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 = 1.00

prob. of survival (fitness) 0.8 0.8 0.2

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

prob. of survival (fitness) 0.8 0.8 0.2

Relative Fitness 1 1 0.25

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

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

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

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

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

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

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

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

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

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

Genotypes, F1 0.3025 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 = 1.00

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 q = 0.42

Genotypes, F1 0.34 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 = 1.00

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 q = 0.51

Genotypes, F1 0.24 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)tps = t - ptps +pt = tp(s + t) = tpeq = 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)tps = t - ptps +pt = tp(s + t) = tpeq = 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 = 1.00

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 0.48 0.16 = 100

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 = 1.00

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 0.46 0.12 = 100

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 = 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

4. 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

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 = 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

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 = 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

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 = 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

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!!!!