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