Response to selection can be fast!
Selection is strong
Favored allele is partially dominant
Both alleles are common
Selection is not always “Directional”
• Heterozygote advantage
• Frequency dependence
• Selection varying in space or time
Heterozygote advantage
Fitness
A a a aA A
HbA/HbA HbA/HbS HbS/HbS
Relative Fitness 0.88 1.0 0.14
Fitness (in symbols) 1-t 1 1-s
Selection coefficients t=0.12 s=0.86
Relative fitness of hemoglobin genotypes in Yorubans
Equilibrium frequencies:
peq = s/(s+t) = 0.86/(0.12+0.86) = 0.88
qeq = t/(s+t) = 0.12/(0.12+0.86) = 0.12
Predict the genotype frequencies (at birth):HW proportions 0.774 0.211 0.0144
Variable selection: genotypes have different fitness effects in different environments
0.4
0.5
0.6
0.7
0.8
0.9
1
Env. 1 Env. 2 Env. 3
AAAaaa
Fitness
Frequency-dependent selection
Selection
Whether directional or stabilizing, causes adaptive changes in allele
frequencies
Forces causing evolution:
Random Genetic Drift
Changes in allele frequency due to random sampling: not adaptive
10 Populations, N=15
Drift occurs even in large populations!N=10,000
Genetic drift eliminates genetic variation
Forces that cause evolution
Mutation
Ultimate source of all genetic variation
Mutation is generally not adaptive
How common is mutation?
• Dominant autosomal allele
• Recurrent mutation rate: 3/200,000 = 0.000015 per generation
• q0=0.0; q1 = 0.000015, q2 = 0.000030
Achondroplastic dwarfism
Mutation/Selection Balance
Even highly deleterious mutations can persist at substantial frequency, especially if they are recessive:
Selection against a recessive allele is s
Genotype AA Aa aaFitness 1 1 1-s
For recessive lethal, s = 1
Mutation-selection equilibrium
Recessive deleterious alleles:
qe = √(/s)
If a recessive lethal (s=1) has a recurrent mutation rate of 1.5*10-5, what is it’s equilibrium frequency?
qe = 0.004
Mutation maintains substantial genetic variation
Deleterious mutationsOrganism per genome/gener’nC. Elegans 0.04D. melanogaster 0.14Mouse 0.9Human 1.6
HIV virus is thought to have mutation rate ~10 X greater than humans!
Forces causing evolution:
Non-random mating:Inbreeding
Mating between relatives
What happens to genotype frequencies under inbreeding?
Most extreme form of inbreeding is selfing
P: Aa x Aa
F1: 25% AA 50% Aa 25% aa
F2: 37.5% AA 25% Aa 37.5% aa
F3: 43.75% AA 12.5% Aa 43.75% aa
Fewer heterozygotes and more homozygotes each generation
What happens to heterozygosity under inbreeding?
Generations Heterozygosity:
of selfing Prop. of heterozygotes
0 100% Aa
1 50% Aa
2 25% Aa
3 12.5% Aa
What happens to allele frequencies under inbreeding?
P: Aa x Aa
F1: 25% AA 50% Aa 25% aa
F2: 37.5% AA 25% Aa 37.5% aa
F3: 43.75% AA 12.5% Aa 43.75% aa
Allele frequencies do not change under inbreeding, but population is perturbed from
H-W proportions.
0
10
20
30
40
50
60
70
0 0.25 0.5 0.75 1
Inbreeding Depression
Inbreeding Coefficient
Yield
Pup survival relative to Inbreeding
Inbreeding CoefficientSurvival
< 0.19 75%
0.25-0.67 51%
> 0.67 25%
Brother-sister or parent-offspring mating reduces the heterozygosity by 25% per generation:
G0: H=1G1: H= ?G2: H= ?
Proportions of individuals w/ genetic disease who are products of first
cousin marriages
Migration between subpopulations
Tends to equalize allele frequencies among
subpopulations, even if the allele frequencies differ because of differing selection pressure
Migration: island model
q' = (1-m)q + mqm = q - m(q - qm)
q = 0.1
Migration rate= m=0.05qm = 0.9
q' = 0.1 +0.04 = 0.14
Evolution is the result of violating assumptions of H-W
• These ideas are straightforward.
• Mathematics can be complicated, especially when multiple
evolutionary forces are occurring simultaneously
Practical Considerations
• Evolution of pathogens (HIV, SARS, West Nile Virus, etc.)
• Evolution of antibiotic resistance• Evolution of pesticide and herbicide
resistance• Conservation of genetic diversity in
natural, captive, and agricultural species.
