Population Genetics Introduction

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Population Genetics Introduction

• Lecture 24 November 29, 2005
• Algorithms in Biosequence Analysis
• Nathan Edwards - Fall, 2005

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Genomic Polymorphism

• We all have a slightly different genome
• DNA replication isnt perfect!
• Two humans (today) have about 1 difference per
  1000 base-pairs on average.
• Insert, deletion, substitution
• Most of these dont matterbut some do!
• Color-blindness is a result of a single
  nucleotide change!

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Population Genetics

• Population genetics uses statistics to understand
  how genetics affects large numbers of
  individuals.
• Well established field
• (Mostly) based on easily observed phenotypes
• Changing due to biotechnologies that can
  determine SNPs in individuals.
• Actual nucleotide at a particular position.

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Terminology

• We are diploid organisms
• Two copies of each chromosome
• The two copies are not exactly the same.
• Each copy is called a haplotype
• Each pair of copies is called a genotype
• Each position on a chromosome is a locus
• Each variant at a locus is an allele
• A genotype with (two) of one allele is
  homozygous,...
• ...with two alleles is heterozygous.

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Haplotypes

• 1ACGACTCAGATCACTACGTACGACT
• 1ACGACTCAGATAACTACGGACGACT
• 2ACGACTCAGATCACTACGTACGACT
• 2ACGACTCAGATCACTACGTACGACT
• 3ACGAGTCAGATCACTACGTACGACT
• 3ACGAGTCAGATAACTACGGACGACT

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Haplotypes

• 1ACGACTCAGATCACTACGTACGACT
• 1ACGACTCAGATAACTACGGACGACT
• 2ACGACTCAGATCACTACGTACGACT
• 2ACGACTCAGATCACTACGTACGACT
• 3ACGAGTCAGATCACTACGTACGACT
• 3ACGAGTCAGATAACTACGGACGACT

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Genotypes

• ACGACCTCAGATCAACTACGTGACGACT
• ACGACCTCAGATCCACTACGTTACGACT
• ACGAGGTCAGATCAACTACGTGACGACT

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Genotyping Technology

• Can only tell us about a particular locus, so we
  lose information about an individuals haplotypes
• 1 C, A,C, G,T
• 2 C, C, T
• 3 G, A,C, G,T

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Genotyping Technology

• Can only tell us about a particular locus, so we
  lose information about an individuals haplotypes
• 1 0, 2, 2
• 2 0, 1, 1
• 3 1, 2, 2

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Haplotypes

• Haplotypes are important because they are
  inherited...
• not genotypes
• We inherit one copy of each chromosome from each
  parent
• One haplotype from each parent
• If no mutation or recombination, we receive one
  of each parents two haplotypes
• and so on, back to founder population

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Haplotypes

• How do new haplotypes enter the population?
• mutation recombination when germ cells are
  produced in each parent
• Mutation isnt that rare, but two mutations at a
  particular locus is very rare
• 3x10-9 that any particular site is chosen once
• Infinite sites model assumes that each DNA
  position can change at most once.

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Infinite sites model

• What are the implications of the infinite sites
  model?
• We never revert at a locus
• Shared alleles must be from a common ancestor.
• At most 2 alleles at each polymorphic locus
• If no recombination, we could unambiguously trace
  our lineage back through time.

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Recombination

• In addition to DNA mutations, new haplotypes are
  introduced by recombination during germ cell
  production.
• Recombination merges parental haplotypes.
• new haplotypes are passed to offspring.

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Recombination
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Recombination

• Consider two loci, each with two alleles.
• A and a, B and b.
• Paternal haplotype has A and B,
• Maternal haplotype has a and b
• Without recombination, child gets one haplotype
  with either A and B, or a and b.
• Due to recombination, child might (with some
  probability) get one haplotype with A and b, or B
  and a.
• What is the chance of a recombination event
  between these loci?
• Decreases with the distance between two loci.

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Recombination

• Two point mutations close to one another on one
  chromosome are more likely to be inherited
  together
• Two point mutations on different chromosomes or
  far from each other will be observed independently

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Harvey-Weinberg Equilibrium

• Given a locus with 2 alleles, A and a
• p is frequency of A in the (haplotype) population
  
• q 1-p is frequency of a in the population
• Three genotypes are possible AA, Aa, aa
• If various assumptions are satisfied (random
  mating, no natural selection, etc)
• P AA p2, P Aa 2pq, P aa q2

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Harvey-Weinberg Equilibrium

• Assumptions include
• Diploid
• Sexual reproduction
• Random mating
• Bi-allelic sites
• Large population size
• Basic model Each individual randomly picks his
  two haplotypes from the population

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Linkage (Dis)-equilibrium

• HWE provides a model for observed genotypes at a
  single locus.
• What about alleles on a single haplotype at two
  loci?
• If extensive recombination
• PA,B(0,0) 0.375
• PA,B(0,1) 0.125
• PA,B(1,0) 0.375
• PA,B(1,1) 0.125
• Linkage equilibrium

A B 0 1 0 1 0 0 0 0 1 0 1
0 1 0 1 0
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Linkage (Dis)-equilibrium

• HWE provides a model for observed genotypes at a
  single locus.
• What about alleles on a single haplotype at two
  loci?
• If no recombination
• PA,B(0,0) 0.25
• PA,B(0,1) 0.25
• PA,B(1,0) 0.5
• PA,B(1,1) 0.0
• Linkage disequilibrium (LD)

A B 0 1 0 1 0 0 0 0 1 0 1
0 1 0 1 0
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Measures of LD

• Two bi-allelic sites A and B with 0,1 alleles
• Let P00 P A 0 B 0 P0 P A 0
  , P0 P B 0 ,
• If P00 P0 P0, then linkage equilibrium
• D abs(P00 - P0 P0) abs(P01 - P0 P1) ...
  

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LD over time

• With random mating, and fixed recombination rate
  (r) between sites, LD will disappear
• Let D(t) LD at time t
• P(t)00 (1-r)P(t-1)00 r P(t-1)0 P(t-1)0
• D(t) P(t)00 - P(t)0 P(t)0 P(t)00 -
  P(t-1)0 P(t-1)0 (HWE)
• D(t) (1-r) D(t-1) (1-r)t D(0)
• LD decays exponentially with time.

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Halotype phasing

• Current technology doesnt provide information
  about haplotypes, we get geneotypes instead.
• Haplotype phasing is the resolution of a genotype
  into two haplotypes.

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Genotyping Technology
Probes for each allele
Genomic DNA
SNP site
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Genotyping Technology
Genomic DNA
SNP site
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Genotyping Technology
Genomic DNA
SNP site
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Haplotype phasing

• When is phasing easy?
• g1 0 1 0 0 0 1 1 0 0 1 1
• g2 1 0 0 1 1 0 1 0 0 1 0
• g3 0 1 1 0 1 1 0 1 0 1 1
• g4 0 1 0 1 0 1 2 0 0 0 1

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Haplotype phasing

• When is phasing easy?
• h11 0 1 0 0 0 1 1 0 0 1 1
• h12 0 1 0 0 0 1 1 0 0 1 1
• ...
• h41 0 1 0 1 0 1 0 0 0 0 1
• h42 0 1 0 1 0 1 1 0 0 0 1

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Haplotype Phasing

• What happens if we have more than one ambiguous
  site?
• g5 0 2 0 2 0 1 1 0 2 1 1 (s 3)
• h51 0 0 0 0 0 1 1 0 0 1 1
• h52 0 1 0 1 0 1 1 0 1 1 1
• 3 other phasings are possible. (2s-1)

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Halotype phasing

• Rely on linkage disequilibrium
• Many fewer haplotypes than 2S-1
• Assume (haplotype) population consists of a small
  number of distinct haplotypes
• We tend to share haplotypes
• Or at least chunks of haplotypes
• Clarks rule (1990) proposed a common sense
  approach.

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Clarks Rule

• Find unambiguous individuals
• (at most 1 ambiguous locus)
• Form initial list of known haplotypes
• Resolve ambiguous individuals
• If possible, use two known haplotypes
• Otherwise, use one known haplotype and add new
  haplotype to list.
• If unphased individuals remain
• Assign phase randomly for one individual

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Clarks Rule

• Basic principle
• Rely on known haplotypes
• Create as few haplotypes as possible
• What can go wrong?
• How to start if no unambiguous individuals?
• What happens when we get stuck?
• Unambiguous 00 forces 22 to 11, when 01, 10 might
  be more likely.
• Maybe 00 is a rare event?
• Often works pretty well, if unambiguous
  individuals sample common haplotypes
  thoroughly.
• Fast!

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Clarks Rule

• We can enhance Clarks rule by selecting
  genotypes to phase and haplotypes to use, based
  on their frequency.
• Many different models, objectives are plausible,
  and they give different results!

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HapMap Consortium

• International consortium measuring genotypes and
  comparing SNP and haplotype information across
  the human genome
• 90 Africans (30 parent-child trios)
• 90 Americans (30 parent-child trios)
• 45 Chinese
• 44 Japanese

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HapMap Data
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HapMap Data