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Inferring human demographic history from DNA sequence
data
Apr. 28, 2009
J. WallInstitute for Human Genetics, UCSF
Standard model of human evolution
Standard model of human evolution(Origin and spread of genus Homo)
2 – 2.5 Mya
Standard model of human evolution(Origin and spread of genus Homo)
1.6 – 1.8 Mya
?
?
Standard model of human evolution(Origin and spread of genus Homo)
0.8 – 1.0 Mya
Standard model of human evolutionOrigin and spread of ‘modern’ humans
150 – 200 Kya
Standard model of human evolutionOrigin and spread of ‘modern’ humans
~ 100 Kya
Standard model of human evolutionOrigin and spread of ‘modern’ humans
40 – 60 Kya
Standard model of human evolutionOrigin and spread of ‘modern’ humans
15 – 30 Kya
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?
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
African populations
10 populations
229 individuals
African populations
San (bushmen)
Biaka (pygmies)
Mandenka (bantu)
61 autosomal loci~ 350 Kb sequence data
A simple model of African population history
T
mg1
g2
Mandenka Biaka
(or San)
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
Tajima’s D
FST
Fu and Li’s D*
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
Tajima’s D
FST
Fu and Li’s D*
Estimating likelihoods
Pop1 Pop2
Estimating likelihoods
Pop1 Pop2
Pop 1 private polymorphisms
Estimating likelihoods
Pop1 Pop2
Pop 1 private polymorphisms
Pop 2 private polymorphisms
Estimating likelihoods
Pop1 Pop2
Pop 1 private polymorphisms
Pop 2 private polymorphisms
Shared polymorphisms
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
Tajima’s D
FST
Fu and Li’s D*
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.
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
Estimates (with 95% CI’s)
Parameter Man-Bia Man-San
g1 (000’s) 0 (0 – 3.8) 0 (0 – 3.8)
g2 (000’s) 4 (0 – 7.9) 2 (0 – 11)
T (000’s) 450 (300 – 640) 100 (77 – 550)
M (= 4Nm) 10 (8.4 – 12) 3 (2.2 – 4)
Fit of the null model
How well does the demographic null model fit the
patterns of genetic variation found in the actual
data?
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.,
Tajima’s D in each population) as well as other
aspects of the data (e.g., estimates of ρ = 4Nr)
Estimates (with 95% CI’s)
Parameter Man-Bia Man-San
g1 (000’s) 0 (0 – 3.8) 0 (0 – 3.8)
g2 (000’s) 4 (0 – 7.9) 2 (0 – 11)
T (000’s) 450 (300 – 640) 100 (77 – 550)
M (= 4Nm) 10 (8.4 – 12) 3 (2.2 – 4)
Population growth
time
popu
latio
n si
ze
Population growth
time
popu
latio
n si
ze
spread of agriculture and animal husbandry?
Estimates (with 95% CI’s)
Parameter Man-Bia Man-San
g1 (000’s) 0 (0 – 3.8) 0 (0 – 3.8)
g2 (000’s) 4 (0 – 7.9) 2 (0 – 11)
T (000’s) 450 (300 – 640) 100 (77 – 550)
M (= 4Nm) 10 (8.4 – 12) 3 (2.2 – 4)
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?
Model of ancestral structure
T
mg1
g2
Mandenka Biaka
(or San)
Archaic human population
Standard model of human evolutionOrigin and spread of ‘modern’ humans
~ 100 Kya
Admixture mappingModern human DNA Neandertal DNA
Admixture mappingModern human DNA Neandertal DNA
Admixture mappingModern human DNA Neandertal DNA
Admixture mappingModern human DNA Neandertal DNA
Admixture mappingModern human DNA Neandertal DNA
Orange chunks are ~10 – 100 Kb in length
Genealogy with archaic ancestrytime
present
Modern humans
Archaic humans
Genealogy without archaic ancestrytime
present
Modern humans
Archaic humans
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 > 0?
Genealogy with archaic ancestry(Mutations added)
time
present
Modern humans
Archaic humans
Genealogy with archaic ancestry(Mutations added)
time
present
Modern humans
Archaic humans
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
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
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
Linkage disequilibrium (LD)LD is the nonrandom association of alleles at different sites.
Low LD: A C High LD: A CA T A CA C A CA T A CG C G TG T G TG C G TG T G T
High recombination Low recombination
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, ij+1) is a function of both congruence (or near
congruence) and physical distance between ij and ij+1.
)(max},...2,1{IS
nI
1
11),(
k
jjj iiS
An example
An example (CHRNA4)
An example (CHRNA4)
How often is S* from simulations greater than or equal to the S* value from the actual data?
An example (CHRNA4)
How often is S* from simulations greater than or equal to the S* value from the actual data? p = 0.025
S* is sensitive to ancient admixture
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.
Distribution of p-values(Mandenka and San)
p-value
Distribution of p-values(Mandenka and San)
p-value
Global p-value: 2.5 * 10-5
Estimating ancient admixture rates
The global p-values for S* are highly significant in every population that we’ve studied!
If we estimate the ancient admixture rate in our (composite)-likelihood framework, we can exclude no ancient admixture for all populations studied.
A region on chromosome 4
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 < 10-3)
This corresponds to isolation lasting ~1.5 million years!
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
Acknowledgments
Collaborators:Mike Hammer (U. of Arizona)Vincent Plagnol (Cambridge University)
Samples: Foundation Jean Dausset (CEPH)Y chromosome consortium (YCC)
Funding: National Science FoundationNational Institutes for Health