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

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The Hardy-Weinberg-Castle Equilibrium

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Godfrey Hardy Wilhelm Weinberg William Castle

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Conclusions of the Hardy-Weinberg principle

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Conclusions of the Hardy-Weinberg principle 1. Allele frequencies will not change from generation to generation.

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Conclusions of the Hardy-Weinberg principle 1. Allele frequencies will not change from generation to generation. 2. Genotype proportions determined by the “square law”.

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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 = p 2 + 2pq + q 2

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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 = p 2 + 2pq + q 2 for three alleles (p + q + r) 2 = p 2 + q 2 + r 2 + 2pq + 2pr +2qr

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Conclusions of the Hardy-Weinberg principle 3. Hardy-Weinberg equilibrium occurs independently of allelic frequencies

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Conclusions of the Hardy-Weinberg principle 3. Hardy-Weinberg equilibrium occurs independently of allelic frequencies Allele frequencies Genotype frequencies A 1 = 0.80, A 2 = 0.20 A 1 A 1 = 0.64, A 1 A 2 = 0.32, A 2 A 2 = 0.04

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Conclusions of the Hardy-Weinberg principle 3. Hardy-Weinberg equilibrium occurs independently of allelic frequencies Allele frequencies Genotype frequencies A 1 = 0.80, A 2 = 0.20 A 1 A 1 = 0.64, A 1 A 2 = 0.32, A 2 A 2 = 0.04 A 1 = 0.50, A 2 = 0.50 A 1 A 1 = 0.25, A 1 A 2 = 0.50, A 2 A 2 = 0.25

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Conclusions of the Hardy-Weinberg principle 3. Hardy-Weinberg equilibrium occurs independently of allelic frequencies Allele frequencies Genotype frequencies A 1 = 0.80, A 2 = 0.20 A 1 A 1 = 0.64, A 1 A 2 = 0.32, A 2 A 2 = 0.04 A 1 = 0.50, A 2 = 0.50 A 1 A 1 = 0.25, A 1 A 2 = 0.50, A 2 A 2 = 0.25 A 1 = 0.10, A 2 = 0.90 A 1 A 1 = 0.01, A 1 A 2 = 0.18, A 2 A 2 = 0.81

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Assumptions of Hardy-Weinberg equilibrium

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1. Mating is random

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Assumptions of Hardy-Weinberg equilibrium 1. Mating is random… but some traits experience positive assortative mating

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Assumptions of Hardy-Weinberg equilibrium 1. Mating is random 2. Population size is infinite (i.e., no genetic drift)

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Assumptions of Hardy-Weinberg equilibrium 1. Mating is random 2. Population size is infinite (i.e., no genetic drift) 3. No migration

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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

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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

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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.

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Does Hardy-Weinberg equilibrium ever exist in nature?

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Example: Atlantic cod (Gadus morhua) in Nova Scotia

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Does Hardy-Weinberg equilibrium ever exist in nature? Example: Atlantic cod (Gadus morhua) in Nova Scotia as a juvenile…

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Does Hardy-Weinberg equilibrium ever exist in nature? Example: Atlantic cod (Gadus morhua) in Nova Scotia … and as an adult

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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)

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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) A 1 A 1 = 109 A 1 A 2 = 182 A 2 A 2 = 73

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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) A 1 A 1 = 109 A 1 A 2 = 182 A 2 A 2 = 73 Question: Is this population in Hardy-Weinberg equilibrium?

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Testing for Hardy-Weinberg equilibrium

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Step 1: Estimate genotype frequencies

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Testing for Hardy-Weinberg equilibrium Step 1: Estimate genotype frequencies Step 2: Estimate allele frequencies

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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

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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.

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A simple model of directional selection

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Persistent selection changes allele frequencies over generations (Obvious) Conclusion: Natural selection can cause rapid evolutionary change!

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A simple model of directional selection consider a single locus with two alleles A and a

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A simple model of directional selection consider a single locus with two alleles A and a let p = frequency of A allele

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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

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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: AAAaaa w11 w12 w22

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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: AAAaaa w 11 w 12 w 22 it is also possible to determine relative fitness of the A and a alleles:

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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: AAAaaa w11 w12 w22 it is also possible to determine relative fitness of the A and a alleles: let w 1 = fitness of the A allele

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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: AAAaaa w11 w12 w22 it is also possible to determine relative fitnesses of the A and a alleles: let w 1 = fitness of the A allele let w 2 = fitness of the a allele

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The fitness of the A allele = w 1 = pw 11 + qw 12

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The fitness of the a allele = w 2 = qw 22 + pw 12

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Directional selection let p = frequency of A allele let q = frequency of a allele relative fitness of different genotypes are: AAAaaa w 11 w 12 w 22 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

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