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Population Genetics

Population Genetics. Dr Pupak Derakhshandeh-Peykar, PhD Ass Prof of Medical Science of Tehran University Ref.: Population and Evolutionary Genetics: A primer. What is Population Genetics ?. The genetical study of the process of evolution

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Population Genetics

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  1. Population Genetics Dr Pupak Derakhshandeh-Peykar, PhD Ass Prof of Medical Science of Tehran University Ref.: Population and Evolutionary Genetics: A primer

  2. What is Population Genetics? • The genetical study of the process of evolution • (The study of the change of allele frequencies, genotype frequencies, and phenotype frequencies)

  3. Population genetics: • One of the oldest and richest examples of success of mathematical theory in biology • Mendelian genetics and Darwinian natural selection in the first part of the 20th century  “modern synthesis”

  4. Population Genetics is… • About microevolution (evolution within species) • Strongly dependent on mathematical models • A relatively young science (most important discoveries are from after 1930)

  5. Factors causing genotype frequency changes • Selection • Mutation • Random Drift • Migration • Recombination • Non-random Mating

  6. What forces are responsible for divergence among populations? • Mutation genetic diversity • Selection  genetic diversity • Genetic drift  genetic diversity • Migration  genetic diversity • Non-random  genetic diversity mating

  7. What's the most important factor in evolution? SELECTION • Natural selection causes evolution: • There is variation in fitness (selection( • That variation can be passed from one generation to the next (inheritance( • This is the central insight of Darwin

  8. THEORIES of EVOLUTION and the DARWINIAN REVOLUTION

  9. Darwin's Theory of Evolution Four Basic Themes: • Descent with Modification from Common Ancestor • Diversity is result of Differential Survival • and/or Differential Reproduction among individuals • with different Heritable characteristics = Process of Natural Selection Law of Evolution by Natural Selection

  10. Charles Darwin (1809-1882)

  11. Theory of Evolution by Natural Selection (1859)Charles Darwin (1809-1882) Inherited Variation among individuals ↓ Differential survival and/or reproduction (“hard” inheritance) ↓ Change in genetic composition of population ↓↓↓↓ Evolution

  12. Jean Baptiste Lamarck (1744-1829)

  13. Theory of Evolutionby Inheritance of Acquired Characteristics(1809)Jean Baptiste Lamarck (1744-1829) Environmental change ↓ Change in organismal form ↓ Inheritance of acquired characteristics (“soft inheritance”) ↓ Change in composition of population ↓↓↓ Evolution

  14. Lamarck’s vs. Darwin’s Theories انقراض= اصلاح ن‍ژاد هدفدار=

  15. Dates, Contributors to Evolutionary Thinking - 1

  16. Dates, Contributors to Evolutionary Thinking - 2

  17. Genes in Populations: Hardy Weinberg Equilibrium

  18. Alleles • Alternative forms of a particular sequence • Each allele has a frequency

  19. Alleles • Yeast: 12 Mb ; 6,340 genes • Nematode elegance: 97 Mb; 19,100genes • Human: 3,700 Mb; 75,000 genes !

  20. Methods used to measure genetic variation: • Genetic variation contains information about an organism’s ancestry • determines an organism’s potential for evolutionary change, adaptation, and survival • 1960s-1970s: genetic variation was first measured by protein electrophoresis (e.g., allozymes)

  21. 1980s-2008s: genetic variation measured directly at the DNA level (1): • Restriction Fragement Length Polymorphisms (RFLPs) • Minisatellites (VNTRs) • DNA sequence • DNA length polymorphisms • Single-stranded Conformation Polymorphism (SSCP)

  22. 1980s-2008s: genetic variation measured directly at the DNA level (2): • Microsatellites (STRs) • Random Amplified Polymorphic DNAs (RAPDs) • Amplified Fragment Length Polymorphisms (AFLPs) • Single Nucleotide Polymorphisms (SNPs)

  23. Types of measures of genetic variation (1): • Polymorphism = % of loci or nucleotide positions showing more than one allele or base pair. • Heterozygosity (H) = % of individuals that are heterozygotes • Allele/haplotype diversity = measure of diversity and different alleles/haplotypes within a population.

  24. Types of measures of genetic variation (2): • Nucleotide diversity = measure of number and diversity of variable nucleotide positions within sequences of a population. • Genetic distance = measure of number of base pair differences between two homologous sequences. • Synonomous/nonsynonomous substitutions = % of nucleotide substitutions that do not/do result in amino acid replacement.

  25. Hardy-Weinberg equilibrium • Properties of alleles in a population • Allele frequencies • Genotypes frequencies

  26. Allele Frequency • For two alleles • Usually labeled p and q = 1 – p • For more than 2 alleles • Usually labeled pA, pB, pC ... • … subscripts A, B and C indicate allele name

  27. Genotype • The pair of alleles carried by an individual • If there are n alternative alleles … • … there will be n(n+1)/2 possible genotypes • Homozygotes • The two alleles are in the same state • Heterozygotes • The two alleles are different

  28. The simple part … • Genotype frequencies lead to allele frequencies… • For example, for two alleles: • pA = pAA + ½ pAB (> p=P+1/2 H*) • pB = pBB + ½ pAB (> q=Q+1/2 H) • However, the reverse is also possible! *H=2pq

  29. Hardy-Weinberg Equilibrium • Relationship described in 1908 • Hardy, British mathematician • Weinberg, German physician • Random union of games • Shows n allele frequencies determine • n(n+1)/2 genotype frequencies • Large populations

  30. Hardy-Weinberg Equilibrium Explains how Mendelian segregation influences allelic and genotypic frequencies in a population

  31. Required Assumptions in Hardy-Weinberg law (1): • Diploid, sexual organism (Parthenogenetic) • Non-overlapping generations • Autosomal locus • Large population • Random mating • Equal genotype frequencies among sexes

  32. Required Assumptions in Hardy-Weinberg law (2): • Absence of natural selection • Population is infinitely large, to avoid effects of genetic drift • No mutation • No migration < If assumptions are met, population will be in genetic equilibrium

  33. Two expected predictions: • Allele frequencies do not change over generations • After one generation of random mating, genotypic frequencies will remain in the following proportions: p2 (frequency of AA) 2pq (frequency of Aa) q2 (frequency of aa) *p = allelic frequency of A *q = allelic frequency of a *p2 + 2pq + q2 = 1

  34. population is at equilibrium

  35. Random Mating:Mating Type Frequencies P2 2PH 2PQ H2 2QH Q2

  36. Mendelian Segregation:Offspring Genotype Frequencies P2 _ _ P2 2PH 2PQ H2 2QH Q2 _ PH PH _ _ 2PQ ¼ H2 ½ H2 ¼ H2 QH QH _ _ Q2 _ Total 1 p2 2pq q2

  37. Conclusion • Genotype frequencies are function of allele frequencies • Equilibrium reached in one generation • Independent of initial genotype frequencies • Random mating, etc. required • Conform to binomial expansion

  38. Simple HWE Exercise • If the defective alleles of the cystic fibrosis (CFTR) gene have cumulative frequency of 1/50 what is: • The proportion of carriers in the population? p=P+1/2H H=2pq=2(p-P)=0.04 p=0.98 P=0.96 q=0.02 Q=0.0004 • The proportion of affected children at birth?

  39. Frequencies of genotypes AA, Aa, and aa relative to the frequencies of alleles A and a in populations at Hardy-Weinberg equilibrium Max. heterozygosity p = q = 0.5

  40. Hardy-Weinberg for loci with more than two alleles: • For three alleles (A, B, and C) with frequencies p, q, and r: • Binomial expansion  • (p + q + r)2 = p2(AA) + 2pq(AB) + q2(BB) + 2pr(AC) + 2qr(BC) + r2(CC) • For four alleles (A, B, C, and D) with frequencies p, q, r, and s: • (p + q + r + s) 2 = p2(AA) + 2pq(AB) + q2(BB) + 2pr(AC) + 2qr(BC) + r2(CC) + 2ps(AD) + 2qs(BD) + 2rs(CD) + s2(DD)

  41. Hardy-Weinberg for X-linked alleles (1): e.g., Humans and Drosophila (XX = female, XY = male)

  42. Hardy-Weinberg for X-linked alleles (2): • Females • Hardy-Weinberg frequencies are the same for any other locus: • p2 + 2pq + q2 = 1 • Males • Genotype frequencies are the same as allele frequencies: • p + q = 1 • Recessive X-linked traits are more common among males.

  43. Checking Hardy-Weinberg Equilibrium • A common first step in any genetic study is to verify that the data conforms to Hardy-Weinberg equilibrium • Deviations can occur due to: • Systematic errors in genotyping • Unexpected population structure • Presence of homologous regions in the genome

  44. TestingHardy Weinberg Equilibrium • Consider a sample of 2N alleles • nA alleles of type A • nB alleles of type B • nAA genotypes of type AA • nAB genotypes of type AB • nBB genotypes of type BB

  45. nA=nAA + ½ nAB / N nB=nBB + ½ nAB / N

  46. Simple Approach • Calculate allele frequencies (o) and expected counts (e) • Construct chi-squared test statistic • Convenient, but can be inaccurate: • especially when one allele is rare

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