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Hardy Weinberg Equilibrium

Gregor Mendel. Hardy Weinberg Equilibrium. Wilhem Weinberg (1862 – 1937). (1822-1884). G. H. Hardy (1877 - 1947). Recall from Previous Lectures. Darwin’s Observation. Evolution acts through changes in allele frequency at each generation

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Hardy Weinberg Equilibrium

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  1. Gregor Mendel Hardy Weinberg Equilibrium Wilhem Weinberg (1862 – 1937) (1822-1884) G. H. Hardy (1877 - 1947)

  2. Recall from Previous Lectures Darwin’s Observation Evolution acts through changes in allele frequency at each generation Leads to average change in characteristic of the population

  3. Lectures 4-11: Mechanisms of Evolution (Microevolution) • Hardy Weinberg Principle (Mendelian Inheritance) • Genetic Drift • Mutation • Recombination • Epigenetic Inheritance • Natural Selection These are mechanisms acting WITHIN populations, hence called “population genetics”—EXCEPT for epigenetic modifications, which act on individuals in a Lamarckian manner

  4. 4 Major Evolutionary Mechanisms acting at the population level, changing allele frequencies: • Genetic Drift • Natural Selection • Mutation • Migration

  5. Testing for Hardy-Weinberg equilibrium can be used to assess whether a population is evolving

  6. The Hardy-Weinberg Principle • A population that is not evolving shows allele and genotypic frequencies that are in Hardy Weinberg equilibrium • If a population is not in Hardy-Weinberg equilibrium, it can be concluded that the population is evolving

  7. Fig. 23-5a MAP AREA CANADA ALASKA • What is a “population?” • A group of individuals within a species that is capable of interbreeding and producing fertile offspring • (definition for sexual species) Beaufort Sea NORTHWEST TERRITORIES Porcupine herd range Fortymile herd range YUKON ALASKA

  8. Fig. 23-5 Porcupine herd MAP AREA CANADA ALASKA Beaufort Sea NORTHWEST TERRITORIES Porcupine herd range Fortymile herd range YUKON ALASKA Fortymile herd

  9. Hardy-Weinberg Principle • Mathematical description of Mendelian inheritance

  10. Hardy-Weinberg Equilibrium • According to the Hardy-Weinberg principle, frequencies of alleles and genotypes in a population remain constant from generation to generation • In a given population where gametes contribute to the next generation randomly, allele frequencies will not change • Allelic and genotypic frequencies follow the transmission rules of Mendelian inheritance, which maintains constant proportions in a population across generations

  11. In the absence of Evolution… Patterns of inheritance should always be in “Hardy Weinberg Equilibrium” Following the transmission rules of Mendel

  12. Requirements of HWEvolution Violation Large population size Genetic drift Random MatingInbreeding & other No MutationsMutations No Natural SelectionNatural Selection No Migration Migration An evolving population is one that violates Hardy-Weinberg Assumptions

  13. “Null Model” • No Evolution: Null Model to test if no evolution is happening should simply be a population in Hardy-Weinberg Equilibrium • No Selection: Null Model to test whether Natural Selection is occurring should have no selection, but should include Genetic Drift • This is because Genetic Drift is operating even when there is no Natural Selection

  14. Hardy-Weinberg Theorem In a non-evolving population, frequency of alleles and genotypes remain constantover generations

  15. important concepts • gene: A region of genome sequence (DNA or RNA), that is the unit of inheritance , the product of which contributes to phenotype • locus: Location in a genome (used interchangeably with “gene,” if the location is at a gene… but, locus can be anywhere, so meaning is broader than gene) • loci: Plural of locus • allele: Variant forms of a gene (e.g. alleles for different eye colors, BRCA1 breast cancer allele, etc.) • genotype: The combination of alleles at a locus (gene) • phenotype: The expression of a trait, as a result of the genotype and regulation of genes (green eyes, brown hair, body size, finger length, cystic fibrosis, etc.)

  16. important concepts • allele: Variant forms of a gene (e.g. alleles for different eye colors, BRCA1 breast cancer allele, etc.) • We are diploid (2 chromosomes), so we have 2 alleles at a locus (any location in the genome) • However, there can be many alleles at a locus in a population. • For example, you might have inherited a blue eye allele from your mom and a brown eye allele from your dad… you can’t have more alleles than that (only 2 chromosomes, one from each parent) • BUT, there could be many alleles at this locus in the population, blue, green, grey, brown, etc.

  17. A2 A1 Eggs A3 A1 A2 A1 A4 • Alleles in a population of diploid organisms A2 A1 A3 Sperm A4 A1 A1 Random Mating (Sex) A1A1 A1A1 Zygotes A1A3 A1A1 • Genotypes A2A4 A3A1

  18. A2 A1 Eggs A3 A1 A2 A1 A4 So then can we predict the % of alleles and genotypes in the population at each generation? A2 A1 A3 Sperm A4 A1 A1 A1A1 A1A1 Zygotes A1A3 A1A1 A2A4 A3A1

  19. Hardy-Weinberg Theorem In a non-evolving population, frequency of alleles and genotypes remain constantover generations

  20. Fig. 23-6 Alleles in the population Frequencies of alleles Gametes produced p = frequency of Each egg: Each sperm: CR allele = 0.8 q = frequency of 80% chance 80% chance 20% chance 20% chance CW allele = 0.2 Hardy-Weinberg proportions indicate the expected allele and genotype frequencies, given the starting frequencies

  21. By convention, if there are 2 alleles at a locus, p and q are used to represent their frequencies • The frequency of all alleles in a population will add up to 1 • For example, p + q = 1

  22. If p and q represent the relative frequencies of the only two possible alleles in a population at a particular locus, then for a diploid organism (2 chromosomes), (p + q) 2 = 1 = p2 + 2pq + q2 = 1 • where p2 and q2 represent the frequencies of the homozygous genotypes and 2pq represents the frequency of the heterozygous genotype

  23. What about for a triploid organism?

  24. What about for a triploid organism? • (p + q)3 = 1 = p3 + 3p2q+ 3pq2 + q3 = 1 Potential offspring: ppp, ppq, pqp, qpp, qqp, pqq, qpq, qqq How about tetraploid? You work it out.

  25. Hardy Weinberg Theorem ALLELES Probability of A= pp+ q= 1 Probability of a= q GENOTYPES AA: pxp= p2 Aa: pxq+ qxp= 2pq aa:qxq= q2 p2+ 2pq+ q2 = 1

  26. More General HW Equations • One locus three alleles: (p + q + r)2 = p2 + q2 + r2 + 2pq +2pr + 2qr • One locus n # alleles: (p1 + p2 + p3 + p4 … …+ pn)2 = p12 + p22 + p32 + p42… …+ pn2 + 2p1p2 + 2p1p3 + 2p2p3 + 2p1p4 + 2p1p5 + … … + 2pn-1pn • For a polyploid (more than two chromosomes): (p + q)c, where c = number of chromosomes • If multiple loci (genes) code for a trait, each locus follows the HW principle independently, and then the alleles at each loci interact to influence the trait

  27. ALLELE Frequencies Frequency of A = p = 0.8 Frequency of a = q = 0.2 • p + q = 1 Expected GENOTYPE Frequencies AA: pxp = p2 = 0.8 x 0.8 = 0.64 Aa: pxq + qxp = 2pq = 2 x (0.8 x 0.2) = 0.32 aa: qxq = q2 = 0.2 x 0.2 = 0.04 p2 + 2pq + q2 = 0.64 + 0.32 + 0.04 = 1 Allele frequencies remain the same at next generation • Expected Allele Frequencies at 2nd Generation • p = AA + Aa/2 = 0.64 + (0.32/2) = 0.8 • q = aa + Aa/2 = 0.04 + (0.32/2) = 0.2

  28. Hardy Weinberg Theorem ALLELE Frequency Frequency of A = p = 0.8 p + q = 1 Frequency of a = q = 0.2 Expected GENOTYPE Frequency AA: pxp = p2 = 0.8 x 0.8 = 0.64 Aa: pxq + qxp = 2pq = 2 x (0.8 x 0.2) = 0.32 aa : qxq = q2 = 0.2 x 0.2 = 0.04 p2 + 2pq + q2 = 0.64 + 0.32 + 0.04 = 1 Expected Allele Frequency at 2nd Generation p = AA + Aa/2 = 0.64 + (0.32/2) = 0.8 q = aa + Aa/2 = 0.04 + (0.32/2) = 0.2

  29. Similar example, But with different starting allele frequencies q p

  30. p2 2pq q2

  31. Fig. 23-7-4 80% CR( p = 0.8) 20% CW(q = 0.2) Sperm CW (20%) CR (80%) Perform the same calculations using percentages CR (80%) Eggs 64% ( p2) CR CR 16% ( pq) CR CW 16% (qp) CR CW 4% (q2) CW CW CW (20%) 64% CR CR,32% CR CW, and4% CW CW Gametes of this generation: 64% CR +16% CR=   80% CR = 0.8 = p 4% CW+16% CW=  20% CW = 0.2 = q Genotypes in the next generation: 64% CR CR,32% CR CW, and4% CW CW plants

  32. Fig. 23-7-1 80% CR(p = 0.8) 20% CW(q = 0.2) Sperm CW (20%) CR (80%) CR (80%) Eggs 16% (pq) CRCW 64% (p2) CRCR 4% (q2) CW CW 16% (qp) CRCW CW (20%)

  33. Fig. 23-7-2 64% CRCR,32% CRCW, and4% CWCW Gametes of this generation: 64% CR+16% CR=80% CR = 0.8 = p 4% CW+16% CW=20% CW= 0.2 = q

  34. Fig. 23-7-3 64% CRCR,32% CRCW, and4% CWCW Gametes of this generation: 64% CR+16% CR=80% CR = 0.8 = p 4% CW+16% CW=20% CW= 0.2 = q Genotypes in the next generation: 64% CRCR,32% CRCW, and4% CWCWplants

  35. Calculating Allele Frequencies from # of Individuals • The frequency of an allele in a population can be calculated from # of individuals: • For diploid organisms, the total number of alleles at a locus is the total number of individuals x 2 • The total number of dominant alleles at a locus is 2 alleles for each homozygous dominant individual • plus 1 allele for each heterozygous individual; the same logic applies for recessive alleles

  36. Calculating Allele and Genotype Frequencies from # of Individuals AA Aa aa 120 60 35 (# of individuals) #A = (2 x AA) + Aa = 240 + 60 = 300 #a = (2 x aa) + Aa = 70 + 60 = 130 Proportion A = 300/total = 300/430 = 0.70 Proportion a = 130/total = 130/430 = 0.30 A + a = 0.70 + 0.30 = 1 Proportion AA = 120/215 = 0.56 Proportion Aa = 60/215 = 0.28 Proportion aa = 35/215 = 0.16 AA + Aa + aa = 0.56 + 0.28 +0.16 = 1

  37. Applying the Hardy-Weinberg Principle • Example: estimate frequency of a disease allele in a population • Phenylketonuria (PKU) is a metabolic disorder that results from homozygosity for a recessive allele • Individuals that are homozygous for the deleterious recessive allele cannot break down phenylalanine, results in build up  mental retardation

  38. The occurrence of PKU is 1 per 10,000 births • How many carriers of this disease in the population?

  39. Rare deleterious recessives often remain in a population because they are hidden in the heterozygous state (the “carriers”) • Natural selection can only act on the homozygous individuals where the phenotype is exposed (individuals who show symptoms of PKU) • We can assume HW equilibrium if: • There is no migration from a population with different allele frequency • Random mating • No genetic drift • Etc

  40. So, let’s calculate HW frequencies • The occurrence of PKU is 1 per 10,000 births (frequency of the disease allele): q2 = 0.0001 q = sqrt(q2 ) = sqrt(0.0001) = 0.01 • The frequency of normal alleles is: p = 1 – q= 1 – 0.01 = 0.99 • The frequency of carriers (heterozygotes) of the deleterious allele is: 2pq = 2 x 0.99 x 0.01 = 0.0198 or approximately 2% of the U.S. population

  41. Conditions for Hardy-Weinberg Equilibrium • The Hardy-Weinberg theorem describes a hypothetical population • The five conditions for nonevolving populations are rarely met in nature: • No mutations • Random mating • No natural selection • Extremely large population size • No gene flow • So, in real populations, allele and genotype frequencies do change over time

  42. DEVIATION from Hardy-Weinberg Equilibrium Indicates that EVOLUTION Is happening

  43. 4 Major Evolutionary Mechanisms: • Genetic Drift • Natural Selection • Mutation • Migration

  44. Hardy-Weinberg across a Genome • In natural populations, some loci might be out of HW equilibrium, while being in Hardy-Weinberg equilibrium at other loci • For example, some loci might be undergoing natural selection and become out of HW equilibrium, while the rest of the genome remains in HW equilibrium

  45. Allele A1 Demo

  46. Examples of Deviation from Hardy-Weinberg Equilibrium

  47. What would Genetic Drift look like? • Most populations are experiencing some level of genetic drift, unless they are incredibly large

  48. Examples of Deviation from Hardy-Weinberg Equilibrium AA Aaaa Generation 1 0.64 0.32 0.04 Generation 2 0.63 0.33 0.04 Generation 3 0.64 0.315 0.045 Generation 4 0.65 0.31 0.04 Is this population in HW equilibrium? If not, how does it deviate? What could be the reason?

  49. Examples of Deviation from Hardy-Weinberg Equilibrium AA Aaaa Generation 1 0.64 0.32 0.04 Generation 2 0.63 0.33 0.04 Generation 3 0.64 0.315 0.045 Generation 4 0.65 0.31 0.04 This is a case of Genetic Drift, where allele frequencies are fluctuating randomly across generations

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