Transcript Document

BIOE 109
Summer 2009
Lecture 5- Part I
Hardy- Weinberg Equilibrium
The Hardy-Weinberg-Castle Equilibrium
The Hardy-Weinberg-Castle Equilibrium
Godfrey Hardy
Wilhelm Weinberg
William Castle
Conclusions of the Hardy-Weinberg
principle
Conclusions of the Hardy-Weinberg
principle
1. Allele frequencies will not change from generation to
generation.
Conclusions of the Hardy-Weinberg
principle
1. Allele frequencies will not change from generation to
generation.
2. Genotype proportions determined by the “square law”.
Conclusions of the Hardy-Weinberg
principle
1. Allele frequencies will not change from generation to
generation.
2. Genotype proportions determined by the “square law”.
• for two alleles = (p + q)2 = p2 + 2pq + q2
Conclusions of the Hardy-Weinberg
principle
1. Allele frequencies will not change from generation to
generation.
2. Genotype proportions determined by the “square law”.
• for two alleles = (p + q)2 = p2 + 2pq + q2
• for three alleles (p + q + r)2 = p2 + q2 + r2 + 2pq + 2pr +2qr
Conclusions of the Hardy-Weinberg
principle
3. Hardy-Weinberg equilibrium occurs independently of
allelic frequencies
Conclusions of the Hardy-Weinberg
principle
3. Hardy-Weinberg equilibrium occurs independently of
allelic frequencies
Allele frequencies
A1 = 0.80, A2 = 0.20
Genotype frequencies
A1A1 = 0.64, A1A2 = 0.32, A2A2 = 0.04
Conclusions of the Hardy-Weinberg
principle
3. Hardy-Weinberg equilibrium occurs independently of
allelic frequencies
Allele frequencies
Genotype frequencies
A1 = 0.80, A2 = 0.20
A1A1 = 0.64, A1A2 = 0.32, A2A2 = 0.04
A1 = 0.50, A2 = 0.50
A1A1 = 0.25, A1A2 = 0.50, A2A2 = 0.25
Conclusions of the Hardy-Weinberg
principle
3. Hardy-Weinberg equilibrium occurs independently of
allelic frequencies
Allele frequencies
Genotype frequencies
A1 = 0.80, A2 = 0.20
A1A1 = 0.64, A1A2 = 0.32, A2A2 = 0.04
A1 = 0.50, A2 = 0.50
A1A1 = 0.25, A1A2 = 0.50, A2A2 = 0.25
A1 = 0.10, A2 = 0.90
A1A1 = 0.01, A1A2 = 0.18, A2A2 = 0.81
Assumptions of Hardy-Weinberg
equilibrium
Assumptions of Hardy-Weinberg
equilibrium
1. Mating is random
Assumptions of Hardy-Weinberg
equilibrium
1. Mating is random… but some traits experience
positive assortative mating
Assumptions of Hardy-Weinberg
equilibrium
1. Mating is random
2. Population size is infinite (i.e., no genetic drift)
Assumptions of Hardy-Weinberg
equilibrium
1. Mating is random
2. Population size is infinite (i.e., no genetic drift)
3. No migration
Assumptions of Hardy-Weinberg
equilibrium
1. Mating is random
2. Population size is infinite (i.e., no genetic drift)
3. No migration
4. No mutation
Assumptions of Hardy-Weinberg
equilibrium
1. Mating is random
2. Population size is infinite (i.e., no genetic drift)
3. No migration
4. No mutation
5. No selection
Hardy-Weinberg principle: A null model
1. Mating is random
2. Population size is infinite (i.e., no genetic drift)
3. No migration
4. No mutation
5. No selection
The Hardy-Weinberg equilibrium principle thus
specifies conditions under which the population will
NOT evolve.
In other words, H-W principle identifies the set
of events that can cause evolution in real
world.
Does Hardy-Weinberg equilibrium ever
exist in nature?
Does Hardy-Weinberg equilibrium ever
exist in nature?
Example: Atlantic cod (Gadus morhua) in Nova Scotia
Does Hardy-Weinberg equilibrium ever
exist in nature?
Example: Atlantic cod (Gadus morhua) in Nova Scotia
as a juvenile…
Does Hardy-Weinberg equilibrium ever
exist in nature?
Example: Atlantic cod (Gadus morhua) in Nova Scotia
… and as an adult
Does Hardy-Weinberg equilibrium ever
exist in nature?
Example: Atlantic cod (Gadus morhua) in Nova Scotia
• a sample of 364 fish were scored for a single nucleotide
polymorphism (SNP)
Does Hardy-Weinberg equilibrium ever
exist in nature?
Example: Atlantic cod (Gadus morhua) in Nova Scotia
• a sample of 364 fish were scored for a single nucleotide
polymorphism (SNP)
A1A1 = 109
A1A2 = 182
A2A2 = 73
Does Hardy-Weinberg equilibrium ever
exist in nature?
Example: Atlantic cod (Gadus morhua) in Nova Scotia
• a sample of 364 fish were scored for a single nucleotide
polymorphism (SNP)
A1A1 = 109
A1A2 = 182
A2A2 = 73
Question: Is this population in Hardy-Weinberg equilibrium?
Testing for Hardy-Weinberg equilibrium
Testing for Hardy-Weinberg equilibrium
Step 1: Estimate genotype frequencies
Testing for Hardy-Weinberg equilibrium
Step 1: Estimate genotype frequencies
Step 2: Estimate allele frequencies
Testing for Hardy-Weinberg equilibrium
Step 1: Estimate genotype frequencies
Step 2: Estimate allele frequencies
Step 3: Estimate expected genotype frequencies
under the assumption of H-W equilibrium
Testing for Hardy-Weinberg equilibrium
Step 1: Estimate genotype frequencies
Step 2: Estimate allele frequencies
Step 3: Estimate expected genotype frequencies
under the assumption of H-W equilibrium
Step 4: Compare observed and expected numbers
of genotypes
2 =  (Obs. – Exp.)2
Exp.
A simple model of directional selection
Persistent selection changes allele frequencies
over generations
(Obvious) Conclusion:
Natural selection can cause rapid evolutionary
change!
A simple model of directional selection
• consider a single locus with two alleles A and a
A simple model of directional selection
• consider a single locus with two alleles A and a
• let p = frequency of A allele
A simple model of directional selection
• consider a single locus with two alleles A and a
• let p = frequency of A allele
• let q = frequency of a allele
A simple model of directional selection
• consider a single locus with two alleles A and a
• let p = frequency of A allele
• let q = frequency of a allele
• relative fitnesses are:
AA
Aa
aa
w11 w12 w22
A simple model of directional selection
• consider a single locus with two alleles A and a
• let p = frequency of A allele
• let q = frequency of a allele
• relative fitnesses are:
AA
w11
Aa
w12
aa
w22
• it is also possible to determine relative fitness of the A and a
alleles:
A simple model of directional selection
• consider a single locus with two alleles A and a
• let p = frequency of A allele
• let q = frequency of a allele
• relative fitnesses are:
AA
w11
Aa
w12
aa
w22
• it is also possible to determine relative fitness of the A and a
alleles:
let w1 = fitness of the A allele
A simple model of directional selection
• consider a single locus with two alleles A and a
• let p = frequency of A allele
• let q = frequency of a allele
• relative fitnesses are:
AA
w11
Aa
w12
aa
w22
• it is also possible to determine relative fitnesses of the A and a
alleles:
let w1 = fitness of the A allele
let w2 = fitness of the a allele
The fitness of the A allele = w1 = pw11 + qw12
The fitness of the A allele = w1 = pw11 + qw12
The fitness of the a allele = w2 = qw22 + pw12
Directional selection
• let p = frequency of A allele
• let q = frequency of a allele
• relative fitness of different genotypes are:
AA
w11
Aa
w12
aa
w22
• it is also possible to determine relative fitness of the A and a
alleles:
The fitness of the A allele = w1 = pw11 + qw12
The fitness of the a allele = w2 = qw22 + pw12
• Mean population fitness = w = pw1 + qw2