algorithms for ascertaining markers for controlling for...

Efficient algorithms for ascertaining markers for controlling for population substructure

Oscar LaoDepartment of Forensic Molecular Biology

Erasmus Medical Center (Rotterdam)New Jersey 2009

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Workflow1. Human population substructure

‐ How to detect it?

‐ How much?

‐Where does it come from?

2. Why does it matter?

3. Ancestry Sensitive Markers (ASMs) / Ancestry Informative Markers (AIMs)

‐ Hypothesis driven. Particular individual clusters are preferred‐ ASMs

‐ PhenoASMs

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How much there is and how much can be detected. The two sides of the same coin

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Population substructure

Plato’s cave myth

– STRUCTURE

– BAPS

– FRAPPE

– GENELAND

– PCA/MDS + K means

– Neural Networks

– …

Sometimes results are NOT reproducible

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Population substructureDETECTION

Which type?‐ Phenotype

‐ GenotypeY chromosome

mtDNA

Autosomal markers

Where?‐Worldwide

‐ Regional (I will focus on Europe)

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Population substructureHOW MUCH?

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Phenotypic substructure

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Y chromosome

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mtDNA

Cavalli‐Sforza et al 19944/27/2009 9New Jersey 2009

Classical markers

1064 samples 51 human populations of global distribution

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CEPH-HGDP panel

993 autosomal markers


M. EastAfrica Europe C/S-Asia E-Asia AmeriO

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Autosomal STRs

Rosenberg et al Science 2002

Rosenberg et al Plos Genetics 2005

Li et al Science 2008

650,000 SNPs (FRAPPE)

Jakobsson et al Nature 2008

550,000 SNPs (STRUCTURE) Haplotypes

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Autosomal SNPs

23 populations

500 Affy Array

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A set of European populations

Lao and Lu et al Current Biology 2008

300,000 SNPs

r=0.7

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Autosomal SNPs in Europe

Novembre et al Nature 2008

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K = 2; Admixture

Correlation with latitude

R2 = 0.86

Correlation with longitude

R2 = 0.01

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World Europe

Anayet peak (2574 m), Pyrenees Keukenhoof garden(‐2 m), Netherlands

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EDAR (positive selection in Asians)

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Non random distribution ofpopulation substructure

LCT (positive selection in North European populations)

Lao and Lu et al Current Biology 2008

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Non random distribution ofpopulation substructure

Cavalli‐Sforza & Feldman Nature Genetics 2003

Simoni et al AJHG 2000

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Demography shapes thepopulation substructure

• Selective pressures within the species (locus specific)

Lactose toleranceMalaria resistenceHuman pigmentation…

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Selection shapes thepopulation substructure

• Population substructure & pigmentation (5 SNPs)

-1 -0.5 0 0.5 1 1.5

-1.5

-1

-0.5

0

0.5

1

Europe

Africa

Middle East

Oceania

America

C/SAsia

EAsia

N Africa

MDS

5 to 12

12 to 16

16 to 20

20 to 24

24 to 30

Biasutti skin pigmentation units Lao et al Ann Hum Genet 2007

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Selection shapes thepopulation substructure

CASES CONTROLS

A

G

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Why population substructure:Confounding factor

Plato’s cave myth

CHANGE THE ALGORITHM FOR DETECTING POPULATION SUBSTRUCTURE

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Population substructure: improving the detection

Plato’s cave myth

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Population substructure: improving the detection

INCREASE THE RESOLUTION TO SEE THE OBJECTS

• Markers that capture most of the genetic ancestry– Estimate ancestry

– Reduce the number of markers to test for genetic homogeneity

• Time cost (clustering algorithms can be extremely computational intensive)

• Economical cost (i.e exclude individuals BEFORE doing the GWA)

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AIMs/ASMs

• Based on the existing diversity between individuals (i.e Paschou et al 2008)

• Based on predefined groups of individuals– No phenotype linked

• Large Genetic distances

• Signals of positive selection

– Phenotype linked• Covariates with the phenotype of interest

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Strategies to ascertain ASMs

• Use a statistic to quantify the amount of differentiation between populations

• Compute the OVERAL non‐redundant amount of In between set of SNPs

• Take the best combination of markers from all the possible combinations

• Repeat the process until the information of the set of markers is maximum

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A basic algorithm to ascertain ASMs

( ) ∑ ∑= =

⎟⎟⎠

⎞⎜⎜⎝

⎛+−=

N

j

K

iij

ijjjn p

Kp

ppJQI1 1

loglog;

Am J Hum Genet. 2003 Dec;73(6):1402-22

informativeness for assignment

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A statistic to ascertain ASMs

• How much information a marker contains about the ancestry of one individual (measured in nats)

• Ranges from 0 to the natural logarithm of the number of clusters and it is proportional to the number of differentiated clusters

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• Computes the non‐redundant amount of information when considering more than one marker

• Requires computing the frequency of ALL the allelic combinations when considering more than 1 locus

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• Problem: The number of combinations increases exponentially with the number of markers. – Number of allelic combinations considering 50 SNPs:

4906,842,621,125,899,250 =

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A way to compute In

( ) ∑ ∑= =

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j

K

i

ijjn K

HHJQI

1 1;

( )∑=

≈N

ip

NH

1ln1 By applying the

Asymptotic Equipartition Property of Entropy

( ) ∑ ∑= =

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⎞⎜⎜⎝

⎛+−=

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j

K

iij

ijjjn p

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ppJQI1 1

loglog;

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A way to compute In

• Problem: Considering 8,000 markers, ascertaining the best set of 50 markers requires computing :

( )130104

!50000,8!508,000!

×≈−

=nscombinatioN

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A method to ascertain ASMs

Population of answers

Select best answers (>In)

Random mating

Recombination/Mutation

Next generation

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A method to ascertain ASMs

10k Affymetrix Array(~9000 SNPs after excluding X-SNPs & missing SNPs)

SNP ascertainment(10 SNPs) (10 SNPs)

YCC-panel76 human individuals 21 sampling localities

CEPH-HGDP panel1064 samples 51 human populations of global distribution

Perlegen Database3 Human populations~1,500,000 SNPs(most informative 5 SNPs)

Reproducibility of geographic structure in a

different dataset

Test for signatures of

positive selection(EHH test)

Lao et al. Am J Hum Genet. 2006 Apr;78(4):680‐90

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ASMs for continental differentiation using Affy 10k

0

10

20

30

40

50

60

70

80

90

100

1 2 3 4 5 6 7 8 9 10

Number of SNPs

perc

enta

geof

info

rmat

ion

The genetic algorithm was applied increasing every time the

number of selected SNPs

Marker name

Chromosome Gene name IN (%) from 4 groups YCC panel

IN (%) from 7 groups CEPH-HGDP

rs722869 14 VRK1 29.066 7.960 rs1858465 17 25.637 9.228 rs1876482 2 LOC442008 24.589 10.290 rs1344870 3 22.810 11.074 rs1363448 5 PCDHGB1 19.418 4.552 rs952718 2 ABCA12 18.739 9.472 rs2352476 7 18.317 5.603 rs714857 11 18.083 6.157 rs1823718 15 17.845 5.451 rs735612 15 RYR3 14.315 5.530

Selected SNPs in the final 10 SNPs run


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ASMs for continental differentiation using Affy 10k

Europe AfricaM. EastC/S-AsiaE-AsiaAmeri O

10 SNPs No admixture

Admixture



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ASMs for continental differentiationASMs for continental differentiation using Affy 10k

K = 6 (1000 (randomly ascertained) markers, Admixture, 10,000 burning, 10,000 retained simulations)

Africa Sub‐Saharan Europe India East Asia Am

K = 5 (50 markers, Admixture, 500,000 burning, 500,000 retained simulations)

K = 6 (100 markers, Admixture, 100,000 burning, 100,000 retained simulations)

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ASMs for continental differentiation using HapMap III

E Asia

Oceania

Africa

Europe

Middle East

Central Asia

Amerindians

25 ascertained markers. PCA

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ASMs for continental differentiation using Illumina 650k

• CEPH550,000 SNPs

K = 5 (50 ascertained markers, Admixture, 500,000 burning, 500,000 retained simulations)

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ASMs for continental differentiation using Illumina 650k

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Africa Europe‐Meast‐Casia Easia Oceania Amerindian

K=Oceania

K=Europe‐Meast‐Casia

K=Amerindian

K=Africa

K=Easia

Real geographic location

Inferred geographic location

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Specificity of the ascertained markers

K = 2 (5000 random markers, Admixture, 10,000 burning, 10,000 retained simulations)

K = 3 (500 ascertained markers, Admixture, 10,000 burning, 10,000 retained simulations)

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ASMs for population differentiation in the European continent using Affymetrix 500k

05

101520253035404550

25.9 25.95 26 26.05 26.1 26.15 26.2 26.25

-log1

0(P-

valu

e)

Physical position (Mb)

Association between OCA_HERC2 region and iris coloradjusted for ancestry sensitive markers

500KSNPs

498AncestrySensitiveSNPs

Random498SNPs

NoAdjustment(Orignial_AJHG)

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Use of the 500 ASMs for correcting the effect of population substructure

• Recall– Population substructure is only a problem when PHENOTIPIC and GENOTYPIC variation covariates

– Why not ascertaining markers that are associated to the particular spatial pattern of the phenotype?

);();;()|;( JQIJPQIJPQI nnn −=

“Amount of information of the phenotype (P) conditional on the genotype (J): How well could we correctly classify one individual given that we know his phenotype if we already know his genotype in a particular locus”

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PhenoASMs

LCT

HERC2

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PhenoASMs for lactose tolerance

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PhenoASMs for Crohn disease

• Update θ with a Metropolis algorithm• Update the covariance matrix of the proposal distribution by means of a “quasi‐perfect adaptive MCMC” (Andrieu and Atchade)

• Compute the harmonic mean of the likelihood in order to obtain a rough estimate of P(M|D)

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PhenoASMs: a Bayesian approach

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Phenotype-genotype association for eye color

TAS2R38

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Phenotype-genotype association for bitter taste

TAS2R38

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• Low to moderate human population differentiation

• Mainly associated to geography

• No sharp discontinuities, except in particular genomic regions (selection?)

• Results depend on the clustering algorithm

• ASMs can improve the detection of population substructure

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Conclusions

• In is a good statistic for ascertaining markers to differentiate predefined populations

• If a prior definition of a population is used, ASMs will tend to differentiate such population, independently of the biological meaning

• PhenoASMs as the next level of ASMs?

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Conclusions

M. Balascakova, C. Becker, J. Bertranpetit, L.A. Bindoff, D. Comas, U. Gether, C. Gieger, G. Holmlund, A. Kouvatski, M. Macek, I. Mollet, M. Nelson, P. Nuernberg, W. Parson, R. Ploski, A. Ruether, A. Sajantila, S. Schreiber, A. Tagliabracci, A. Uiterlinden, T. Werge, and E. Wichmann.

In collaboration with

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Acknowledgements

Tim LuMichael KrawczakManfred Kayser

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Petros Drineas

Andreas Wollstein

Peristeia Paschou

Thank you very much!

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