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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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0.00
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Scatter plot for axis of max. diff. (azimut=6°)
Distances along the given projection
Fst
R^2=0.39
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Scatter plot for axis of min. diff. (azimut=75°)
Distances along the given projection
Fst
R^2=0
AFRICA AMERICA
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Scatter plot for axis of max. diff. (azimut=67°)
Distances along the given projection
R^2=0.13
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Distances along the given projection
Fst
R^2=0.51
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Scatter plot for axis of min. diff. (azimut=179°)
Distances along the given projection
Fst
R^2=0
ASIA EUROPE
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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
atio
ns (%
)
Africa America Asia Europe
0.01
0.1
110
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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
0025
0030
0035
00
Alg
eria
Bam
oun
Bia
ka P
ygm
yB
rong
Bul
ala
Egy
ptFa
ngFu
lani
Had
zaH
ausa
Igbo
Kab
aKo
ngo
Liby
aLu
hya
Maa
sai
Mad
aM
ande
nka
Mbu
tiPyg
my
Mor
occo
N.
Mor
occo
S.
Moz
abite
Sah
ara
occ.
San
NB
San
SA
San
daw
eTu
nisi
aX
hosa
Yoru
ba
050
010
0015
0020
00
Alb
ania
Aust
riaB
elgi
umB
osni
aB
ulga
riaC
roat
iaC
ypru
sC
zech
Den
mar
kFi
nlan
dFr
ance
Ger
man
yG
reec
eH
unga
ryIre
land
Italy
Koso
voLa
tvia
LS−F
inland
Mac
edon
iaN
ethe
rland
sN
orw
ayPo
land
Portu
gal
Rom
ania
Rus
sian
Sco
tland
Ser
bia
Slo
vaki
aS
love
nia
Spa
inS
wed
enSwiss−French
Swiss−Ger
man
Swiss−Italian
Turk
eyU
krai
neU
nite
d
A AFRICA
D EUROPE
B AMERICA
020
040
060
080
010
0012
00
AYM
CU
RG
UE
KA
RM
YC
PIM
QE
CS
UR
YU
C
010
0020
0030
0040
0050
0060
00
Bal
ochi
Bra
hui
Bur
usho
Cam
bodi
an Dai
Dau
rH
anH
azar
aH
ezhe
nJa
pane
seK
alas
hLa
huM
akra
niM
iaoz
uM
ongo
laN
axi
Oro
qen
Path
anS
heS
indh
iTu
Tujia
Uyg
urX
ibo
Yaku
tYi
zu
C ASIA
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
020
040
0
Nor
mal
ized
err
ors
0.00
0.10
0.20
0.30
Africa America Asia Europe
E-WE-W E-W E-W
E-WE-WE-WE-W
N-S
N-S N-S N-S
N-S N-S
N-S
N-S
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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