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Lecture 22: Signatures of Selection and Introduction to Linkage Disequilibrium

Lecture 22: Signatures of Selection and Introduction to Linkage Disequilibrium. March 17, 2014. Exam 2. Wednesday, March 26 at 6:30 in lab Genetic Drift, Population Structure, Population Assignment, Individual Identity, Paternity Analysis, and Linkage Disequilibrium

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Lecture 22: Signatures of Selection and Introduction to Linkage Disequilibrium

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  1. Lecture 22: Signatures of Selection and Introduction to Linkage Disequilibrium March 17, 2014

  2. Exam 2 • Wednesday, March 26 at 6:30 in lab • Genetic Drift, Population Structure, Population Assignment, Individual Identity, Paternity Analysis, and Linkage Disequilibrium • Sample exam posted on website • Review on Monday, March 24

  3. Last Time • Population assignment • Forensic evidence and individual identity • Paternity analysis

  4. Today • Multiple loci and independent segregation • Estimating linkage disequilibrium • Causes of linkage disequilibrium

  5. Extending to Multiple Loci • So far, only considering dynamics of alleles at single loci • Loci occur on chromosomes, linked to other loci! “The fitness of a single locus ripped from its interactive context is about as relevant to real problems of evolutionary genetics as the study of the psychology of individuals isolated from their social context is to an understanding of man’s sociopolitical evolution” Richard Lewontin (quoted in Hedrick 2005) • Size of region that must be considered depends on Linkage Disequilibrium

  6. Gametic (Linkage) Disequilibrium (LD) • Nonrandom association of alleles at different loci into gametes • Haplotype: Genotype of a group loci in LD • LD is a major factor in evolution • LD itself provides insights into population history • Estimation of LD is critical for ALL population genetic data

  7. Nomenclature and concepts A1 B1 A2 B2 Two loci, two alleles • Frequency of allele i at locus 1 is pi • Frequency of allele i at locus 2 is qi p1 q1 p2 q2

  8. Nomenclature and concepts A1 B1 A2 B2 B1 A1 A2 B2 B1 and A2 B2 are haplotypes A1 • Genotype is written as A1 and B1 are in coupling phase A1 and B2 are in repulsion phase

  9. Gametic Disequilibrium B1 A1 A2 B2 Meiosis A1 B1 A1 A2 B2 B2 A2 B1 • Easiest to think about physically linked loci, but not necessarily the case What Are Expected Frequencies of Gametes in a Population Under Independent Assortment? p1q1 p1q2 p2q1 p2q2

  10. Meiosis A1 B1 A1 A2 A2 B2 B2 B1 What are expected frequencies of gametes with complete linkage? A1 B1 p1 q1 A2 B2 p2 q2 A1 B2 p1 q1 A2 B1 p2 q2 x11 x21 x22 x12 The frequency of the gametes in the current population. Expected to stay stable in the absence of other departures from H-W

  11. Linkage disequilibrium measure, D Independent Assortment: With LD: Substituting p1 and q1 from above table:

  12. Problem: D is sensitive to allele frequencies • Gamete frequencies must be between 0 and 1 • Maximum D set by allele frequencies Solution: D' = D/Dmax ranges from -1 to 1 Example, if D is positive: p1=0.5, q2=0.5, Dmax=0.25 but p1=0.1, q2=0.9, Dmax=0.09 Dmax Calculation: If D is positive, Dmax is lesser of p1q2 or p2q1 If D is negative, Dmax is lesser of p1q1 or p2q2

  13. LD can also be estimated as correlation between alleles • r can also be standardized to a -1 to 1 scale • It is equivalent to D’ in this case

  14. Recombination B1 A1 A2 B2 A1 B1 A1 B2 A2 B2 A2 B1 • Shuffling of parental alleles during meiosis • Occurs for unlinked loci and linked loci • Rate of recombination for linked markers is partially a function of physical distance

  15. Recombination Rate B1 A1 A2 B2 Meiosis A1 B1 A1 A2 B2 B2 A2 B1 Products of Recombination Coupling Repulsion Coupling Repulsion Where nr is number of repulsion phase gametes, and nc is number of coupling phase gametes What is the expected recombination rate for unlinked loci?

  16. Expected Gamete Frequencies: Double Homozygote B1 A1 B1 A1 Meiosis A1 B1 A1 A1 B1 A1 B1 B1 NonRecombinant NonRecombinant Recombinant Recombinant

  17. Expected Gamete Frequencies: Double Heterozygote B1 A1 B2 A2 Meiosis A1 B2 A1 A2 B1 A2 B2 B1 NonRecombinant NonRecombinant Recombinant Recombinant

  18. LD is partially a function of recombination rate • Expected proportions of haplotypes produced in a population after 1 generation of mating Offspring Genotypes Offpsring Haplotype Frequencies (accounting for parental recombination) Parent Haplotype Frequencies Where c is the recombination rate and D0 is the initial amount of LD

  19. Recombination degrades LD over time Where t is time (in generations) and e is base of natural log (2.718)

  20. Effects of recombination rate on LD • Decline in LD over time with different theoretical recombination rates (c) • Even with independent segregation (c=0.5), multiple generations required to break up allelic associations Where t is time (in generations) and e is base of natural log (2.718)

  21. LD varies substantially across human genome NATURE|Vol 437|27 October 2005 • LD affected by location relative to telomeres and centromeres, chromosome length, GC content, sequence polymorphism, and repeat composition • Highest and lowest levels of LD found in gene-rich regions Average r2 for pairs of SNP separated by 30 kb in 1 Mb windows

  22. Human HapMap Project and Whole Genome Scans • LD structure of human Chromosome 19 (www.hapmap.org) • 1 common SNP genotyped every 700 bp for 270 individuals (3.4 million SNP) • 9.2 million SNP in total NATURE|Vol 437|27 October 2005

  23. 1 1 3 2 2 4 5 1 2 3 LD in the Poplar Genome • LD declines rapidly with distance • LD higher in genes than in genome as a whole • Loci separated by kilobases still in LD! Slavov et al. 2012 New Phyt 196:713-725

  24. Recombination Across Poplar Chromosomes • Substantial variation in recombination rate • Related to repeat composition, methylation, and distance from centromere

  25. Recombination rate varies among individuals • Rate is often higher in females than males • Rate varies among individuals within males and females Variation in recombination rate in the MHC region (3.3 Mb in human sperm donors

  26. Genetic Drift and LD • Begin with highly diverse haplotype pool • Drift leads to chance increase of certain haplotypes • Generates nonrandom association between alleles at different loci (LD)

  27. Genetic Drift and LD • Why doesn’t recombination reduce LD in this situation?

  28. LD is partially a function of recombination rate • Expected proportions of gametes produced by various genotypes over two generations • Effective LD increases with homozygosity Double heterozygote is only case where recombination matters

  29. Effect of Drift on LD • Drift and recombination will have opposing effects on LD Where r2 is the squared correlation coefficient for alleles at two loci,Ne is effective population size, and c is recombination rate • 4Nec is “population recombination rate”, • Expression approaches 0 for large populations or high recombination rates

  30. Combined effects of Drift and Recombination • LD declines as a function of population recombination rate (Ner in this figure, same as Nec) • Effects of chance fluctuation of gamete frequencies

  31. How should inbreeding affect linkage disequilibrium?

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