population admixture - data.broadinstitute.org filealkes price harvard school of public health...

Alkes Price

Harvard School of Public Health

February 19 & February 21, 2019

EPI 511, Advanced Population and Medical Genetics

Week 4:

• Population admixture

Outline

1. Admixture leads to variation in genome-wide ancestry

2. Admixture creates mosaic chromosomes

3. Local ancestry inference

4. Evaluating local ancestry inference algorithms

Hellenthal et al. 2014 Science

What is an admixed population?

An admixed population is a population with recent

ancestry from two or more continents

(e.g. within the past 1,000 years).

What is an admixed population?

An admixed population is a population with recent

ancestry from two or more continents

(e.g. within the past 1,000 years).

Note: the word “admixture” is also sometimes used to

refer to more ancient admixture events. (e.g. Patterson et al. 2012 Genetics, Hellenthal et al. 2014 Science)

Population structure vs. Population admixture:

What’s the difference?

Population structure: [Week 3]

• Genetic differences due to geographic ancestry.

• Use genome-wide data to infer genome-wide ancestry.

Population admixture: [Week 4]

• Mixed ancestry from multiple continental populations.

• e.g. African Americans, Latino Americans.

• Infer local ancestry at each location in the genome.

Population admixture implies population structure.

Population structure does not imply population admixture.

Examples of admixed populations

African Americans:

• Inherit African and European ancestry

• >10% of U.S. population

Smith et al. 2004 Am J Hum Genet

also see Bryc et al. 2015 Am J Hum Genet


Hispanic/Latino Americans:

• Inherit European and Native American

or European, Native American and African ancestry

• e.g. Mexican Americans, Puerto Ricans, etc.

• >15% of U.S. population

Bryc, Velez et al. 2010 PNAS



Latinos outside the U.S.:

• Inherit European and Native American

or European, Native American and African ancestry

• hundreds of millions of people throughout Latin America



An aside: Characteristics of African,

European and Native American populations

African populations:

• High within-population diversity, low LD (no bottleneck).

• Low genetic distance (FST) between West African populations

European populations:

• Lower within-population diversity, higher LD (bottleneck).

• Low genetic distance (FST) between European populations

Native American populations:

• Lowest within-population diversity, highest LD due to

multiple population bottlenecks.

• Very high FST between Native American populations

Cavalli-Sforza et al. 1994 The History and Geography of Human Genes

Reich et al. 2012 Nature

Other examples of admixed populations

Native Hawaiians (Polynesian, European, East Asian ancestry)

Uyghurs (East Asian and European-related ancestry)

A population that self-identifies and is described in the

the academic literature as “South African Coloured” (San African, Bantu African, European, S Asian, SE Asian ancestry)

Haiman et al. 2003 Hum Mol Genet,

Haiman et al. 2007 Nat Genet

Xu, Huang et al. 2008 Am J Hum Genet,

Xu & Jin 2008 Am J Hum Genet

de Wit et al. 2010 Hum Genet, Patterson et al. 2010 Hum Mol Genet,

Tishkoff et al. 2009 Science, Chimusa et al. 2013 Hum Mol Genet

Inferring genome-wide ancestry proportions

Apply the usual clustering programs, allowing fractional ancestry

(see Week 3 slides):

• STRUCTURE (Pritchard et al. 2000 Genetics, Falush et al. 2003 Genetics)

• FRAPPE (Tang et al. 2005 Genet Epidemiol, Li et al. 2008 Science)

• ADMIXTURE (Alexander et al. 2009 Genome Res)

Inferring genome-wide ancestry proportions

Apply the usual clustering programs, allowing fractional ancestry


• STRUCTURE (Pritchard et al. 2000 Genetics, Falush et al. 2003 Genetics)

• FRAPPE (Tang et al. 2005 Genet Epidemiol, Li et al. 2008 Science)

• ADMIXTURE (Alexander et al. 2009 Genome Res)

Or, apply principal components analysis


• PCA (Price et al. 2006 Nat Genet, Patterson et al. 2006 PLoS Genet)

Admixture leads to variation in genome-wide ancestry

AA: 21% ± 14%

European ancestry

YRI

CHB+JPT

CEU

African Americans

Price, Patterson et al. 2008 PLoS Genet

also see Smith et al. 2004 Am J Hum Genet; Bryc et al. 2015 Am J Hum Genet

(from Week 3)

PC1

PC2

Admixture proportion varies across individuals,

but also varies with U.S. geographic location

Kittles et al. 2007 CJHP

also see Bryc et al. 2015 Am J Hum Genet, Baharian et al. 2016 PLoS Genet

% European ancestry in African American populations

Latino populations: 3-way admixture

Bryc, Velez et al. 2010 PNAS; also see Bryc et al. 2015 Am J Hum Genet

European

Native American

African


Price et al. 2007 Am J Hum Genet; also see Bryc, Velez et al. 2010 PNAS;

Moreno-Estrada et al. 2014 Science; Bryc et al. 2015 Am J Hum Genet

Mexican Americans

50% European, 45% Native American, 5% African on average,

with substantial variation among individuals.

Puerto Ricans


with substantial variation among individuals.

Brazilians and Colombians


with substantial variation among individuals. [For populations sampled. Values may not apply to all populations.]

Different Native American ancestral populations

for Latino populations in different regions

Wang et al. 2008 PLoS Genet

also see Price et al. 2007 Am J Hum Genet

CEU northern European USA 180

CHB Chinese China 90

JPT Japanese Japan 90

YRI Yoruba Nigeria 180

TSI Tuscan Italy 90

CHD Chinese USA 100

LWK Luhya Kenya 90

MKK Maasai Kenya 180

ASW African-American USA 90

MXL Mexican-American USA 90

GIH Gujarati-American USA 90

Which HapMap3 populations are admixed?

PCA of all HapMap3 populations

International HapMap3 Consortium 2010 Nature (see Supp Figures)

These populations are “homogeneous”

in their continental ancestry


ASW, MKK and LWK are admixed


ASW, MKK and LWK are admixed


Bantu expansion

(2000 BC – 1000 AD)

Arab migrations

(500 – 1500 AD)

(Cavalli-Sforza et al. 1994,

The History and Geography

Of Human Genes)

X Ancestral East African population

STRUCTURE results on African populations

= West African/Bantu

= East African

= Khoisan

= Pygmy

= European/Middle Eastern

Tishkoff et al. 2009 Science; also see Gurdasani et al. 2015 Nature

K=14:

(from Week 3)

MXL (Mexican Americans) are admixed


Are GIH (Gujarati Americans) admixed?


also see Reich et al. 2009 Nature, Nakatsuka et al. 2017 Nat Genet

Which HGDP populations are admixed?

Li et al. 2008 Science

938 HGDP individuals

Illumina 650K chip (from Week 3)

Which HGDP populations are admixed?

Li et al. 2008 Science

admixture in

Middle East / North Africa?

Recent? Or not? (Price, Tandon et al. 2009 PLoS Genet)

European Americans: 3-way admixture!

Bryc et al. 2015 Am J Hum Genet

European Americans

>99% European,

0.2% Native American,

0.2% African on average

with substantial variation

among individuals.

Trees can also describe population structure

Unrooted tree Rooted tree Jakobsson et al. 2008 Nature Li et al. 2008 Science

(from Week 3)

also see Cavalli-Sforza et al. 2003 Nat Genet

Trees cannot model recent admixture

root

YRI CEU

root

YRI CEU ASW ASW

WRONG. WRONG.

Outline





Admixture creates mosaic chromosomes

Population 1 Population 2

1 generation later


2 generations later



several generations later


Local ancestry = 0, 1 or 2

copies from population 1



several generations later



Average segment length (in Morgans) ~ 1/g

where g = average #generations since admixture

g ≈ 6 for African Americans, g ≈ 10 for Latino populations

Smith et al. 2004 Am J Hum Genet, Price et al. 2007 Am J Hum Genet

Mosaic chromosomes create admixture-LD

Toy example: Admixed population with 50% POP1, 50% POP2

SNP1 = A/C SNP, A allele has frequency 0.10 in POP1, 0.90 in POP2


SNP1 and SNP2 are unlinked in POP1, unlinked in POP2.

SNP1 and SNP2 are 200kb apart: (nearly) always same local ancestry.







P(SNP1=A, SNP2=A) = 50%·0.10·0.10 + 50%·0.90·0.90 = 0.41

POP1 POP2







P(SNP1=A, SNP2=A) = 50%·0.10·0.10 + 50%·0.90·0.90 = 0.41

P(SNP1=A, SNP2=C) = 50%·0.10·0.90 + 50%·0.90·0.10 = 0.09

P(SNP1=C, SNP2=A) = 50%·0.90·0.10 + 50%·0.10·0.90 = 0.09

P(SNP1=C, SNP2=C) = 50%·0.90·0.90 + 50%·0.10·0.10 = 0.41







P(SNP1=A, SNP2=A) = 50%·0.10·0.10 + 50%·0.90·0.90 = 0.41

P(SNP1=A, SNP2=C) = 50%·0.10·0.90 + 50%·0.90·0.10 = 0.09

P(SNP1=C, SNP2=A) = 50%·0.90·0.10 + 50%·0.10·0.90 = 0.09

P(SNP1=C, SNP2=C) = 50%·0.90·0.90 + 50%·0.10·0.10 = 0.41

SNP1 and SNP2 are in admixture-LD in the admixed population!

slide repeated in Week 6

Admixture-LD depends on allele frequency differences






P(SNP1=A, SNP2=A) = 50%·0.10·0.10 + 50%·0.10·0.90 = 0.05

P(SNP1=A, SNP2=C) = 50%·0.10·0.90 + 50%·0.10·0.10 = 0.05

P(SNP1=C, SNP2=A) = 50%·0.90·0.10 + 50%·0.90·0.90 = 0.45

P(SNP1=C, SNP2=C) = 50%·0.90·0.90 + 50%·0.90·0.10 = 0.45

No allele frequency difference in SNP1 => no admixture-LD.


Real example of admixture-LD:

rs164781: 0.42 in CEU, 0.88 in YRI (HapMap3)


These SNPs are located roughly 3Mb apart.

r2 between rs164781 and rs10495758:

0.01 in CEU, 0.01 in YRI, 0.28 in ASW (HapMap3)

rs164781 and rs10495758 are in admixture-LD in ASW!

International HapMap3 Consortium 2010 Nature

SNPs chosen from Tandon et al. 2011 Genet Epidemiol

slide repeated in Week 4 bonus slides


Collins-Schramm et al. 2003 Hum Genet

No LD in Europeans (P-values for LD not significant)


Collins-Schramm et al. 2003 Hum Genet

Admixture-LD in African Americans (significant P-values)



at a specific locus

Local ancestry vs. Genome-wide ancestry

Local

ancestry

Genome-wide

ancestry

Genome-wide ancestry

(e.g. 20% European)

Outline





Ancestry-informative marker (AIM) panels for

local ancestry inference in African Americans

The most

informative

~1% of

SNPs

provide

powerful

information

about

ancestry

0%

20%

40%

60%

80%

100%

0% 20% 40% 60% 80% 100%

European American Frequency

We

st

Afr

ica

n F

req

ue

nc

y

Smith et al. 2004

• Choose 1,500-3,000 SNPs with large Δ(EUR,AFR)

(unlinked, i.e. not in LD, in ancestral populations)

Smith et al. 2004 Am J Hum Genet

Tian et al. 2006 Am J Hum Genet (slide from David Reich)

The most informative SNPs

provide powerful information

about local ancestry

“African-American

admixture map”

Ancestry-informative marker (AIM) panels for

local ancestry inference in Latino populations

Price et al. 2007 Am J Hum Genet

Mao et al. 2007 Am J Hum Genet

Tian et al. 2007 Am J Hum Genet

The most informative SNPs

provide powerful information

about local ancestry

“Latino admixture map”

• Choose 1,500-3,000 SNPs with large Δ(EUR,NA)

(unlinked, i.e. not in LD, in ancestral populations)



at a specific locus

Local ancestry vs. Genome-wide ancestry

Local

ancestry

Genome-wide

ancestry

Genome-wide ancestry

(e.g. 20% European)

25-50 AIMs

1,500-3,000 AIMs

Inferring local ancestry using AIM panels

SNP chr position Eur freq Afr freq

rs2814778 1 159,174,683 0% 100%

1 SNP with Δ=100%: perfect information about local ancestry

Duffy blood group locus

see Hamblin et al. 2000 Am J Hum Genet, Hamblin et al. 2002 Am J Hum Genet

slide repeated in Week 6 bonus slides, slide repeated in Week 7



rs1962508

rs2806424

rs1780349

1

1

1

158,677,077

159,423,117

161,340963

4%

84%

44%

74%

26%

99%

Several SNPs with Δ=60-80%: ???



rs1962508

rs2806424

rs1780349

1

1

1

158,677,077

159,423,117

161,340963

4%

84%

44%

74%

26%

99%

Several SNPs with Δ=60-80%: Hidden Markov Model methods

STRUCTURE (Falush et al. 2003 Genetics), ADMIXMAP (Hoggart et al. 2004

Am J Hum Genet), ANCESTRYMAP (Patterson et al. 2004 Am J Hum Genet)

(unobserved) state:



Overview of Hidden Markov Model approach

• Simplifying assumption: for a individual i, suppose we know

M = genome-wide ancestry (e.g. 20%)

λ = average #generations since admixture (e.g. 6)

• Let Xj = the (unobserved) state (0, 1 or 2 European chromosomes)

of this individual at marker j along the genome.

INITIAL PROBABILITIES (e.g. left end of chromosome):

TRANSITION PROBABILITIES

EMISSION PROBABILITIES

Patterson et al. 2004 Am J Hum Genet; also HMM refs: Lander & Green 1987 PNAS,

Rabiner 1987 Proceedings of the IEEE, Durbin et al 1998 Biological Sequence Analysis








P(X0 = 0) = (1 – M)2

P(X0 = 1) = 2M(1 – M)

P(X0 = 2) = M2









TRANSITION PROBABILITIES:

Let d be the genetic distance (in Morgans) between markers j and j+1.

P(Xj+1 = 0 | Xj = 0) = e–2λd + 2e–λd(1 – e–λd)(1 – M) + (1 – e–λd)2(1 – M)2



0 of 2

chrom.

recombine

1 of 2

chrom.

recombine

2 of 2

chrom.

recombine









P(Xj+1 = 0 | Xj = 0) = e–2λd + 2e–λd(1 – e–λd)(1 – M) + (1 – e–λd)2(1 – M)2

P(Xj+1 = 1 | Xj = 0) = 2e–λd(1 – e–λd)M + (1 – e–λd)22M(1 – M)

P(Xj+1 = 2 | Xj = 0) = (1 – e–λd)2M2











P(Xj+1 = 0 | Xj = 1) = 2e–λd(1 – e–λd)(1 – M) + (1 – e–λd)2(1 – M)2

P(Xj+1 = 1 | Xj = 1) = e–2λd + e–λd(1 – e–λd) + (1 – e–λd)22M(1 – M)

P(Xj+1 = 2 | Xj = 1) = e–λd(1 – e–λd)M + (1 – e–λd)2M2











P(Xj+1 = 0 | Xj = 2) = (1 – e–λd)2(1 – M)2

P(Xj+1 = 1 | Xj = 2) = 2e–λd(1 – e–λd)(1 – M) + (1 – e–λd)22M(1 – M)

P(Xj+1 = 2 | Xj = 2) = e–2λd + 2e–λd(1 – e–λd)M + (1 – e–λd)2M2









EMISSION PROBABILITIES:

Let pA and pE be genotype frequencies of marker j in AFR and EUR.

P(gj = 0 | Xj = 0) = (1 – pA)2

P(gj = 1 | Xj = 0) = 2pA(1 – pA)

P(gj = 2 | Xj = 0) = pA2











P(gj = 0 | Xj = 1) = (1 – pA)(1 – pE)

P(gj = 1 | Xj = 1) = pA(1 – pE) + pE(1 – pA)

P(gj = 2 | Xj = 1) = pApE











P(gj = 0 | Xj = 2) = (1 – pE)2

P(gj = 1 | Xj = 2) = 2pE(1 – pE)

P(gj = 2 | Xj = 2) = pE2












Then apply forward-backward algorithm to infer P(Xj | genotypes).





P(X1|g1) P(Xj|g1…gj) P(XM-1|g1…gM-1) P(XM|g1…gM)

(FORWARD PROBABILITIES)

Durbin et al 1998 Biological Sequence Analysis




(FORWARD PROBABILITIES)

P(g2…gM|X1) P(gj+1…gM|Xj) P(gM|XM-1) 1

(BACKWARD PROBABILITIES)












(Or, use MCMC to integrate over uncertainty in M, λ, pA, pE.)



Big trouble if markers are in LD in ancestral populations

Example: Admixed population with 80% POP1, 20% POP2 ancestry


A allele has frequency 80%·0.25 + 20%·0.75 = 0.35 in Admixed pop.

Inference of local ancestry of a haploid chromosome using SNP1:

prob 0.35: P(POP1 | A) = 80%·0.25/(80%·0.25 + 20%·0.75 ) = 57%

prob 0.65: P(POP1 | C) = 80%·0.75/(80%·0.75 + 20%·0.25) = 92%

Overall: P(POP1) = 57%·0.35 + 92%·0.65 = 80%. Unbiased.


Big trouble if markers are in LD in ancestral populations

Example: Admixed population with 80% POP1, 20% POP2 ancestry


SNP2 = A/C SNP in perfect LD with SNP1 in POP1, POP2

A allele has frequency 80%·0.25 + 20%·0.75 = 0.35 in Admixed pop.

Inference of local ancestry of a haploid chr using SNP1, SNP2:

prob 0.35: P(POP1 | AA) = 80%·0.252/(80%·0.252 + 20%·0.752) =

31%

prob 0.65: P(POP1 | CC) = 80%·0.752/(80%·0.752 + 20%·0.252) =

97%

Overall: P(POP1) = 31%·0.35 + 97%·0.65 = 74%. Biased.


Inferring local ancestry using GWAS chip data

Advantages of AIM panels of 1,500+ SNPs:

• Lower cost: $80/sample

(vs. $300+sample for GWAS chips).

Advantages of GWAS chips:

• Dense SNP coverage enables LD mapping

• More accurate local ancestry inference?


• ANCESTRYMAP using a subset of ~8,000 unlinked AIMs

(Patterson et al. 2004 Am J Hum Genet; Tandon et al. 2011 Genet Epidemiol)

New methods developed for GWAS chip data: • SABER (Tang et al. 2006 Am J Hum Genet)

• LAMP (Sankararaman et al. 2008 Am J Hum Genet)

• uSWITCH (Sankararaman et al. 2008 Genome Res)

• HAPAA (Sundquist et al. 2008 Genome Res)

• HAPMIX (Price, Tandon et al. 2009 PLoS Genet)

• WINPOP (Pasaniuc et al. 2009 Bioinformatics)

• GEDI-ADMX (Pasaniuc et al. 2009 Lect Notes Comput Sci)

• PCA-based method (Bryc, Auton et al. 2010 PNAS)

• LAMP-LD (Baran et al. 2012 Bioinformatics)

• MULTIMIX (Churchhouse & Marchini 2013 Genet Epidemiol)

• RFMix (Maples et al. 2013 Am J Hum Genet)

reviewed in Seldin et al. 2011 Nat Rev Genet


• ANCESTRYMAP using a subset of ~8,000 unlinked AIMs

(Patterson et al. 2004 Am J Hum Genet; Tandon et al. 2011 Genet Epidemiol)

New methods developed for GWAS chip data: • SABER (Tang et al. 2006 Am J Hum Genet)

• LAMP (Sankararaman et al. 2008 Am J Hum Genet) • uSWITCH (Sankararaman et al. 2008 Genome Res)

• HAPAA (Sundquist et al. 2008 Genome Res)

• HAPMIX (Price, Tandon et al. 2009 PLoS Genet) • WINPOP (Pasaniuc et al. 2009 Bioinformatics)

• GEDI-ADMX (Pasaniuc et al. 2009 Lect Notes Comput Sci)

• PCA-based method (Bryc, Auton et al. 2010 PNAS)

• LAMP-LD (Baran et al. 2012 Bioinformatics)

• MULTIMIX (Churchhouse & Marchini 2013 Genet Epidemiol)

• RFMix (Maples et al. 2013 Am J Hum Genet)


Inferring local ancestry: LAMP method

LAMP method: (allele frequencies in ancestral populations not known)

• Prune SNP set to restrict to unlinked markers (r2 < 0.10)

• Choose fixed window length l

• Infer local ancestry within each window of length l via EM algorithm

(Unsupervised clustering, integer-valued haploid local ancestries)

• For each SNP, compute majority vote of local ancestry across

all windows overlapping that SNP.

Sankararaman et al. 2008 Am J Hum Genet

1

2

3

4

5

6

7

Window window length l

Inferring local ancestry: LAMP-ANC method

LAMP-ANC: (allele frequencies in ancestral populations are known)



• Infer local ancestry within each window of length l via max likelihood

(Supervised clustering, integer-valued haploid local ancestries)

• For each SNP, compute majority vote of local ancestry across

all windows overlapping that SNP.


1

2

3

4

5

6

7

Window window length l

Inferring local ancestry: LAMP and LAMP-ANC

LAMP and LAMP-ANC:



• Infer local ancestry within each window of length l

• For each SNP, compute majority vote across windows containing SNP

Choice of window length l is key. If window length is

• too small: not enough information to infer local ancestry

• too big: violates assumption of constant local ancestry within window

window length l



LAMP and LAMP-ANC:





Choice of window length l is key. If window length is

• too small: not enough information to infer local ancestry

• too big: violates assumption of constant local ancestry within window

Use window length l which is

inversely proportional to # generations since admixture,

i.e. proportional to ancestry segment lengths

window length l



LAMP and LAMP-ANC:





Advantages:

• Simple and transparent approach, low computational cost

Disadvantages:

• Information from neighboring windows is not used

• Does not make use of haplotype information

window length l


WINPOP improvement to LAMP-ANC

LAMP and LAMP-ANC:





WINPOP:

• Allow variable window length l depending on local genetic

structure of ancestral populations.

• Explicitly model the possibility of one recombination event per window,

enabling larger windows.

window length l

Pasaniuc et al. 2009 Bioinformatics

also see Baran et al. 2012 Bioinformatics

Inferring local ancestry: HAPMIX method

HAPMIX method: nested Hidden Markov Models

• Large-scale HMM: transitions between local ancestry states

(Patterson et al. 2004 Am J Hum Genet).

• Small-scale HMM: transitions between haplotypes from

ancestral reference populations (Li & Stephens 2003 Genetics)

Price, Tandon et al. 2009 PLoS Genet

POP1

POP2

hap1

hap2

hap3

hap4

hap5

hap1

hap2

hap3

hap4

hap5


HAPMIX method: nested Hidden Markov Models

• States: local ancestry AND haplotype from POP1 or POP2.

• Given initial, transition and emission probabilities: use

forward-backward algorithm to infer P(states | data).

(Durbin et al. 1998 Biological Sequence Analysis + other HMM refs)


POP1

POP2

hap1

hap2

hap3

hap4

hap5

hap1

hap2

hap3

hap4

hap5


Advantages:

• Large-scale + Small-scale HMM use all information in GWAS chip data

Disadvantages:

• Increased complexity and running time

POP1

POP2

hap1

hap2

hap3

hap4

hap5

hap1

hap2

hap3

hap4

hap5


Next steps to understanding local ancestry inference

Rhythm is gonna get you.

-- Gloria S.

Data is gonna get you.

-- Alkes

http://www.historyforsale.com/gloria-estefan-photograph-signed/dc256742

https://www.youtube.com/watch?v=UzcQrqG8wsY

Example on real data actual chr1 local ancestry of one African-American sample,

estimated by HAPMIX, ANCESTRYMAP, LAMP


Johnson et al. 2011 PLoS Genet

also see Moreno-Estrada et al. 2013 PLoS Genet, Gravel et al. 2013 PLoS Genet

Other uses of local ancestry information

(besides population genetics)

Freedman et al. 2006 PNAS

also see Seldin et al. 2011 Nat Rev Genet

Genovese et al. 2013 Nat Genet

also see Genovese et al. 2013 Am J Hum Genet

Zaitlen et al. 2014 Nat Genet

Outline





How to evaluate local ancestry inference methods?

• % of haploid segments whose ancestry is inferred correctly (0 or 1)

(analogue of imputation accuracy; Huang et al. 2009 Am J Hum Genet)

• % of diploid loci whose ancestry is inferred correctly (0 or 1 or 2)

(diploid accuracy; Sankararaman et al. 2008 Am J Hum Genet)

• Squared correlation (r2) between estimated and true local ancestry

(Price et al. 2009 PLoS Genet; #samples for given power ~ 1/r2)

Assessing accuracy:









e.g. 95% accuracy for haploid segments

90% accuracy for diploid loci (if genome-wide ancestry = 20%)

r2 = 0.84

Assessing accuracy:









Simulated African Americans with 6 generations since admixture:

ANCESTRYMAP r2 = 0.83

LAMP r2 = 0.84

WINPOP r2 = 0.94

HAPMIX r2 = 0.98

Assessing accuracy:



Even more important than assessing accuracy: no spurious peaks

Average HAPMIX local ancestry estimates of 6,209 AA from CARe

HAPMIX

Pasaniuc et al. PLoS Genet 2011;

also see Price, Tandon et al. 2009 PLoS Genet




Average ANCESTRYMAP local ancestry estimates of CARe AA

Admixture peaks should be evaluated

using two independent algorithms

(Reich et al. 2005 Phil Trans R Soc B)

Pasaniuc et al. PLoS Genet 2011

Tandon et al. 2011 Genet Epidemiol



European

Native American

African

Local ancestry inference in Latino populations

Main challenge:

• Lack of accurate Native American ancestral reference panels

can lead to spurious deviations in local ancestry

Additional challenges:

• Some local ancestry algorithms do not support 3-way admixture

• Native American reference panels may themselves be admixed

• European reference panels: N. Europe panels may be inaccurate

reference population for S. Europe ancestral population

Seldin et al. 2011 Nat Rev Genet


Local ancestry inference in Latino populations

Main challenge:

• Lack of accurate Native American ancestral reference panels

can lead to spurious deviations in local ancestry

Solutions:

• Use Native American segments of Latinos as reference panels

• Use trio data to assess regions with Mendelian inconsistencies

in inferred local ancestry.


Maples et al. 2013 Am J Hum Genet

• In an admixed population, different people have different

genome-wide ancestry proportions.

• Each individual from an admixed population has mosaic

chromosomes with segments of different continental ancestry.

These mosaic chromosomes lead to admixture-LD.

• Local ancestry can be inferred from AIM panels with decent

accuracy and from GWAS chip data with high accuracy.

• Local ancestry inference accuracy can be evaluated using r2

and lack of spurious peaks in large empirical data sets.

Conclusions

Outline





Bonus: extra content on admixture mapping

Outline (admixture mapping)

1. Introduction to admixture mapping

2. Admixture mapping statistics: case-control and case-only

3. Real examples of admixture mapping studies

4. Admixture association vs. SNP association

Autosomal recessive diseases (genetic):

Cystic fibrosis ( European ancestry)

Sickle-cell anemia ( African ancestry)

Background: population differences in disease




Complex diseases (genetic and/or environmental):

Multiple sclerosis ( European ancestry)

Prostate cancer ( African ancestry)

Type 2 diabetes ( Native American ancestry)





Complex diseases (genetic and/or environmental):

Multiple sclerosis ( European ancestry)

Prostate cancer ( African ancestry)

Type 2 diabetes ( Native American ancestry)

African Americans: African + European ancestry

Latinos: European + Native American + African ancestry


Using admixture to map disease

Admixture association: a location of the genome

where average local ancestry in disease cases has an

unusual deviation.

Using admixture to map disease:

toy example

Example: HBB gene (risk locus for sickle-cell anemia)

• Sickle-cell mutation exists at allele frequency

0%* in European populations, 5%* in African populations.

[mutations on both chromosomes => sickle-cell anemia]

• Local ancestry of African American chromosomes at HBB:

20% have European local ancestry

76% have African local ancestry without sickle-cell mutation

4% have African local ancestry with sickle-cell mutation

Mears et al. 1981 J Clin Invest


toy example

100%

75%

50%

African Americans with sickle-cell anemia have

100 % African ancestry at HBB locus.

Position in the genome


toy example #2

Example: CFTR gene (risk locus for cystic fibrosis)

• Cystic fibrosis mutations exist at allele frequency

2%* in European populations, 0%* in African populations.

[mutations on both chromosomes => cystic fibrosis]

• Local ancestry of African American chromosomes at CFTR:

80% have African local ancestry

19.6% have European local ancestry without CFTR mutation

0.4% have European local ancestry with CFTR mutation

Morton 1968 Am J Hum Genet


toy example #2

100%

50%

0%

African Americans with cystic fibrosis have

0% African ancestry at CFTR locus.


100%

75%

50%


African Americans with common disease X have

higher % African ancestry at disease locus.


realistic example

100%

75%

50%


African Americans with common disease X have

higher % African ancestry at disease locus.

• Risk allele has higher freq in Africans than Europeans

• disease is more common in Africans than Europeans


realistic example

Disease locus

Admixture association is different

from SNP association

• Requires fewer markers, since local ancestry can be

inferred using <2,000 ancestry-informative markers

(Smith et al. 2004 Am J Hum Genet, Tian et al. 2006 Am J Hum Genet)

• Poor localization: admixture association signal spans

several megabases.

• Lower multiple hypothesis testing burden than GWAS:

effective number of regions tested is only hundreds.

• Does not require data from controls (case-only statistics).

LD enables (indirect) SNP association …

Admixture-LD enables admixture association

Real example of admixture-LD:



These SNPs are located roughly 3Mb apart.

r2 between rs164781 and rs10495758:

0.01 in CEU, 0.01 in YRI, 0.28 in ASW (HapMap3)

rs164781 and rs10495758 are in admixture-LD in ASW!

(from Week 4)

International HapMap3 Consortium 2010 Nature

SNPs chosen from Tandon et al. 2011 Genet Epidemiol

Outline





Case-control admixture association

Case-control admixture association: a location of the

genome where average local ancestry in disease cases

has an unusual deviation compared to average

local ancestry in controls.

Case-control admixture association, simplified

• Armitage Trend Test for case-control SNP association:

Nρ(genotype at candidate SNP, phenotype)2

Armitage 1955 Biometrics




• Armitage Trend Test for case-control admixture association:

Nρ(local ancestry at candidate locus, phenotype)2





[If population stratification is a concern:

correct for genome-wide ancestry of each individual.]

• Armitage Trend Test for case-control admixture association:

Nρ(local ancestry at candidate locus, phenotype)2

[If population stratification is a concern:

correct for genome-wide ancestry of each individual.]


Toy example: Admixed population with 50% POP1, 50% POP2.


Suppose that SNP1 is the causal variant, with Odds Ratio = 1.5.

Case-control admixture association: toy example




Probabilities of values of SNP1 and local ancestry:

Controls: P(SNP1=A) = 0.50 Cases: P(SNP1=A) = 0.60

P(SNP1=A, POP1) = 0.05 P(SNP1=A, POP1) = 0.06


P(SNP1=C, POP1) = 0.45 P(SNP1=C, POP1) = 0.36


P(POP2) = 0.50 P(POP2) = 0.58

Thus, there is a case-control admixture association at this locus.







Controls: P(SNP1=A) = 0.50 Cases: P(SNP1=A) = 0.60





P(POP2) = 0.50 P(POP2) = 0.58

Thus, there is a case-control admixture association at this locus.

To detect admixture association: necessary to infer local ancestry,

but not necessary to genotype SNP1.


SNP odds ratio vs. Ancestry odds ratio

Recall: The SNP odds ratio R is the ratio of ref vs. var alleles in

disease cases as compared to ref vs. var alleles in controls.

ref var Equivalently,

Controls: p : 1–p pcase(1 – pcontrol)

Cases: Rp : 1–p pcontrol(1 – pcase)

[Or, the SNP odds ratio R is the ratio of case vs. control odds for

ref allele as compared to case vs. control odds for var allele.]

R =



Definition: The ancestry odds ratio Ω is the ratio of

European vs. African chromosomes in disease cases as compared

to European vs. African chromosomes in controls.

European African Equivalently,

Controls: γ : 1–γ γcase(1 – γcontrol)

Cases: Ωγ : 1–γ γcontrol(1 – γcase)

[Or, the ancestry odds ratio Ω is the ratio of case vs. control odds

for Eur chr as compared to case vs. control odds for Afr chr.]

Ω =





European African

ref var ref var

Controls: γpE : γ(1–pE) : (1–γ)pA : (1–γ)(1–pA)

Cases: γRpE : γ(1–pE) : (1–γ)RpA : (1–γ)(1–pA)





European (ref + var) African (ref + var)

Controls: γ : 1–γ

Cases: γ(RpE + 1–pE) : (1–γ)(RpA + 1–pA)





European (ref + var) African (ref + var)

Controls: γ : 1–γ

Cases: γ(RpE + 1–pE) : (1–γ)(RpA + 1–pA)

This implies that the ancestry odds ratio Ω is equal to

RpE + 1–pE

RpA + 1–pA


The ancestry odds ratio Ω is equal to

RpE + 1–pE

RpA + 1–pA

R pE pA Ω

1.50 100% 0% 1.50

1.50 0% 100% 0.67

1.50 90% 10% 1.38

1.50 75% 25% 1.22

1.50 60% 40% 1.08

1.50 50% 50% 1.00

(see toy example)

Case-only admixture association

Case-only admixture association: a location of the


has an unusual deviation compared to local ancestry

in the same disease cases elsewhere in the genome.






Case-only (a.k.a. locus-genome) admixture statistics are

more powerful than case-control statistics, due to the

lack of statistical noise introduced from controls.

Patterson et al. 2004 Am J Hum Genet






Case-only (a.k.a. locus-genome) admixture statistics

require no deviations in average local ancestry in controls

(e.g. due to artifacts, selection since admixture, etc.)


Case-only admixture statistics require no spurious peaks


Average HAPMIX local ancestry estimates of 6,209 AA from CARe

HAPMIX

Pasaniuc et al. PLoS Genet 2011;

also see Price, Tandon et al. 2009 PLoS Genet (from Week 4)

Case-only admixture association, simplified

In a given set of disease cases, suppose we observe

Genome-wide ancestry θ in each individual

Average local ancestry γ at candidate disease locus

i.e. 2Nγ European chromosomes, 2N(1–γ) African chromosomes

[Note: 0 ≤ γ ≤ 1 # European chromosomes = 0 or 1 or 2]






NULL MODEL (γ* = θ):

log P(data | NULL) = 2Nγlog(θ) + 2N(1–γ)log(1–θ)

CAUSAL MODEL (γ* ≠ θ, highest likelihood at γ* = γ):

log P(data | CAUSAL) = 2Nγlog(γ) + 2N(1–γ)log(1–γ)

Note: all logs are loge unless otherwise indicated






NULL MODEL (γ* = θ):

log P(data | NULL) = 2Nγlog(θ) + 2N(1–γ)log(1–θ)

CAUSAL MODEL (γ* ≠ θ, highest likelihood at γ* = γ):

log P(data | CAUSAL) = 2Nγlog(γ) + 2N(1–γ)log(1–γ)

Likelihood-ratio test, χ2(1 dof):

2[2Nγlog(γ/θ) + 2N(1–γ)log((1–γ)/(1–θ))]




Case-only admixture association: toy example





Cases, genome-wide: Cases: P(SNP1=A) = 0.60

P(SNP1=A, POP1) = 0.06

P(SNP1=A, POP2) = 0.54

P(SNP1=C, POP1) = 0.36

P(SNP1=C, POP2) = 0.04

P(POP2) = 0.50 P(POP2) = 0.58

Thus, there is a case-only admixture association at this locus.







P(SNP1=A, POP1) = 0.06

P(SNP1=A, POP2) = 0.54

P(SNP1=C, POP1) = 0.36

P(SNP1=C, POP2) = 0.04

P(POP2) = 0.50 P(POP2) = 0.58


θ = 0.50, γ = 0.58 => χ2(1 dof) = 0.051·N,

assuming N diploid disease cases and γ equal to its expected value.







P(SNP1=A, POP1) = 0.06

P(SNP1=A, POP2) = 0.54

P(SNP1=C, POP1) = 0.36

P(SNP1=C, POP2) = 0.04

P(POP2) = 0.50 P(POP2) = 0.58


θ = 0.50, γ = 0.58 => χ2(1 dof) = 0.051·N (for N diploid disease cases)

vs. SNP case-control χ2(1 dof) = 0.040·N (for N cases, N controls)







P(SNP1=A, POP1) = 0.06

P(SNP1=A, POP2) = 0.54

P(SNP1=C, POP1) = 0.36

P(SNP1=C, POP2) = 0.04

P(POP2) = 0.50 P(POP2) = 0.58


To detect admixture association: necessary to infer local ancestry,

but not necessary to genotype SNP1.


Case-only admixture association, generalized






2[2Nγlog(γ/θ) + 2N(1–γ)log((1–γ)/(1–θ))]

Generalizations:






2[2Nγlog(γ/θ) + 2N(1–γ)log((1–γ)/(1–θ))]

Generalizations:

• Different θi for each disease case i. [Ω relates θi to γi.]







2[2Nγlog(γ/θ) + 2N(1–γ)log((1–γ)/(1–θ))]

Generalizations:


• Explicit probabilities for 0, 1 or 2 European chromosomes.







2[2Nγlog(γ/θ) + 2N(1–γ)log((1–γ)/(1–θ))]

Generalizations:


• Explicit probabilities for 0, 1 or 2 European chromosomes.

• ANCESTRYMAP approach: use MCMC to integrate over

uncertainty in θi and uncertainty in local ancestry estimates.








2[2Nγlog(γ/θ) + 2N(1–γ)log((1–γ)/(1–θ))]

Generalizations:

• Also see “Admixture aberration analysis: application to

mapping in admixed populations using pooled DNA”

Bercovici & Geiger RECOMB 2010 conference


Next steps to understanding admixture mapping

Rhythm is gonna get you.

-- Gloria S.

Data is gonna get you.

-- Alkes

http://www.historyforsale.com/gloria-estefan-photograph-signed/dc256742

https://www.youtube.com/watch?v=UzcQrqG8wsY

Outline





100%

75%

50%


African Americans with prostate cancer have

higher % African ancestry at 8q24 disease locus.


prostate cancer


LOD (log10 odds) score = 7.14

100%

75%

50%




Ancestry risk Ω=1.54 at 8q24 is sufficient to explain

higher rate of prostate cancer in African Americans.

Admixture peak spans position 125-130Mb on chr8.


prostate cancer




100%

75%

50%




rs6983561, a SNP associated to prostate cancer,

has frequency 3% in Europeans but frequency

58% in Africans.


prostate cancer


Haiman et al. 2007 Nat Genet




multiple sclerosis

Reich et al. 2005 Nat Genet



multiple sclerosis

Reich et al. 2005 Nat Genet


Ancestry effect at chr1 locus is

sufficient to explain lower rate

of MS in African Americans


hypertension

Zhu et al. 2005 Nat Genet

Z score > 4

chr 6q

Z score > 4

chr 21q


hypertension

Zhu et al. 2005 Nat Genet

Deo et al. 2007 PLoS Genet

Z score > 4

chr 6q

Z score > 4

chr 21q


low white blood cell (WBC) count

Nalls et al. 2007 Am J Hum Genet

also see Reich et al. 2009 PLoS Genet

LOD (log10 odds) score > 20

chr 1q


low white blood cell (WBC) count

Nalls et al. 2007 Am J Hum Genet

also see Reich et al. 2009 PLoS Genet

LOD (log10 odds) score > 20

chr 1q

Ancestry effect at chr1 locus is

sufficient to explain lower WBC

in African Americans



chr 22q


End-stage renal disease Ancestry effect at chr22 locus is

sufficient to explain higher rate

of ESRD in African Americans

Kao et al. 2008 Nat Genet

also see Kopp et al. 2008 Nat Genet, Genovese et al. 2010 Science


Yang, Cheng et al. 2011 Nat Genet

Disease phenotype: relapse of ALL

(acute lymphoblastic leukemia)

Case-control admixture association.


relapse of ALL in a multi-ethnic U.S. cohort

Yang, Cheng et al. 2011 Nat Genet

Population stratification???

Dangers of population stratification in

case-control admixture association studies

Disease phenotype: relapse of ALL

(acute lymphoblastic leukemia)

Fejerman et al. 2012 Hum Mol Genet

Use admixture to map disease:

breast cancer in US Latinas

Disease phenotype: Breast cancer

US Latinas: higher European ancestry => higher risk,

even after correcting for known non-genetic risk factors.

6q25 locus: ancestry odds ratio 0.75 per Native American chr,

95% confidence interval 0.65-0.85, Pcorrected = 0.02.

Fejerman et al. 2012 Hum Mol Genet

Use admixture to map disease:

breast cancer in US Latinas

Disease phenotype: Breast cancer

US Latinas: higher European ancestry => higher risk,

even after correcting for known non-genetic risk factors.

6q25 locus: ancestry odds ratio 0.75 per Native American chr,

95% confidence interval 0.65-0.85, Pcorrected = 0.02.

“We evaluated significance via a permutation test.

Case/control status was permuted to reproduce the asymmetry

of the global ancestry distribution between cases and controls.

Outline





Admixture association vs. SNP association

“The idea of mapping disease using admixture techniques has

been around for ages, but is probably one whose time has come

and gone, before having any useful successes ... it no longer

has a strong rationale in an age when genotype costs have

fallen so dramatically and the typing of 100's of thousands of

SNPs from throughout the genome is often comparable to

typing smaller more painstakingly selected SNP pools.”


“The idea of mapping disease using admixture techniques has

been around for ages, but is probably one whose time has come

and gone, before having any useful successes ... it no longer

has a strong rationale in an age when genotype costs have

fallen so dramatically and the typing of 100's of thousands of

SNPs from throughout the genome is often comparable to

typing smaller more painstakingly selected SNP pools.”

–Anonymous reviewer

(Price et al. 2007 Am J Hum Genet)


• Can often be carried out using <2,000 genetic markers

(lower genotyping costs: $100/sample instead of $300/sample)

• Can often be carried out by genotyping cases only

(2x cost savings)

• Case-only statistic: no statistical noise introduced from controls

(potential increase in power)

• Lower multiple hypothesis testing burden

(hundreds of regions instead of 500,000-1,000,000 SNPs)



• Admixture association is only effective if the causal SNP has a

high allele frequency difference between ancestral populations,

and still loses power since local ancestry is an imperfect proxy

for SNP genotype at the causal SNP.

• Admixture association requires inference of local ancestry.

• Admixture association requires (more) additional fine-mapping

after a significant association is identified.


SNP association + admixture association?

Case-control SNP association + case-only admixture association (Pasaniuc et al. 2011 PLoS Genet; Shriner et al. 2011 PLoS Comp Bio)

• 1 degree of freedom test retains power if causal SNP has been

genotyped/imputed.

• 1 degree of freedom test may lose power if causal SNP has not

been genotyped/imputed or if there are multiple causal SNPs.

• Case-only test for admixture component may increase power.


SNP association + admixture association?

Case-control SNP association + case-only admixture association (Pasaniuc et al. 2011 PLoS Genet; Shriner et al. 2011 PLoS Comp Bio)

• 1 degree of freedom test retains power if causal SNP has been

genotyped/imputed.

• 1 degree of freedom test may lose power if causal SNP has not


• Case-only test for admixture component may increase power.

Case-parent SNP association + case-parent admixture association (Tang et al. 2010 Genet Epidemiol), generalizing TDT in trios.

• 2 degree of freedom test may lower power if causal SNP has

been genotyped/imputed.

• 2 degree of freedom test increases power if causal SNP has not



• Admixture mapping, i.e. searching for unusual deviations in

local ancestry, is a potentially useful mapping strategy for

causal variants that differ in frequency between populations.

• Case-only admixture association has greater statistical power

than case-control admixture association, if local ancestry

can be inferred without any artifactual deviations.

• Admixture mapping has been effective in finding disease loci.

• In the age of low genotyping costs, admixture association is

most likely to be useful as a complementary statistical signal

to SNP association in GWAS data sets.

Conclusions

population admixture - data.broadinstitute.org filealkes price harvard school of public health...

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