Inferring human demographic history from DNA sequence data

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Inferring human demographic history from DNA
sequence data

• Apr. 28, 2009
• J. Wall
• Institute for Human Genetics, UCSF

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Standard model of human evolution
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Standard model of human evolution(Origin and
spread of genus Homo)
2 2.5 Mya
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Standard model of human evolution(Origin and
spread of genus Homo)
?
?
1.6 1.8 Mya
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Standard model of human evolution(Origin and
spread of genus Homo)
0.8 1.0 Mya
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Standard model of human evolutionOrigin and
spread of modern humans
150 200 Kya
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Standard model of human evolutionOrigin and
spread of modern humans
100 Kya
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Standard model of human evolutionOrigin and
spread of modern humans
40 60 Kya
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Standard model of human evolutionOrigin and
spread of modern humans
15 30 Kya
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Estimating demographic parameters

• How can we quantify this qualitative scenario
  into an explicit model?
• How can we choose a model that is both
  biologically feasible as well as computationally
  tractable?
• How do we estimate parameters and quantify
  uncertainty in parameter estimates?

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Estimating demographic parameters

• Calculating full likelihoods (under realistic
  models including recombination) is
  computationally infeasible
• So, compromises need to be made if one is
  interested in parameter estimation

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African populations
10 populations 229 individuals
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African populations
Mandenka (bantu)
61 autosomal loci 350 Kb sequence data
Biaka (pygmies)
San (bushmen)
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A simple model of African population history
T
g1
m
g2
Biaka (or San)
Mandenka
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Estimation method

• We use a composite-likelihood method (cf. Plagnol
  and Wall 2006) that uses information from the
  joint frequency spectrum such as
• Numbers of segregating sites
• Numbers of shared and fixed differences
• Tajimas D
• FST
• Fu and Lis D

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Estimation method

• We use a composite-likelihood method (cf. Plagnol
  and Wall 2006) that uses information from the
  joint frequency spectrum such as
• Numbers of segregating sites
• Numbers of shared and fixed differences
• Tajimas D
• FST
• Fu and Lis D

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Estimating likelihoods
Pop1 Pop2
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Estimating likelihoods
Pop 1 private polymorphisms
Pop1 Pop2
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Estimating likelihoods
Pop 1 private polymorphisms Pop 2 private
polymorphisms
Pop1 Pop2
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Estimating likelihoods
Pop 1 private polymorphisms Pop 2 private
polymorphisms Shared polymorphisms
Pop1 Pop2
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Estimation method

• We use a composite-likelihood method (cf. Plagnol
  and Wall 2006) that uses information from the
  joint frequency spectrum such as
• Numbers of segregating sites
• Numbers of shared and fixed differences
• Tajimas D
• FST
• Fu and Lis D

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Estimating likelihoods

• We assume these other statistics are multivariate
  normal.
• Then, we run simulations to estimate the means
  and the covariance matrix.
• This accounts (in a crude way) for dependencies
  across different summary statistics.

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Composite likelihood

• We form a composite likelihood by assuming these
  two classes of summary statistics are independent
  from each other
• We estimate the (composite)-likelihood over a
  grid of values of g1, g2, T and M and tabulate
  the MLE.
• We also use standard asymptotic assumptions to
  estimate confidence intervals

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Estimates (with 95 CIs)

• Parameter Man-Bia Man-San
• g1 (000s) 0 (0 3.8) 0 (0 3.8)
• g2 (000s) 4 (0 7.9) 2 (0 11)
• T (000s) 450 (300 640) 100 (77 550)
• M ( 4Nm) 10 (8.4 12) 3 (2.2 4)

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Fit of the null model

• How well does the demographic null model fit the
• patterns of genetic variation found in the actual
• data?

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Fit of the null model

• How well does the demographic null model fit the
• patterns of genetic variation found in the actual
• data?
• Quite well. The model accurately reproduces both
• parameters used in the original fitting (e.g.,
• Tajimas D in each population) as well as other
• aspects of the data (e.g., estimates of ? 4Nr)

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Estimates (with 95 CIs)

• Parameter Man-Bia Man-San
• g1 (000s) 0 (0 3.8) 0 (0 3.8)
• g2 (000s) 4 (0 7.9) 2 (0 11)
• T (000s) 450 (300 640) 100 (77 550)
• M ( 4Nm) 10 (8.4 12) 3 (2.2 4)

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Population growth
population size
time
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Population growth
population size
time
spread of agriculture and animal husbandry?
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Estimates (with 95 CIs)

• Parameter Man-Bia Man-San
• g1 (000s) 0 (0 3.8) 0 (0 3.8)
• g2 (000s) 4 (0 7.9) 2 (0 11)
• T (000s) 450 (300 640) 100 (77 550)
• M ( 4Nm) 10 (8.4 12) 3 (2.2 4)

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Ancestral structure in Africa

• At face value, these results suggest that
  population structure within Africa is old, and
  predates the migration of modern humans out of
  Africa.
• Is there any evidence for additional (unknown)
  ancient population structure within Africa?

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Model of ancestral structure
Archaic human population
T
g1
m
g2
Biaka (or San)
Mandenka
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Standard model of human evolutionOrigin and
spread of modern humans
100 Kya
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Admixture mapping
Modern human DNA
Neandertal DNA
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Admixture mapping
Modern human DNA
Neandertal DNA
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Admixture mapping
Modern human DNA
Neandertal DNA
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Admixture mapping
Modern human DNA
Neandertal DNA
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Admixture mapping
Modern human DNA
Neandertal DNA
Orange chunks are 10 100 Kb in length
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Genealogy with archaic ancestry
time
Modern humans
Archaic humans
present
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Genealogy without archaic ancestry
time
Modern humans
Archaic humans
present
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Our main questions

• What pattern does archaic ancestry produce in DNA
  sequence polymorphism data (from extant humans)?
• How can we use data to
• estimate the contribution of archaic humans to
  the modern gene pool (c)?
• test whether c gt 0?

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Genealogy with archaic ancestry(Mutations added)
time
Modern humans
Archaic humans
present
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Genealogy with archaic ancestry(Mutations added)
time
Modern humans
Archaic humans
present
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Patterns in DNA sequence data

• Sequence 1 A T C C A C A G C T G
• Sequence 2 A G C C A C G G C T G
• Sequence 3 T G C G G T A A C C T
• Sequence 4 A G C C A C A G C T G
• Sequence 5 T G T G G T A A C C T
• Sequence 6 A G C C A T A G A T G
• Sequence 7 A G C C A T A G A T G

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Patterns in DNA sequence data

• Sequence 1 A T C C A C A G C T G
• Sequence 2 A G C C A C G G C T G
• Sequence 3 T G C G G T A A C C T
• Sequence 4 A G C C A C A G C T G
• Sequence 5 T G T G G T A A C C T
• Sequence 6 A G C C A T A G A T G
• Sequence 7 A G C C A T A G A T G

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Patterns in DNA sequence data

• Sequence 1 A T C C A C A G C T G
• Sequence 2 A G C C A C G G C T G
• Sequence 3 T G C G G T A A C C T
• Sequence 4 A G C C A C A G C T G
• Sequence 5 T G T G G T A A C C T
• Sequence 6 A G C C A T A G A T G
• Sequence 7 A G C C A T A G A T G

We call the sites in red congruent sites these
are sites inferred to be on the same branch of an
unrooted tree
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Linkage disequilibrium (LD)

• LD is the nonrandom association of alleles at
  different sites.
• Low LD A C High LD A C
• A T A C
• A C A C
• A T A C
• G C G T
• G T G T
• G C G T
• G T G T

High recombination Low recombination
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Measuring congruence

• To measure the level of congruence in SNP data
  from
• larger regions we define a score function
• S
• where S (i1, . . . ik)
• and S (ij, ij1) is a function of both congruence
  (or near
• congruence) and physical distance between ij and
  ij1.

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An example
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An example (CHRNA4)
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An example (CHRNA4)
How often is S from simulations greater than or
equal to the S value from the actual data?
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An example (CHRNA4)
How often is S from simulations greater than or
equal to the S value from the actual data? p
0.025
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S is sensitive to ancient admixture
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General approach

• We use the model parameters estimated before
  (growth rates, migration rate, split time) as a
  demographic null model.
• Is our null model sufficient to explain the
  patterns of LD in the data?
• We test this by comparing the observed S values
  with the distribution of S values calculated
  from data simulated under the null model.

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Distribution of p-values(Mandenka and San)
frequency
p-value
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Distribution of p-values(Mandenka and San)
frequency
p-value
Global p-value 2.5 10-5
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Estimating ancient admixture rates
The global p-values for S are highly significant
in every population that weve studied! If we
estimate the ancient admixture rate in our
(composite)-likelihood framework, we can exclude
no ancient admixture for all populations
studied.
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A region on chromosome 4
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A region on chromosome 4
19 mutations (from 6 Kb of sequence) separate 3
Biaka sequences from all of the other sequences
in our sample. Simulations suggest this cannot
be caused by recent population structure (p lt
10-3) This corresponds to isolation lasting 1.5
million years!
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Possible explanations

• Isolation followed by later mixing is a recurrent
  feature of human population history
• Mixing between archaic humans and modern humans
  happened at least once prior to the exodus of
  modern humans out of Africa
• Some other feature of population structure is
  unaccounted for in our simple models

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Acknowledgments

• Collaborators
• Mike Hammer (U. of Arizona)
• Vincent Plagnol (Cambridge University)
• Samples
• Foundation Jean Dausset (CEPH)
• Y chromosome consortium (YCC)
• Funding
• National Science Foundation
• National Institutes for Health