BIOE 109Summer 2009

Lecture 5- Part IHardy- 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 Genotype frequencies

A1 = 0.80, A2 = 0.20 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 = 109A1A2 = 182A2A2 = 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 = 109A1A2 = 182A2A2 = 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 Aa aa w11 w12 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 Aa aa w11 w12 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 Aa aa w11 w12 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 Aa aa w11 w12 w22

 

• it is also possible to determine relative fitness of the A and a alleles:

The fitness of the A allele = w1 = pw11 + qw12The fitness of the a allele = w2 = qw22 + pw12

• Mean population fitness = w = pw1 + qw2