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

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

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

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

  2. The Hardy-Weinberg-Castle Equilibrium

  3. The Hardy-Weinberg-Castle Equilibrium Godfrey Hardy Wilhelm Weinberg William Castle

  4. Conclusions of the Hardy-Weinberg principle

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

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

  7. 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

  8. 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

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

  10. 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

  11. 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

  12. 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

  13. Assumptions of Hardy-Weinberg equilibrium

  14. Assumptions of Hardy-Weinberg equilibrium 1. Mating is random

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

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

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

  18. 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

  19. 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

  20. 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.

  21. Does Hardy-Weinberg equilibrium ever exist in nature?

  22. Does Hardy-Weinberg equilibrium ever exist in nature? Example: Atlantic cod (Gadus morhua) in Nova Scotia

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

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

  25. 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)

  26. 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

  27. 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?

  28. Testing for Hardy-Weinberg equilibrium

  29. Testing for Hardy-Weinberg equilibrium Step 1: Estimate genotype frequencies

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

  31. 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

  32. 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.

  33. A simple model of directional selection

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

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

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

  37. 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

  38. 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

  39. 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:

  40. 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

  41. 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

  42. The fitness of the A allele = w1 = pw11 + qw12

  43. The fitness of the A allele = w1 = pw11 + qw12 The fitness of the a allele = w2 = qw22 + pw12

  44. 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 + qw12 The fitness of the a allele = w2 = qw22 + pw12 • Mean population fitness = w = pw1 + qw2

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