- = 0.084/0.85 = 0.1
- so:
III. Modeling Selection
A. Selection for a Dominant Allele
Δp = spq2/1-sq2
- next generation: (.75)(.55)(.2025)/1 - (.75)(.2025)
- = 0.084/0.85 = 0.1
- so:
p0 to p1 = 0.15
p1 to p2 = 0.1
III. Modeling Selection
A. Selection for a Dominant Allele
so, Δp declines with each generation.
III. Modeling Selection
A. Selection for a Dominant Allele
so, Δp declines with each generation.
BECAUSE: as q declines, a greater proportion of
q alleles are present in heterozygotes (and invisible to
selection). As q declines, q2 declines more rapidly...
III. Modeling Selection
A. Selection for a Dominant Allele
so, Δp declines with each generation.
BECAUSE: as q declines, a greater proportion of
q alleles are present in heterozygotes (and invisible to
selection). As q declines, q2 declines more rapidly...
So, in large populations, it is hard for selection to
completely eliminate a deleterious allele....
III. Modeling Selection
A. Selection for a Dominant Allele
B. Selection for an Incompletely Dominant Allele
B. Selection for an Incompletely Dominant Allele
p = 0.4, q = 0.6
AA
Aa
aa
Parental "zygotes"
0.16
0.48
0.36
prob. of survival (fitness)
0.8
0.4
0.2
Relative Fitness
1
0.5
0.25
Survival to Reproduction
0.16
0.24
0.09
= 0.49
Geno. Freq., breeders
0.33
0..50
0.17
= 1.00
Gene Freq's, gene pool
p = 0.58
Genotypes, F1
0.34
= 1.00
q = 0.42
0..48
0.18
= 100
B. Selection for an Incompletely Dominant Allele
- deleterious alleles can no longer hide in the
heterozygote; its presence always causes a reduction in
fitness, and so it can be eliminated from a population.
III. Modeling Selection
A. Selection for a Dominant Allele
B. Selection for an Incompletely Dominant Allele
C. Selection that Maintains Variation
C. Selection that Maintains Variation
1. Heterosis - selection for the heterozygote
p = 0.4, q = 0.6
AA
Aa
aa
Parental "zygotes"
0.16
0.48
0.36
prob. of survival (fitness)
0.4
0.8
0.2
Relative Fitness
0.5 (1-s) 1
0.25 (1-t)
Survival to Reproduction
0.08
0.48
0.09
= 0.65
Geno. Freq., breeders
0.12
0.74
0.14
= 1.00
Gene Freq's, gene pool
p = 0.49
Genotypes, F1
0.24
= 1.00
q = 0.51
0.50
0.26
= 100
C. Selection that Maintains Variation
1. Heterosis - selection for the heterozygote
- Consider an 'A" allele. It's probability of being
lost from the population is a function of:
C. Selection that Maintains Variation
1. Heterosis - selection for the heterozygote
- Consider an 'A" allele. It's probability of being
lost from the population is a function of:
1) probability it meets another 'A' (p)
C. Selection that Maintains Variation
1. Heterosis - selection for the heterozygote
- Consider an 'A" allele. It's probability of being
lost from the population is a function of:
1) probability it meets another 'A' (p)
2) rate at which these AA are lost (s).
C. Selection that Maintains Variation
1. Heterosis - selection for the heterozygote
- Consider an 'A" allele. It's probability of being
lost from the population is a function of:
1) probability it meets another 'A' (p)
2) rate at which these AA are lost (s).
- So, prob of losing an 'A' allele = ps
C. Selection that Maintains Variation
1. Heterosis - selection for the heterozygote
- Consider an 'A" allele. It's probability of being
lost from the population is a function of:
1) probability it meets another 'A' (p)
2) rate at which these AA are lost (s).
- So, prob of losing an 'A' allele = ps
- Likewise the probability of losing an 'a' = qt
C. Selection that Maintains Variation
1. Heterosis - selection for the heterozygote
- Consider an 'A" allele. It's probability of being
lost from the population is a function of:
1) probability it meets another 'A' (p)
2) rate at which these AA are lost (s).
- So, prob of losing an 'A' allele = ps
- Likewise the probability of losing an 'a' = qt
- An equilibrium will occur, when the probability
of losing A an a are equal; when ps = qt.
C. Selection that Maintains Variation
1. Heterosis - selection for the heterozygote
- An equilibrium will occur, when the probability
of losing A an a are equal; when ps = qt.
C. Selection that Maintains Variation
1. Heterosis - selection for the heterozygote
- An equilibrium will occur, when the probability
of losing A an a are equal; when ps = qt.
- substituting (1-p) for q, ps = (1-p)t
ps = t - pt
ps +pt = t
p(s + t) = t
peq = t/(s + t)
C. Selection that Maintains Variation
1. Heterosis - selection for the heterozygote
- An equilibrium will occur, when the probability
of losing A an a are equal; when ps = qt.
- substituting (1-p) for q, ps = (1-p)t
ps = t - pt
ps +pt = t
p(s + t) = t
peq = t/(s + t)
- So, for our example, t = 0.75, s = 0.5
- so, peq = .75/1.25 = 0.6
C. Selection that Maintains Variation
1. Heterosis - selection for the heterozygote
- so, peq = .75/1.25 = 0.6
p = 0.6, q = 0.4
AA
Aa
aa
Parental "zygotes"
0.36
0.48
0.16
prob. of survival (fitness)
0.4
0.8
0.2
Relative Fitness
0.5 (1-s) 1
0.25 (1-t)
Survival to Reproduction
0.18
0.48
0.04
= 0.70
Geno. Freq., breeders
0.26
0.68
0.06
= 1.00
Gene Freq's, gene pool
p = 0.6
q = 0.4
CHECK
Genotypes, F1
0.36
0.16
= 100
0.48
= 1.00
C. Selection that Maintains Variation
1. Heterosis - selection for the heterozygote
- so, peq = .75/1.25 = 0.6
- so, if p > 0.6, it should decline to this peq
p = 0.7, q = 0.3
AA
Aa
aa
Parental "zygotes"
0.49
0.42
0.09
prob. of survival (fitness)
0.4
0.8
0.2
Relative Fitness
0.5 (1-s) 1
0.25 (1-t)
Survival to Reproduction
0.25
0.48
0.02
= 0.75
Geno. Freq., breeders
0.33
0.64
0.03
= 1.00
Gene Freq's, gene pool
p = 0.65
q = 0.35
CHECK
Genotypes, F1
0.42
0.12
= 100
0.46
= 1.00
C. Selection that Maintains Variation
1. Heterosis - selection for the heterozygote
- so, peq = .75/1.25 = 0.6
- so, if p > 0.6, it should decline to this peq
0.6
C. Selection that Maintains Variation
1. Heterosis - selection for the heterozygote
2. Multiple Niche Polymorphism -
C. Selection that Maintains Variation
1. Heterosis - selection for the heterozygote
2. Multiple Niche Polymorphism -
- equilibrium can occur if AA and aa are each fit
in a given niche, within the population. The equilibrium
will depend on the relative frequencies of the niches and
the selection differentials...
C. Selection that Maintains Variation
1. Heterosis - selection for the heterozygote
2. Multiple Niche Polymorphism -
- equilibrium can occur if AA and aa are each fit
in a given niche, within the population. The equilibrium
will depend on the relative frequencies of the niches and
the selection differentials...
- can you think of an example??
C. Selection that Maintains Variation
1. Heterosis - selection for the heterozygote
2. Multiple Niche Polymorphism -
- equilibrium can occur if AA and aa are each fit
in a given niche, within the population. The equilibrium
will depend on the relative frequencies of the niches and
the selection differentials...
- can you think of an example??
Papilio butterflies... females mimic different
models and an equilibrium is maintained; in fact, an
equilibrium at each locus, which are also maintained in
linkage disequilibrium.
C. Selection that Maintains Variation
1. Heterosis - selection for the heterozygote
2. Multiple Niche Polymorphism
3. Frequency Dependent Selection
C. Selection that Maintains Variation
1. Heterosis - selection for the heterozygote
2. Multiple Niche Polymorphism
3. Frequency Dependent Selection
- the fitness depends on the frequency...
C. Selection that Maintains Variation
1. Heterosis - selection for the heterozygote
2. Multiple Niche Polymorphism
3. Frequency Dependent Selection
- the fitness depends on the frequency...
- as a gene becomes rare, it becomes
advantageous and is maintained in the population...
C. Selection that Maintains Variation
1. Heterosis - selection for the heterozygote
2. Multiple Niche Polymorphism
3. Frequency Dependent Selection
- the fitness depends on the frequency...
- as a gene becomes rare, it becomes
advantageous and is maintained in the population...
- "Rare mate" phenomenon...
- Morphs of Heliconius melpomene and H. erato
Mullerian complex between two distasteful species...
positive frequency dependence in both populations to
look like the most abundant morph
C. Selection that Maintains Variation
1. Heterosis - selection for the heterozygote
2. Multiple Niche Polymorphism
3. Frequency Dependent Selection
4. Selection Against the Heterozygote
p = 0.4, q = 0.6
AA
Aa
aa
Parental "zygotes"
0.16
0.48
0.36
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
= 1.00
4. Selection Against the Heterozygote
p = 0.4, q = 0.6
AA
Aa
aa
Parental "zygotes"
0.16
0.48
0.36
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
= 1.00
4. Selection Against the Heterozygote
- peq = t/(s + t)
p = 0.4, q = 0.6
AA
Aa
aa
Parental "zygotes"
0.16
0.48
0.36
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
= 1.00
4. Selection Against the Heterozygote
- peq = t/(s + t)
- here = .25/(.50 + .25) = .33
p = 0.4, q = 0.6
AA
Aa
aa
Parental "zygotes"
0.16
0.48
0.36
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
= 1.00
4. Selection Against the Heterozygote
- peq = t/(s + t)
- here = .25/(.50 + .25) = .33
- if p > 0.33, then it will keep increasing to
fixation.
p = 0.4, q = 0.6
AA
Aa
aa
Parental "zygotes"
0.16
0.48
0.36
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
= 1.00
4. Selection Against the Heterozygote
- peq = t/(s + t)
- here = .25/(.50 + .25) = .33
- if p > 0.33, then it will keep increasing to
fixation.
- However, if p < 0.33, then p will decline to zero...
AND THERE WILL BE FIXATION FOR A SUBOPTIMAL
ALLELE....'a'... !! UNSTABLE EQUILIBRIUM!!!!