Lecture 16: Introduction to Linkage Disequilibrium

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Lecture 16 Introduction to Linkage Disequilibrium
October 19, 2015
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Exam 2

• Wednesday, October 28 at 630 in lab
• Genetic Drift, Population Structure, Population
  Assignment, Individual Identity, Paternity
  Analysis, and Linkage Disequilibrium
• Sample exam posted on website
• Review on Monday, October 26

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Last Time

• Population structure and gene flow
• Introduction to paternity analysis

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Today

• Multiple loci and independent segregation
• Estimating linkage disequilibrium
• Causes of linkage disequilibrium

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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 mans
  sociopolitical evolution
• Richard Lewontin (quoted in Hedrick 2005)

• Size of region that must be considered depends on
  Linkage Disequilibrium

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Gametic (Linkage) Disequilibrium (LD)

• Nonrandom association of alleles at different
  loci into gametes
• Haplotype Genotype of a group of 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

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Nomenclature and concepts

• Two loci, two alleles
• Frequency of allele i at locus 1 is pi
• Frequency of allele i at locus 2 is qi

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Nomenclature and concepts

• Genotype is written as

B1
A1
A2
B2
A1 and B1 are in coupling phase A1 and B2 are in
repulsion phase
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Gametic Disequilibrium

• Easiest to think about physically linked loci,
  but not necessarily the case

What Are Expected Frequencies of Gametes in a
Population Under Independent Assortment?
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What are expected frequencies of gametes with
complete linkage?
The frequency of the gametes in the current
population. Expected to stay stable in the
absence of other departures from H-W
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Linkage disequilibrium measure, D
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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 p10.5, q20.5,
Dmax0.25 but p10.1, q20.9, Dmax0.09
Dmax Calculation If D is positive, Dmax is
lesser of p1q2 or p2q1 If D is negative, Dmax is
lesser of p1q1 or p2q2
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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

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Recombination

• 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

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Recombination Rate
What is the expected recombination rate for
unlinked loci?
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Expected Gamete Frequencies Double Homozygote
A1
B1
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Expected Gamete Frequencies Double Heterozygote
A2
B2
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LD is partially a function of recombination rate

• Expected proportions of haplotypes produced in a
  population after 1 generation of mating

Offspring Genotypes
Where c is the recombination rate
and D0 is the initial amount of LD
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Recombination degrades LD over time
Where t is time (in generations) and e is base of
natural log (2.718)
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Effects of recombination rate on LD

• Decline in LD over time with different
  theoretical recombination rates (c)
• Even with independent segregation (c0.5),
  multiple generations required to break up allelic
  associations

Where t is time (in generations) and e is base of
natural log (2.718)
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LD varies substantially across human genome
NATUREVol 43727 October 2005
Average r2 for pairs of SNP separated by 30 kb in
1 Mb windows

• 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

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Human HapMap Project and Whole Genome Scans
NATUREVol 43727 October 2005

• 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

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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 196713-725
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Recombination Across Poplar Chromosomes

• Substantial variation in recombination rate
• Related to repeat composition, methylation, and
  distance from centromere

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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
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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)

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Genetic Drift and LD

• Why doesnt recombination reduce LD in this
  situation?

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LD is partially a function of recombination rate

• Expected proportions of gametes produced by
  various genotypes over two generations
• Effective LD increases with homozygosity

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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

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Combined effects of Drift and Recombination

• LD declines as a function of population
  recombination rate
• Effects of chance fluctuation of gamete
  frequencies

Nec
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How should inbreeding affect linkage
disequilibrium?