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Deviations from HWE
I. Mutation
II. Migration
III. Non-Random Mating
IV. Genetic Drift - Sampling Error
V. Selection
Deviations from HWE
I. Mutation
II. Migration
III. Non-Random Mating
IV. Genetic Drift - Sampling Error
V. Selection
1. Measuring “fitness” – differential reproductive success
Deviations from HWE
I. Mutation
II. Migration
III. Non-Random Mating
IV. Genetic Drift - Sampling Error
V. Selection
1. Measuring “fitness” – differential reproductive success
a. The mean number of reproducing offspring (or females)/female
Deviations from HWE
I. Mutation
II. Migration
III. Non-Random Mating
IV. Genetic Drift - Sampling Error
V. Selection
1. Measuring “fitness” – differential reproductive success
a. The mean number of reproducing offspring (or females)/female
b. Components of fitness:
Deviations from HWE
I. Mutation
II. Migration
III. Non-Random Mating
IV. Genetic Drift - Sampling Error
V. Selection
1. Measuring “fitness” – differential reproductive success
a. The mean number of reproducing offspring (or females)/female
b. Components of fitness
- probability of female surviving to reproductive age
Deviations from HWE
I. Mutation
II. Migration
III. Non-Random Mating
IV. Genetic Drift - Sampling Error
V. Selection
1. Measuring “fitness” – differential reproductive success
a. The mean number of reproducing offspring (or females)/female
b. Components of fitness
- probability of female surviving to reproductive age
- number of offspring the female produces
Deviations from HWE
I. Mutation
II. Migration
III. Non-Random Mating
IV. Genetic Drift - Sampling Error
V. Selection
1. Measuring “fitness” – differential reproductive success
a. The mean number of reproducing offspring (or females)/female
b. Components of fitness
- probability of female surviving to reproductive age
- number of offspring the female produces
- probability that offspring survive to reproductive age
Deviations from HWE
I. Mutation
II. Migration
III. Non-Random Mating
IV. Genetic Drift - Sampling Error
V. Selection
1. Measuring “fitness” – differential reproductive success
a. The mean number of reproducing offspring (or females)/female
b. Components of fitness
- probability of female surviving to reproductive age
- number of offspring the female produces
- probability that offspring survive to reproductive age
c. With a limited energy budget, selection cannot maximize all three
components… there will necessarily be TRADE-OFFS.
5. Selection
1. Measuring “fitness” – differential reproductive success
2. Relationships with Energy Budgets
5. Selection
1. Measuring “fitness” – differential reproductive success
2. Relationships with Energy Budgets
GROWTH
METABOLISM
REPRODUCTION
5. Selection
1. Measuring “fitness” – differential reproductive success
2. Relationships with Energy Budgets
Maximize probability of survival
Maximize reproduction
GROWTH
GROWTH
METABOLISM
REPRODUCTION
METABOLISM
REPRODUCTION
5. Selection
1. Measuring “fitness” – differential reproductive success
2. Relationships with Energy Budgets
Trade-offs within reproduction
REPRODUCTION
METABOLISM
REPRODUCTION
METABOLISM
Lots of small, low
prob of survival
A few large, high
prob of survival
5. Selection
1. Measuring “fitness” – differential reproductive success
2. Relationships with Energy Budgets
3. Modeling Selection
5. Modeling Selection
Selection for a Dominant Allele
p = 0.4, q = 0.6
AA
Aa
aa
Parental "zygotes"
0.16
0.48
0.36
= 1.00
3. Modeling Selection
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
3. Modeling Selection
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 (ω)
1
1
0.25
= 1.00
3. Modeling Selection
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 (ω)
1
1
0.25
Survival to Reproduction
0.16
0.48
0.09
= 1.00
3. Modeling Selection
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
This = “mean fitness of
the population” (ω)
3. Modeling Selection
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
3. Modeling Selection
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
3. Modeling Selection
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
3. Modeling Selection
Selection for a Dominant Allele
Δp declines with each generation.
3. Modeling Selection
Selection for a Dominant Allele
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...
3. Modeling Selection
Selection for a Dominant Allele
Δp declines with each generation.
So, in large populations, it is
hard for selection to
completely eliminate a
deleterious allele....
3. Modeling Selection
Selection for a Dominant Allele
Δp declines with each generation.
Also, this means that in
different populations with
different gene frequencies,
the rate at which p changes
will vary (even though the
relative fitness differences
are the same)
3. Modeling Selection
Selection for a Dominant Allele
Δp declines with each generation.
Rate of change also depends on the strength of selection;
the difference in reproductive success among genotypes.
3. Modeling Selection
Selection for a Dominant Allele
Selection for an Incompletely Dominant Allele
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
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.
In this case, the beneficial allele is said to have an
‘additive’ effect, because one dose is ‘good’ but two
doses in the homozygote is ‘better’.
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
q = 0.51
0.50
0.26
Maintains both genes in
the gene pool
peq = t/s+t
= 0.75/1.25 = 0.6
AA
= 1.00
Aa
aa
= 100
Maintains both genes in
the gene pool
peq = t/s+t
= 0.75/1.25 = 0.6
Heterosis - selection for the heterozygote
Sickle cell caused by a SNP of valine for glutamic acid
at the 6th position in the beta globin protein in
hemoglobin (147 amino acids long).
NN
NS
SS
The malarial parasite (Plasmodium falciparum) cannot
complete development in red blood cells with this
hemoglobin, because O2 levels are too low in these
cells.
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
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
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
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
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!!!!
E. Selection
1. Measuring “fitness” – differential reproductive success
2. Relationships with Energy Budgets
3. Modeling Selection
4. Types of Selection
E. Selection
4. Types of Selection - Directional
E. Selection
4. Types of Selection - Directional
E. Selection
4. Types of Selection - Stabilizing
E. Selection
4. Types of Selection - Disruptive
Lab experiment – “bidirectional
selection” – create two lines by
directionally selecting for extremes.
Populations are ‘isolated’ and don’t
reproduce.
E. Selection
4. Types of Selection - Disruptive
African Fire-Bellied Seed Crackers
E. Selection
1. Measuring “fitness” – differential reproductive success
2. Relationships with Energy Budgets
3. Modeling Selection
4. Types of Selection
5. Frequency-Dependent Selection
The selective value depends on the frequency of the
allele/phenotype in the population.
“rare mate phenomenon” = negative frequency dependence
Elderflower orchids:
- don’t produce nectar
- bumblebees visit most common flower
color and get discouraged, try the other
color…. Back and forth.
- visit equal NUMBERS of the two
colors, but that means that a greater
proportion of the rarer flower color is
visited.
As phenotype gets rare, fitness
increases. Maintains alleles in
population
(of yellow flowers)
- 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 in a given area
E. Selection
1. Measuring “fitness” – differential reproductive success
2. Relationships with Energy Budgets
3. Modeling Selection
4. Types of Selection
5. Interactive Effects
E. Selection
1. Measuring “fitness” – differential reproductive success
2. Relationships with Energy Budgets
3. Modeling Selection
4. Types of Selection
5. Interactive Effects
- antagonistic pleiotropy
Pleiotropy
Ester1 allele: confers resistance to insecticide, but increases risk of predation.
Increased in frequency along coast of France, where spraying occurred (benefit > cost)
Did not increase inland much (did increase due to migration), as cost > benefit and selected against
Ester1 was eventually replaced by
the Ester4 allele, which conferred
a weaker benefit for pesticide
resistance BUT had no negative
effects inland… so the net benefit
was greater.
E. Selection
5. Interactive Effects
- mutation-selection balance
A deleterious allele (selectively disadvantageous) can be
maintained in a population by mutation:
Δq = m – sq2 = rate they are added by mutation – rate lost by
selection against the homozygous genotype.
qeq = √m/s
E. Selection
5. Interactive Effects
- mutation-selection balance
- selection and drift
Deterministic Effects of Selection > Random Effects of Drift
At small sizes, it is possible to lose an
adaptive allele.
However, just by chance, adaptive alleles can
become fixed – rapidly increasing the
reproductive success of population