Relatedness and differentiation in arbitrary population ......0.3 Individuals Kinship Ournewkinship...
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Transcript of Relatedness and differentiation in arbitrary population ......0.3 Individuals Kinship Ournewkinship...
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0.2
0.3
0.4
Inbr
eedi
ng c
oeff.
Relatedness and differentiationin arbitrary population structuresAlejandro Ochoa, StatGen Center, Duke University
with John D. Storey, Princeton University7 DrAlexOchoa � ochoalab.github.io R [email protected]
New kinship estimator for arbitrary population structuresxij ∈ {0, 1, 2} : Genotype at locus i of individual j .
Model:
E[xij |T ] = 2pi , Cov(xij , xik |T ) = 4pi (1− pi)ϕjk .
Standard estimator is biased:
p̂i =12n
n∑j=1
xij , ϕ̂stdjk =
m∑i=1
(xij − 2p̂i) (xik − 2p̂i)
4m∑i=1
p̂i (1− p̂i)
a.s.−−−→m→∞
ϕjk − ϕ̄j − ϕ̄k + ϕ̄
1− ϕ̄.
popkin: first unbiased kinship estimator! — R package on CRAN
Ajk =1m
m∑i=1
(xij − 1)(xik − 1)− 1, Amin = minu 6=v
1|Su||Sv |
∑j∈Su
∑k∈Sv
Ajk ,
ϕ̂jk = 1− Ajk
Amin
a.s.−−−→m→∞
ϕjk .
2 / 7
New kinship estimator for arbitrary population structuresxij ∈ {0, 1, 2} : Genotype at locus i of individual j . Model:
E[xij |T ] = 2pi , Cov(xij , xik |T ) = 4pi (1− pi)ϕjk .
Standard estimator is biased:
p̂i =12n
n∑j=1
xij , ϕ̂stdjk =
m∑i=1
(xij − 2p̂i) (xik − 2p̂i)
4m∑i=1
p̂i (1− p̂i)
a.s.−−−→m→∞
ϕjk − ϕ̄j − ϕ̄k + ϕ̄
1− ϕ̄.
popkin: first unbiased kinship estimator! — R package on CRAN
Ajk =1m
m∑i=1
(xij − 1)(xik − 1)− 1, Amin = minu 6=v
1|Su||Sv |
∑j∈Su
∑k∈Sv
Ajk ,
ϕ̂jk = 1− Ajk
Amin
a.s.−−−→m→∞
ϕjk .
2 / 7
New kinship estimator for arbitrary population structuresxij ∈ {0, 1, 2} : Genotype at locus i of individual j . Model:
E[xij |T ] = 2pi , Cov(xij , xik |T ) = 4pi (1− pi)ϕjk .
Standard estimator is biased:
p̂i =12n
n∑j=1
xij , ϕ̂stdjk =
m∑i=1
(xij − 2p̂i) (xik − 2p̂i)
4m∑i=1
p̂i (1− p̂i)
a.s.−−−→m→∞
ϕjk − ϕ̄j − ϕ̄k + ϕ̄
1− ϕ̄.
popkin: first unbiased kinship estimator! — R package on CRAN
Ajk =1m
m∑i=1
(xij − 1)(xik − 1)− 1, Amin = minu 6=v
1|Su||Sv |
∑j∈Su
∑k∈Sv
Ajk ,
ϕ̂jk = 1− Ajk
Amin
a.s.−−−→m→∞
ϕjk .
2 / 7
New kinship estimator for arbitrary population structuresxij ∈ {0, 1, 2} : Genotype at locus i of individual j . Model:
E[xij |T ] = 2pi , Cov(xij , xik |T ) = 4pi (1− pi)ϕjk .
Standard estimator is biased:
p̂i =12n
n∑j=1
xij , ϕ̂stdjk =
m∑i=1
(xij − 2p̂i) (xik − 2p̂i)
4m∑i=1
p̂i (1− p̂i)
a.s.−−−→m→∞
ϕjk − ϕ̄j − ϕ̄k + ϕ̄
1− ϕ̄.
popkin: first unbiased kinship estimator! — R package on CRAN
Ajk =1m
m∑i=1
(xij − 1)(xik − 1)− 1, Amin = minu 6=v
1|Su||Sv |
∑j∈Su
∑k∈Sv
Ajk ,
ϕ̂jk = 1− Ajk
Amin
a.s.−−−→m→∞
ϕjk .
2 / 7
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Our new kinshipestimatesGenotypes from “Human Origins”(Lazaridis et al. 2014, 2016;Skoglund et al. 2016)
Edited from Ephert [CC BY-SA 3.0], viaWikimedia Commons
*Inbreeding coeffs. on diagonal
3 / 7
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Lebanese_ChristianJew_Turkish
AssyrianDruze
LebaneseJew_iraqi
Iranian_BandariIranian
Jew_IranianTurkish
Jew_AshkenaziCypriotMaltese
Canary_IslanderItalian_South
SicilianRomanian
FrenchNSpanishSW
GreekItalian_North
SpanishNEFrenchS
SardinianBasque
OrcadianEnglish
IcelandicNorwegian
IrishIrish_Ulster
ScottishShetlandic
GermanSorb
PolishCzech
CroatianHungarian
AlbanianBulgarian
MordovianFinnish
RussianEstonian
UkrainianBelarusianLithuanianArmenian
Jew_GeorgianGeorgian
AbkhasianAdygei
North_OssetianChechen
LezginKumykBalkarNogai
MakraniBrahui
BalochiJew_Cochin
TajikKalashPathanSindhi
BurushoBrahmin_Tiwari
GujaratiPunjabi
VishwabrahminLodhiMala
BengaliKhariaOnge
ChuvashTurkmen
UzbekHazaraUygur
TubalarMansi
SelkupKyrgyzAltaian
TuvinianNganasan
DolganYakutXibo
HezhenOroqen
UlchiEven
YukagirItelmenKoryak
ChukchiEskimo
AleutAleut_Tlingit
KusundaKalmyk
BurmeseCambodian
ThaiTu
MongolaDaurKinh
VietnameseDai
LahuNaxi
YiTujiaHan
MiaoShe
JapaneseKorean
AmiAtayal
KankanaeyMurut
DusunIlocanoTagalogVisayan
BajoMalayLebbo
ChipewyanCree
AlgonquinOjibwa
PimaMixe
MixtecZapotec
MayanInga
KaqchikelCabecarPiapoco
KaritianaSurui
BolivianAymara
QuechuaGuaraniChilote
MussauSaposa
BukaTeop
TigakAustralian
KoveMelamela
Nakanai_BilekiMangseng
ManusNasoiNailikNotsi
SW_BougainvilleKuot_Kabil
Kuot_LamalauaLavongai
MadakTolai
MengenMamusi
Mamusi_PaleabuNakanai_Loso
AtaSulka
Kol_New_BritainBaining_MalasaitBaining_Marabu
Papuan
SAfrica MAfrica NAfrica MiddleEast Europe Caucasus SAsia NAsia EAsia Americas Oceania
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−0.0
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Kin
ship
Indi
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Standard kinshipestimatesGenotypes from “Human Origins”(Lazaridis et al. 2014, 2016;Skoglund et al. 2016)
Edited from Ephert [CC BY-SA 3.0], viaWikimedia Commons
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Differentiation (FST) previously underestimated
0.0 0.1 0.2 0.3 0.4 0.5
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40
Inbreeding Coefficient
Den
sity
SAfricaMAfricaNAfricaMiddleEastEuropeCaucasusSAsiaNAsiaEAsiaAmericasOceania
Subpopulations
SAfricaMAfricaNAfricaMiddleEastEuropeCaucasusSAsiaNAsiaEAsiaAmericasOceania
FST estimates
BayeScanWeir−CockerhamHudsonKNew
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00.
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20.
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4
Kin
ship
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vidu
als
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EL
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Pop
ulat
ion
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Anc
estr
y
Kinship driven byadmixture in Hispanics
Our new kinship estimates
Genotypes from the 1000 Genomes Project (2013)
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Better kinship estimates will improve GWAS!
¡Muchas gracias!
Princeton UniversityJohn D. StoreyWei Hao
University of WarsawNeo Christopher Chung
FundingNational Institutes of HealthOtsuka Pharmaceutical
Duke StatGen CenterBiostatistics & Bioinformatics
Lewis-Sigler Institute for Integrative Genomics
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