BIOE 109 Summer 2009 Lecture 5- Part I Hardy- Weinberg Equilibrium.

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


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 two alleles = (p + q)2 = p2 + 2pq + q2

• for three alleles (p + q + r)2 = p2 + q2 + r2 + 2pq + 2pr +2qr


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 = 0.80, 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 = 0.80, 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


1. Mating is random


1. Mating is random… but some traits experience positive assortative mating


1. Mating is random

2. Population size is infinite (i.e., no genetic drift)


1. Mating is random


3. No migration


1. Mating is random


3. No migration

4. No mutation


1. Mating is random


3. No migration

4. No mutation

5. No selection

Hardy-Weinberg principle: A null model

1. Mating is random


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?


Example: Atlantic cod (Gadus morhua) in Nova Scotia



as a juvenile…



… and as an adult



• a sample of 364 fish were scored for a single nucleotide polymorphism (SNP)




A1A1 = 109A1A2 = 182A2A2 = 73




A1A1 = 109A1A2 = 182A2A2 = 73

Question: Is this population in Hardy-Weinberg 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 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!


• consider a single locus with two alleles A and a



• let p = frequency of A allele



• let p = frequency of A allele• let q = frequency of a allele


• 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




• relative fitnesses are:


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




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

alleles:

let w1 = fitness of the A allele




• 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


• relative fitness of different genotypes are:


• 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

BIOE 109 Summer 2009 Lecture 5- Part I Hardy- Weinberg Equilibrium.

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