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.