Supplementary Material of ”Anisotropic isolation by distance: the

main orientations of human genetic differentiation”

• Figure S1: First and second components of the multidimensional scaling analysis for each con-tinent.

• Figure S2: Projections of the first principal components for each continent.

• Figure S3: Correspondence between azimuths/bearings (θ) and cardinal directions.

• Figure S4: Fst as a function of the distance computed along the orientation of maximum andminimum differentiation.

• Figure S5: Prediction of average Fst for pairs of populations separated by 0 km and by 1, 000km along the axis of maximum differentiation.

• Figure S6: Grid used for the isolation by distance ms simulations.

• Figure S7: Angular distributions of the angles of maximum differentiation found with the threemethods under anisotropic isolation by distance models

• Figure S8: Boxplots of the individual localization errors for each population from the 4 continents

• Figure S9: Mean error of the localization method in N-S and E-W directions

• Figure S10: Fst of Sub-Saharan populations as a function of the distance computed along theorientation of maximum and minimum differentiation.

• Figure S11: Fst of Native American populations, typed with microsatellites, as a function of thedistance computed along the orientation of maximum and minimum differentiation.

• Table S1: Orientations of maximum differentiation obtained after different transformations ofthe dependent and independent variables

• Table S2: Orientations of maximum differentiation after having moved the geographical coordi-nates by 500 km

• Table S3: Orientations of maximum differentiation obtained with the different methods

• Table S4: Median errors of geographic localization based on the SNP data sets

• Table S5: The different subdivisions of Europe

• Table S6: The different subdivisions of Africa

• Table S7: The different subdivisions of Asia

A AFRICA B AMERICA

C ASIA D EUROPE

−0.10 −0.05 0.00 0.05 0.10

−0.0

20.

000.

020.

040.

06

MDS axis 1

MD

S ax

is 2

Algeria

Bamoun

BiakaPygmy

BrongBulala

Egypt

Fang

Fulani

HADZAHausaIgboKabaKongo

Libya

Luhya

Maasai

Mada

Mandenka

MbutiPygmyMorocco_N

Morocco_S

Mozabite

SANDAWE

SAN_NB

SAN_SA

Sahara_OCC

TUNISIA

Xhosa

Yoruba

−0.05 0.00 0.05 0.10

−0.0

6−0

.04

−0.0

20.

000.

020.

040.

060.

08

MDS axis 1

MD

S ax

is 2

AymaraColombianGuerrero

Karitiana

Maya

Pima

Quechua SuruiYucatan

−0.08 −0.06 −0.04 −0.02 0.00 0.02 0.04

−0.0

2−0

.01

0.00

0.01

0.02

MDS axis 1

MD

S ax

is 2

BalochiBrahuiBurusho

Cambodian

Dai

Daur

Han

Hazara

Hezhen

JapaneseKalash

Lahu

Makrani

Mongola

Naxi

Oroqen

Pathan

SheSindhi

TuTujia

UygurXibo

Miaozu

Yakut

Yizu

−0.01 0.00 0.01 0.02

−0.0

04−0

.002

0.00

00.

002

0.00

40.

006

MDS axis 1

MD

S ax

is 2

AlbaniaAustriaBelgiumBosnia

BulgariaCroatia

Cyprus

Czech

Denmark

Finland

FranceGermany

GreeceHungary

Ireland

Italy

Kosovo

LSFIN

Latvia

MacedoniaNetherlandsNorwayPoland

PortugalRomania

RussianScotland

Serbia

SlovakiaSlovenia

Spain SwedenSwiss−FrenchSwiss−German

Swiss−Italian

Turkey

UK

Ukraine

Figure 1: First and second components of multidimensional scaling analysis (MDS). MDS was appliedseparately in each continent.

2

−100 −90 −80 −70

−10

010

2030

−0.05

0.00

0.05

0.10

0.15

−0.05

0

0.05

0.1

CUR

KAR

MYC

PIM

SUR

AYM

YUCGUE

QEC

−30

−20

−10

010

2030

−20 −10 0 10 20 30 40

−0.06

−0.04

−0.02

0.00

0.02

0.04

0.02

−0.06

−0.04

−0.02

0

0.04 HadzaSandawe

San_SA

BiakaPygmyMbutiPygmy

Mandenka

Yoruba

Luhya

San_NB

Xhosa

Maasai

MozabiteAlgeria

EgyptLibyaMorocco_N

Morocco_S

Sahara_OCC

Tunisia

FulaniMadaKaba

Bulala

Fang

Hausa

Kongo

Brong IgboBamoun

70 80 90 100 110 120 130

020

4060

−0.06

−0.04

−0.02

0.00

0.02

0.04

−0.

04

−0.02

0

0.02

0.04

BrahuiBalochi

Hazara

MakraniSindhi

PathanKalash

Burusho

Cambodian

Japanese

Han

Yakut

TujiaYizuMiaozu

OroqenDaurMongola

Hezhen

XiboUygur

DaiLahu

SheNaxi

Tu

0 10 20 30

3040

5060

70

−0.04

−0.02

0.00

0.02

0.04

0.06

0.08

−0.04

−0.02

0

0.02

0.04

0.06

0.08

Finland

LS−Finland

Croatia Serbia

Czech

BosniaRomania

Bulgaria

HungarySlovakia

Albania

Ukraine

Latvia

Macedonia

Slovenia

UnitedIreland

Sweden

Scotland

KosovoItaly

Germany

Cyprus

PortugalSpain

Greece Turkey

Swiss

Belgium

FranceAustria

PolandNetherlands

Russian

Norway

Denmark

A AFRICA B AMERICA

C ASIA D EUROPE

Figure 2: Spatial interpolation of the first component of principal component analysis (PCA). PCAwas applied separately in each continent. Spatial interpolation was performed using the krig functionwith a trend surface of degree 2.

3

NorthSouth

(0°)

EastWest(90°)

SoutheastNorthwest

(135°)

NortheastSouthwest

(45°)

North-NortheastSouth-Southwest

(22.5°)

East-NortheastWest-Southwest

(67.5°)

East-SoutheastWest-Northwest

(112.5°)

South-SoutheastNorth-Northwest

(157.5°)

θ

Figure 3: Correspondence between azimuths/bearings (θ) and compass directions.

4

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Distances along the given projection

Fst

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Fst

R^2=0

AFRICA AMERICA

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Fst

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Fst

R^2=0

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Figure 4: Fst as a function of the distance computed along the orientation of maximum and minimumdifferentiation. Here the orientation of maximum (resp. minimum) differentiation is the orientationthat maximizes the correlation between Fst and the orientational distances dθ computed along thedifferent orientations.

5

Continents

Fst b

etwe

en p

airs

of p

opul

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)

Africa America Asia Europe

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Figure 5: Prediction of average Fst for pairs of populations separated by 0 km and by 1, 000 km alongthe axis of maximum differentiation. The Fst was regressed with the equation (1) of the main text.

6

−20 −10 0 10 20 30 40

4045

5055

6065

70

Longitude

Latit

ude

All demesPOPRESNarrow bandClustered

Figure 6: Grid used for the isolation by distance ms simulations and the four sampling scheme thatwas considered to pick n = 38 populations.

7

All demes POPRES sampling Narrow band Clustered

All demes POPRES sampling Narrow band Clustered

E-W axis of main diff.

N-S axis of main diff.

Reg. Geo. MDSReg. Geo. MDS

Reg. Geo. MDSReg. Geo. MDS

Reg. Geo. MDSReg. Geo. MDS

Reg. Geo. MDSReg. Geo. MDS

Figure 7: Angular distribution of the angles of maximum differentiation found with the MDS, re-gression, and geometric methods under anisotropic isolation by distance models. A total of 100 IBDsimulations was performed for each scenario and the quadrants show the distribution of the 100 es-timated angles of maximum differentiation. Simulations were performed under anisotropic isolationby distance assuming a 20 (N-S) × 24 (E-W) grid with 4Nm = 1 under the direction of maximumgenetic differentiation and 4Nm = 5 in the other direction. The grid used for the isolation by distancesimulations is shown in Figure S6.

8

050

010

0015

0020

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eria

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enSwiss−French

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man

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A AFRICA

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Figure 8: Boxplots of the individual localization errors for each population from the 4 continents Theerrors were computed using SNP data.

9

Mean error in E-W and N-S directions

Err

ors

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N-S N-S

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Figure 9: Mean error of the localization method in N-S (lat.) and E-W (long.) direction. Upperpanel shows the errors in km and lower panel shows the error after rescaling to account for the intra-continental sampling.

10

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Figure 10: Fst of the Sub-Saharan populations as a function of the distance computed along the orien-tation of maximum and minimum differentiation. Here the orientation of maximum (resp. minimum)differentiation is the orientation that maximizes the correlation between Fst and the orientationaldistances dθ computed along the different orientations.

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Figure 11: Fst of the Native American populations, typed with microsatellites, as a function of thedistance computed along the orientation of maximum and minimum differentiation. Here the orien-tation of maximum (resp. minimum) differentiation is the orientation that maximizes the correlationbetween Fst and the orientational distances dθ computed along the different orientations.

11

Continent Region Regression GeometricFst logFst/(1 − Fst) logFst/(1 − Fst) and log d Fst logFst/(1 − Fst) logFst/(1 − Fst) and log d

Africa All 9 10 0 6 2 177Western 9 9 5 7 7 175Eastern 46 51 58 54 54 38Sub-Sahara 25 35 10 3 173 176North Sahara 79 77 75 21 21 21

Asia All 102 111 97 102 95 90Eastern 177 169 0 6 8 3Western 66 49 62 86 71 66

America All 92 69 15 67 67 1All (microsat.) 139 133 136 86 85 88

Europe All 167 161 165 167 161 0nindiv > 21 163 161 158 164 161 173nindiv > 2, no SEandME2,3 15 20 34 12 48 68nindiv > 2, no SE2 161 166 157 164 168 162nindiv > 2, no ME3 177 167 170 0 179 5nindiv > 2, no Fennoscandia 156 153 161 155 152 122nindiv > 2, SEandME2,3 129 157 156 137 155 167nindiv > 2, Western 154 75 119 173 3 161nindiv > 2, Southern 148 162 160 155 152 158nindiv > 2, Northern 11 176 129 16 15 136nindiv > 2, Middle 152 129 9 164 7 21nindiv > 2, Eastern 159 157 155 158 160 153nindiv > 2, Central 70 11 26 82 80 96

1 nindiv > 2 correspond to the 31 populations with a sample size larger than 22 SE stands for Southeast3 ME stands for Middle East (Cyprus and Turkey here)

Table 1: Orientations of maximum differentiation obtained when regressing Fst on d, logFst/(1 − Fst)on d, and logFst/(1 − Fst) on log d.

.

12

Continent Region Regression1 Geometric1

Africa All 8 (177-18) 5 (176-14))Western 6 (175-16) 4 (172-16)Eastern 37 (1-73) 44(15-74)Sub-Sahara 15 (162-49) 10 (153-46)North Sahara 77 (11-143) 173 (88-77)

Asia All 100 (91-110) 101 (93-110)Eastern 4 (148-39) 10 (167-32)Western 54 (166-121) 66 (171-142)

America All 97 (47-148) 72 (36-110)All (microsat.) 135 (118-152) 90 (77-102)

Europe All 163 (143-3) 162 (143-2)nindiv > 22 159 (144-174) 159 (147-171)nindiv > 2, no SEandME3,4 22 (168-57) 23 (167-58)nindiv > 2, no SE3 154 (138-171) 156 (139-173)nindiv > 2, no ME4 1(160-23) 2 (162-22)nindiv > 2, no Fennoscandia 139 (114-164) 139 (114-164)nindiv > 2, SEandME3,4 120 (64-176) 120 (66-174)nindiv > 2, Western 176 (130-43 178 (132-45))nindiv > 2, Southern 135 (105-165) 141 (114-168)nindiv > 2, Northern 47 (145-128 17 (117-97))nindiv > 2, Middle 178 (112-65) 176 (100-73)nindiv > 2, Eastern 160 (141-0) 160 (141-177)nindiv > 2, Central 91 (22-160) 91 (20-163)

1 The 95% confidence intervals are given in parenthesis and should be readclockwise

2 nindiv > 2 correspond to the 31 populations with a sample size largerthan 2

3 SE stands for Southeast4 ME stands for Middle East (Cyprus and Turkey here)

Table 2: Median angle of maximal differentiation after having moved the geographical coordinatesalong a rhumb line of 500 km with angles chosen uniformly between 0◦ and 360◦. A total of 100 ori-entations of maximum differentiation were calculated and an interval containing 95% of the replicatesis provided in parenthesis (should be read clockwise). No transformation of Fst or distances wereconsidered.

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Continent Region Pop. number MDS Regression GeometricAngle Angle1 Mantel test2 Partial Mantel test3 Angle 1 R2 4

Africa All 29 9 9∗∗∗ (160-33) < 10−4 < 10−4 6 (164-26) 0.4Western 18 NA 9∗∗∗ (166-28) < 10−4 < 10−4 7(162-31) 0.74Eastern 11 NA 46 (164-111) 0.093 0.371 54 (179-112) 0.20Sub-Sahara 21 NA 19 (130-86) 0.091 0.358 0 (103-70) 0.09North Sahara 8 NA 79 (19-127) 0.95 0.921 21 (108-74) 0.01

Asia All 26 109 102∗∗∗ (84-121) < 10−4 < 10−4 102 (80-124) 0.51Eastern 16 NA 177 (131-43) < 10−4 0.060 6 (149-41) 0.51Western 10 NA 66 (172-145) 0.022 0.400 86 (38-152) 0.25

America All 9 67 92 (22-167) 0.133 0.33 67 (10-118) 0.13All (microsat.) 29 NA 139∗ (106-163) 0.93 0.05 86 (54-123) 0.02

Europe All 38 3 167∗ (140-14) < 10−4 0.012 167 (138-14) 0.26nindiv > 25 30 NA 163∗∗∗ (137-9) < 10−4 2 × 10−4 164 (137-9) 0.53nindiv > 2, no SEandME6,7 21 NA 15 (139-71) < 10−4 0.178 12 (146-71) 0.34nindiv > 2, no SE6 23 NA 161∗∗∗ (127-18) < 10−4 5 × 10−4 164 (125-23) 0.56nindiv > 2, no ME7 28 NA 177∗∗ (145-25) < 10−4 0.006 0 (147-28) 0.38nindiv > 2, no Fennoscandia NA 156∗∗ (130-7) < 10−4 < 10−4 155 (127-2) 0.62nindiv > 2, SEandME6,7 9 NA 129 (69-39) 4 × 10−4 0.798 137 (86-9) 0.82nindiv > 2, Western 8 NA 154 (100-65) 0.002 0.677 173 (121-60) 0.61nindiv > 2, Southern 13 NA 148∗∗ (119-5) 0.011 0.007 155 (129-2) 0.61nindiv > 2, Northern 8 NA 11 (117-81) 0.34 0.802 16 (105-73) 0.14nindiv > 2, Middle 8 NA 152 (100-65) 0.023 0.675 164 (84-64) 0.37nindiv > 2, Eastern 14 NA 159∗∗∗ (137-3) < 10−4 < 10−4 158 (142-171) 0.88nindiv > 2, Central 9 NA 70(165-150) < 10−4 0.937 82 (26-159) 0.50

1 The 95% confidence intervals are given in parenthesis and should be read clockwise2 The Mantel test assesses whether there is an effect of the geographic distances on Fst.3 The partial Mantel test assesses whether there is an additional effect of the bearings between two populations when regressing Fst.4 The coefficient R2 is obtained when regressing Fst by the distance computed along the direction of maximum differentiation5 nindiv > 2 correspond to the 31 populations with a sample size larger than 26 SE stands for Southeast7 ME stands for Middle East (Cyprus and Turkey here)

Table 3: Orientations of maximum differentiation obtained with the different methods. A total of10, 000 permutations was performed to provide the P values.

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Continent Number of PC Error E-W error N-S error Rel. error Rel. E-W error Rel. N-S errorAfrica 2 1180 910 480 0.38 0.62 0.27Africa Kopt = 52 430 250 260 0.15 0.14 0.12

America 2 470 330 240 0.19 0.23 0.12America Kopt = 17 250 140 180 0.10 0.09 0.10

Asia 2 1090 390 520 0.39 0.16 0.54Asia Kopt = 34 510 350 200 0.17 0.14 0.19

Europe 2 470 380 230 0.41 0.47 0.33Europe Kopt = 17 280 190 140 0.24 0.23 0.19

Table 4: Median errors (in kilometers) of geographic localization based on SNP and microsatellitedata. The relative errors are computed with respect to a naive localizer which assigns each individualto a population that is chosen at random among the sampled populations.

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n All pops BigPops North Central South West Mid East no SEandCT no ME no SE no Fennoscandia SEandCTSwiss-German 84 x x x x x x x xGermany 71 x x x x x x x xNetherlands 17 x x x x x x x xAustria 14 x x x x x x x xHungary 19 x x x x x x x xCzech 11 x x x x x x x xSlovakia 1 xCyprus 4 x x x x x x xTurkey 4 x x x x x x xSweden 10 x x x x x x xNorway 3 x x x x x x xDenmark 1 xPoland 22 x x x x x x x xRussian 6 x x x x x x x xFinland 41 x x x x x x xLatvia 1 xUkraine 1 xLS-Finland 41 xUnited 200 x x x x x x x xIreland 61 x x x x x x x xScotland 5 x x x x x x x xItaly 219 x x x x x x x xSwiss-Italian 13 x x x x x x x xSerbia 44 x x x x x x xRomania 14 x x x x x x xBosnia 9 x x x x x x xCroatia 8 x x x x x x xGreece 8 x x x x x x xMacedonia 4 x x x x x x xAlbania 3 x x x x x x xBulgaria 2 xKosovo 2 xSlovenia 2 xSpain 136 x x x x x x x xPortugal 128 x x x x x x x xSwiss-French 125 x x x x x x x xFrance 91 x x x x x x x xBelgium 43 x x x x x x x x

Table 5: The different subdivisions of Europe..

all West East North Sahara SubSaharan

Morocco N x x xAlgeria x x x

Tunisia x x x

Mozabite x x xLibya x x x

Morocco S x x x

Egypt x x x

Sahara OCC x x xBulala x x x

Hausa x x x

Mandenka x x x

Fulani x x xMada x x x

Kaba x x xYoruba x x x

Brongx x xIgbo x x x

Bamoun x x x

Biaka Pygmy x x xFang x x x

Mbuti Pygmy x x xLuhya x x x

Maasai x x xHadza x x x

Sandawe x x x

Kongo x x x

San NB x x xSan SA x x x

Xhosa x x x

Table 6: The different subdivisions of Africa..

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All West Asia East Asia

Makrani x x

Balochi x xBrahui x x

Sindhi x x

Hazara x x

Pathan x xKalash x x

Burusho x x

Uygur x xXibo x x

Naxi x x

Dai x x

Lahu x xTu x x

Yizu x x

Cambodian x x

Miaozu x xTujia x x

Han x x

She x x

Mongola x xDaur x x

Oroqen x x

Yakut x xHezhen x x

Japanese x x

Table 7: The different subdivisions of Asia..

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