The whole world on the entropy-rescaled PCA

65 reference groups and 8 projected South Slav, Albanian and Cypriot groups on the entropy-rescaled maps A and B: group means on six axes, and the Southeast European groups on the first two.

Mvagnus Albertus · Popualtion Geneticist

Published November 2, 202621 min read

One PCA carries the whole world: 65 modern Human Origins groups (968 persons) build the axes, and 8 South Slav, Albanian and Cypriot groups (66 persons) are projected onto them. Group positions are read on the entropy-rescaled maps A and B of Taleb et al.¹ PC1 holds the sub-Saharan Africans far from every other group, PC2 orders the non-African groups from the Europeans through the South and Central Asians to the East Asians, and PC4 and PC5 hold the Native Americans and the Oceanians. The Southeast European groups lie inside the compact European cluster, and the first two components separate them only weakly: the Thessaloniki Greeks lie next to the Albanians, the Athens Greeks next to the Cypriots, and the South Slav groups next to one another. A position on a map is not an ancestry share.

Design of the run

One PCA, run 7bbdaf39, carries the whole world. It uses the Human Origins SNP set² (564,989 SNPs), shrinkmode and six components, without outlier removal and without LD pruning.³ The axes are built by 968 reference persons of 65 modern groups, at most 17 persons per group; a person present in the data both as .DG and as .HO was removed, so each person counts once.

Eight further groups with 66 persons did not build the axes. They are projected onto them by the platform's least-squares projection on the same SNPs: Bulgarians (10), Croatians (9), Serbs from Serbia (19), from Bosnia (5), from Croatia (5) and from Montenegro (7), Albanians (6) and Cypriots (5). They carry † in the tables. The Serb groups are named by the locality in the source metadata.

The Greeks are one label in the run and are split for display only, into Athens (5 persons) and Thessaloniki (12); both are reference groups. The platform allows 64 labels per run, so nine East and Southeast Asian groups (Dai, Hmong, Kinh, Kankanaey, Malay, Mongolian, Korean, Miao, Yi) form one label inside the run; the tables list them separately. Crete (2 persons) is left out as too small, and Slovenes and Macedonians are not in Human Origins.

The rescaling is that of Taleb et al.¹; the steps are set out in Entropy-Rescaled PCA, Step by Step. For a person with raw coordinate u on an axis, scaled so that the reference persons have unit norm on that axis, map A is sign(u) · (−½ ln(1 − u²)) · √λ, shown ×10⁻³, with λ the eigenvalue of the axis, and map B is sign(u) · (−½ log₂(1 − u²)), in bits. A group's position is the mean of its persons' rescaled coordinates. Small coordinates become smaller and large ones relatively larger, so the crowded centre contracts, the periphery stretches and a single outlying person gains weight. Rescaled units are not comparable in size with raw units; the order and the pattern are what to compare.

On every axis the two maps differ only by a constant factor, d = ln 2 · √λ (Table 1). They therefore order the groups identically along one axis and differ in how the axes are weighted against each other. Axis signs are arbitrary.

Table 1Axes of run 7bbdaf39: eigenvalue, variance share and the divisor from map A to map B.

Axis	Eigenvalue	Variance (%)	Divisor d
PC1	65.519	6.78	5.611
PC2	35.509	3.67	4.130
PC3	19.300	2.00	3.045
PC4	15.216	1.57	2.704
PC5	12.394	1.28	2.440
PC6	9.168	0.95	2.099

Map B value (×10⁻³ bits) = map A value (×10⁻³) divided by d, with d = ln 2 · √eigenvalue. Example: Spanish on PC2, A −5.206, d 4.130, B −1.2605.

The world on PC1 and PC2

Fig. 1 shows all 1,034 persons of the run on the ordinary PC1 and PC2, with the groups coloured by region. The platform draws the raw coordinates. The positions of the group means on the rescaled maps A and B are in Table 2 and Table 3. Figs. 2 to 13 zoom into the regions with their own PCAs.

Europe (n = 124)
Southeast Europe (n = 83)
Near East and Caucasus (n = 134)
Africa (n = 145)
South and Central Asia (n = 148)
Siberia, East and Southeast Asia (n = 273)
Americas (n = 87)
Oceania (n = 40)
All other genomes
Group centroid

1,034 genomes · 564,989 SNPs

Figure 1The whole world on PC1 and PC2: 1,034 persons of 73 groups. Run 7bbdaf39: 65 reference groups (968 persons) build the axes, 8 projected groups (66 persons) are placed on them. Ordinary PC1 and PC2; the rescaled positions of the group means are in Table 2. Colour: region; grey: the other groups. The Greeks are one label in the run, and nine East and Southeast Asian groups are one label (in the last region). A position on a map, not an ancestry share.

PC1 (6.78 percent of the variance) holds the sub-Saharan Africans far from every other group. On map A the Ju/'hoan lie at 83.84, the Mbuti at 37.89, the Biaka at 32.66, the Mende at 24.99, the Yoruba at 24.36, the Mandenka at 22.84 and the Bantu of Kenya at 21.61; the Somali (6.46), the Mozabite (1.37) and the Egyptians (0.33) stand between, and all non-African groups lie between −2.34 and 0.05.

PC2 (3.67 percent) orders the non-African groups from the Europeans (Sardinian −6.23) through the Near Eastern, South Asian and Central Asian groups to the East Asians (Korean 4.64, Hmong 4.56), with the Americans among the East Asians and the Oceanians in the middle. PC4 (1.57 percent) and PC5 (1.28 percent) hold the Native Americans and the Oceanians: on PC4 the Karitiana (−16.21), Surui (−15.23), Mixe (−11.41), Pima (−11.02) and Maya (−8.85) lie at one end and the Papuans (30.05), Nasioi (17.72) and Aboriginal Australians (10.21) at the other; on PC5 the Papuans (35.41), Nasioi (14.69), Aboriginal Australians (10.11), Karitiana (9.10) and Surui (8.69) lie high and the East and Southeast Asians low (−2.14 to −1.44 for most).

PC3 (2.00 percent) and PC6 (0.95 percent) are carried by one group. The Ju/'hoan mean lies at −189.00 on PC3 and 132.26 on PC6, and all other groups lie between −0.21 and 7.62 on PC3 and between −2.22 and 0.41 on PC6. These two axes do not describe contrasts between regions.

Group means on the rescaled maps

Table 2 gives every group on maps A and B for PC1 and PC2, the plane of Fig. 1, and Table 3 gives PC3 to PC6 on map A; map B follows from Table 1. The numbers are group means of the persons' rescaled coordinates, and n is the number of persons. Groups of five persons (Greek (Athens), Serbs (Bosnia), Serbs (Croatia), Cypriot) have wide uncertainty on the mean.

Table 2Group means on the rescaled maps A (×10⁻³) and B (×10⁻³ bits), PC1 and PC2.

Region	Group	n	A PC1	A PC2	B PC1	B PC2
Europe	Spanish	17	−0.06	−5.21	−0.0103	−1.2605
Europe	Basque	17	−0.10	−5.63	−0.0175	−1.3620
Europe	French	17	−0.11	−5.05	−0.0189	−1.2223
Europe	English	12	−0.12	−5.23	−0.0219	−1.2654
Europe	North Italian	17	−0.08	−5.43	−0.0150	−1.3135
Europe	Sardinian	17	−0.04	−6.23	−0.0079	−1.5087
Europe	Finnish	10	−0.23	−3.52	−0.0408	−0.8522
Europe	Russian	17	−0.18	−3.81	−0.0320	−0.9224
SE Europe	Greek (Athens)	5	−0.06	−5.36	−0.0111	−1.2976
SE Europe	Greek (Thessaloniki)	12	−0.08	−5.25	−0.0136	−1.2699
SE Europe	Albanian †	6	−0.08	−5.23	−0.0138	−1.2651
SE Europe	Bulgarian †	10	−0.09	−5.00	−0.0162	−1.2108
SE Europe	Croatian †	9	−0.11	−4.99	−0.0196	−1.2087
SE Europe	Serbs (Serbia) †	19	−0.10	−4.94	−0.0182	−1.1952
SE Europe	Serbs (Bosnia) †	5	−0.09	−5.06	−0.0155	−1.2258
SE Europe	Serbs (Croatia) †	5	−0.12	−4.93	−0.0214	−1.1939
SE Europe	Serbs (Montenegro) †	7	−0.10	−4.97	−0.0182	−1.2025
SE Europe	Cypriot †	5	−0.02	−5.36	−0.0043	−1.2966
Near East, Caucasus	Turkish	17	−0.10	−3.64	−0.0180	−0.8802
Near East, Caucasus	Georgian	17	−0.06	−5.11	−0.0109	−1.2374
Near East, Caucasus	Armenian	15	−0.04	−5.05	−0.0078	−1.2222
Near East, Caucasus	Adygei	17	−0.13	−3.86	−0.0235	−0.9349
Near East, Caucasus	Iranian	17	−0.05	−3.84	−0.0090	−0.9288
Near East, Caucasus	Druze	17	−0.01	−5.11	−0.0016	−1.2360
Near East, Caucasus	Palestinian	17	0.05	−4.31	0.0087	−1.0428
Near East, Caucasus	Bedouin	17	0.03	−4.82	0.0058	−1.1673
N and E Africa	Mozabite	17	1.37	−2.86	0.2444	−0.6917
N and E Africa	Egyptian	17	0.33	−3.52	0.0587	−0.8514
N and E Africa	Somali	12	6.46	−0.39	1.1506	−0.0936
Sub-Saharan Africa	Mandenka	17	22.84	0.38	4.0704	0.0929
Sub-Saharan Africa	Mende	10	24.99	0.54	4.4534	0.1305
Sub-Saharan Africa	Yoruba	17	24.36	0.49	4.3416	0.1180
Sub-Saharan Africa	Bantu (Kenya)	13	21.61	0.38	3.8523	0.0919
Sub-Saharan Africa	Biaka	17	32.66	1.34	5.8209	0.3253
Sub-Saharan Africa	Mbuti	15	37.89	1.93	6.7531	0.4673
Sub-Saharan Africa	Ju/'hoan	10	83.84	9.02	14.9429	2.1848
South Asia	Balochi	17	−0.05	−2.23	−0.0081	−0.5397
South Asia	Pathan	17	−0.16	−1.78	−0.0280	−0.4308
South Asia	Kalash	17	−0.18	−2.12	−0.0319	−0.5130
South Asia	Burusho	17	−0.25	−0.91	−0.0437	−0.2215
South Asia	Punjabi	12	−0.20	−0.63	−0.0355	−0.1516
South Asia	Gujarati	17	−0.19	−0.92	−0.0332	−0.2224
Central Asia	Hazara	17	−0.67	0.01	−0.1187	0.0034
Central Asia	Uzbek	17	−0.47	−0.28	−0.0836	−0.0687
Central Asia	Kazakh	17	−0.86	0.19	−0.1533	0.0469
Siberia, Arctic	Tuvinian	17	−1.36	1.80	−0.2432	0.4351
Siberia, Arctic	Buryat	17	−1.36	2.27	−0.2418	0.5507
Siberia, Arctic	Yakut	17	−1.53	2.56	−0.2720	0.6194
Siberia, Arctic	Selkup	17	−1.13	0.47	−0.2014	0.1143
Siberia, Arctic	Ket	17	−1.13	0.56	−0.2016	0.1344
Siberia, Arctic	Nganasan	17	−1.80	3.64	−0.3200	0.8804
Siberia, Arctic	Chukchi	17	−1.80	3.26	−0.3200	0.7893
East Asia	Tibetan	17	−1.40	3.49	−0.2499	0.8452
East Asia	Han	17	−1.62	4.47	−0.2881	1.0827
East Asia	Yi	12	−1.53	4.25	−0.2732	1.0299
East Asia	Miao	12	−1.62	4.55	−0.2881	1.1018
East Asia	Mongolian	11	−1.57	3.49	−0.2798	0.8441
East Asia	Korean	7	−1.70	4.64	−0.3034	1.1244
East Asia	Japanese	17	−1.64	4.44	−0.2916	1.0751
SE Asia	Dai	15	−1.50	4.21	−0.2681	1.0193
SE Asia	Hmong	10	−1.55	4.56	−0.2771	1.1043
SE Asia	Kinh (Vietnam)	17	−1.46	4.07	−0.2609	0.9858
SE Asia	Malay	9	−1.06	2.48	−0.1890	0.6013
SE Asia	Kankanaey	10	−1.56	4.55	−0.2775	1.1024
Oceania	Papuan	17	−0.17	1.01	−0.0294	0.2452
Oceania	Nasioi	13	−0.31	1.37	−0.0545	0.3314
Oceania	Aboriginal Australian	10	−0.14	0.16	−0.0250	0.0387
Americas	Naukan Yupik	14	−1.94	3.60	−0.3452	0.8718
Americas	Pima	16	−2.04	3.48	−0.3627	0.8429
Americas	Mixe	13	−2.12	3.71	−0.3770	0.8989
Americas	Maya	17	−1.61	2.38	−0.2862	0.5758
Americas	Karitiana	17	−2.33	4.29	−0.4145	1.0386
Americas	Surui	10	−2.34	4.22	−0.4162	1.0216

† projected group (did not build the axes). n: persons. In the run the Greeks are one label, and Yi, Miao, Mongolian, Korean, Dai, Hmong, Kinh, Malay and Kankanaey are one label.

Table 3Group means on map A (×10⁻³), PC3 to PC6.

Group	A PC3	A PC4	A PC5	A PC6
Spanish	−0.146	−0.033	−0.005	0.006
Basque	−0.183	−0.037	−0.004	0.006
French	−0.181	−0.051	−0.002	0.011
English	−0.193	−0.057	0.000	0.007
North Italian	−0.166	−0.030	−0.009	0.005
Sardinian	−0.146	−0.012	−0.018	0.005
Finnish	−0.181	−0.082	−0.005	0.006
Russian	−0.178	−0.063	−0.005	0.013
Greek (Athens)	−0.132	−0.012	−0.004	0.005
Greek (Thessaloniki)	−0.148	−0.024	−0.006	0.006
Albanian †	−0.146	−0.018	−0.004	0.004
Bulgarian †	−0.161	−0.029	−0.004	0.008
Croatian †	−0.178	−0.045	−0.003	0.008
Serbs (Serbia) †	−0.179	−0.035	−0.003	0.012
Serbs (Bosnia) †	−0.207	−0.039	−0.001	0.019
Serbs (Croatia) †	−0.183	−0.041	0.000	0.012
Serbs (Montenegro) †	−0.181	−0.033	−0.003	0.011
Cypriot †	−0.109	−0.006	−0.019	0.006
Turkish	−0.094	−0.004	−0.027	0.005
Georgian	−0.138	−0.008	−0.006	0.006
Armenian	−0.143	−0.003	−0.005	0.020
Adygei	−0.126	−0.014	−0.012	0.004
Iranian	−0.080	−0.002	−0.004	0.002
Druze	−0.077	−0.004	−0.011	0.003
Palestinian	−0.014	−0.002	−0.011	0.001
Bedouin	−0.016	−0.002	−0.015	0.001
Mozabite	0.265	−0.023	−0.025	−0.012
Egyptian	0.013	−0.006	−0.016	−0.001
Somali	0.989	−0.010	−0.017	−0.010
Mandenka	7.415	−0.171	−0.030	−0.220
Mende	7.255	−0.183	−0.024	−0.189
Yoruba	7.618	−0.176	−0.037	−0.212
Bantu (Kenya)	5.181	−0.128	−0.027	−0.061
Biaka	2.489	−0.155	−0.002	0.412
Mbuti	1.199	−0.177	0.001	−2.219
Ju/'hoan	−189.004	0.293	−0.006	132.263
Balochi	−0.034	0.010	0.005	0.003
Pathan	−0.051	0.019	0.006	0.003
Kalash	−0.074	0.001	0.011	0.002
Burusho	−0.037	0.031	−0.002	0.002
Punjabi	−0.011	0.213	0.025	0.001
Gujarati	−0.020	0.115	0.026	0.002
Hazara	−0.014	0.074	−0.372	0.001
Uzbek	−0.036	0.014	−0.203	0.004
Kazakh	−0.012	0.045	−0.587	0.002
Tuvinian	−0.001	0.066	−1.035	0.002
Buryat	0.000	0.109	−1.217	0.003
Yakut	0.000	0.054	−1.192	0.001
Selkup	−0.028	−0.053	−0.354	0.005
Ket	−0.026	−0.057	−0.400	0.003
Nganasan	−0.001	0.000	−1.357	0.002
Chukchi	−0.009	−0.704	−0.053	0.000
Tibetan	0.011	0.614	−1.439	0.001
Han	0.023	0.847	−2.026	0.000
Yi	0.023	0.772	−1.788	0.000
Miao	0.026	0.968	−2.074	0.000
Mongolian	0.006	0.367	−1.652	0.000
Korean	0.016	0.622	−2.143	0.000
Japanese	0.016	0.588	−1.701	0.000
Dai	0.032	1.192	−1.971	0.000
Hmong	0.027	1.209	−2.140	0.000
Kinh (Vietnam)	0.028	1.116	−1.834	0.000
Malay	0.030	1.337	−0.736	0.000
Kankanaey	0.032	1.328	−2.052	0.000
Papuan	0.512	30.055	35.414	0.079
Nasioi	0.306	17.722	14.693	0.034
Aboriginal Australian	0.177	10.210	10.110	0.030
Naukan Yupik	−0.013	−1.708	0.069	0.000
Pima	−0.063	−11.020	5.497	−0.001
Mixe	−0.070	−11.413	5.447	−0.001
Maya	−0.050	−8.847	4.409	−0.001
Karitiana	−0.082	−16.207	9.105	−0.003
Surui	−0.084	−15.230	8.691	−0.001

† projected group. The Ju/'hoan means (−189.004 on PC3, 132.263 on PC6) lie far outside all other groups.

Southeast Europe on the first two axes

The Southeast European groups lie inside the European cluster, which is compact against the scale of the world. On PC2 of map A the Greek (Athens) mean is at −5.36, the Greek (Thessaloniki) at −5.25, the Albanians at −5.23, the Bulgarians at −5.00, the Croatians at −4.99, the Serb groups between −5.06 and −4.93 and the Cypriots at −5.36, against −5.43 to −5.05 for the Spanish, French, English and North Italians, −6.23 for the Sardinians and −3.81 and −3.52 for the Russians and Finns. The distance on PC1 and PC2 between the two Greek means is 0.116 on map A, between the Spanish and the Turkish 1.571 and between the Spanish and the Finns 1.695. The first two components therefore separate the Southeast European groups only weakly.

Table 4 lists, for each of the ten groups, the three nearest group means of the 73 in the plane of PC1 and PC2. The Athens Greeks lie next to the Cypriots, the Thessaloniki Greeks next to the Albanians, the Bulgarians next to the Croatians and the Serbs of Serbia next to the Serbs of Croatia. Along PC2 the Thessaloniki mean lies between the Athens mean and the Bulgarian mean (−5.36, −5.25, −5.00). Maps A and B give the same three nearest groups for every group, except that the second and third places of the Thessaloniki Greeks are exchanged (Spanish and English on map A, English and Spanish on map B).

These are statements about positions on two components. The Greek groups are read on the distance series of reference panel SB0 in Greeks, the Near East and Slavic-related influence.

Table 4The three nearest group means of the ten Southeast European groups on PC1 and PC2, maps A and B.

Group (n)	Map A: three nearest group means (distance)	Map B: three nearest group means (distance, ×10⁻³ bits)
Greek (Athens) (5)	Cypriot † 0.039; North Italian 0.069; Greek (Thessaloniki) 0.116	Cypriot † 0.0069; North Italian 0.0164; Greek (Thessaloniki) 0.0279
Greek (Thessaloniki) (12)	Albanian † 0.020; Spanish 0.043; English 0.050	Albanian † 0.0048; English 0.0094; Spanish 0.0099
Albanian † (6)	Greek (Thessaloniki) 0.020; Spanish 0.027; English 0.046	Greek (Thessaloniki) 0.0048; Spanish 0.0058; English 0.0081
Bulgarian † (10)	Croatian † 0.021; Serbs (Montenegro) † 0.036; French 0.050	Croatian † 0.0040; Serbs (Montenegro) † 0.0085; French 0.0118
Croatian † (9)	Bulgarian † 0.021; Serbs (Montenegro) † 0.027; Serbs (Serbia) † 0.056	Bulgarian † 0.0040; Serbs (Montenegro) † 0.0063; Serbs (Serbia) † 0.0136
Serbs (Serbia) † (19)	Serbs (Croatia) † 0.019; Serbs (Montenegro) † 0.030; Croatian † 0.056	Serbs (Croatia) † 0.0034; Serbs (Montenegro) † 0.0074; Croatian † 0.0136
Serbs (Bosnia) † (5)	French 0.024; Armenian 0.045; Georgian 0.054	French 0.0050; Armenian 0.0085; Georgian 0.0124
Serbs (Croatia) † (5)	Serbs (Serbia) † 0.019; Serbs (Montenegro) † 0.040; Croatian † 0.062	Serbs (Serbia) † 0.0034; Serbs (Montenegro) † 0.0092; Croatian † 0.0149
Serbs (Montenegro) † (7)	Croatian † 0.027; Serbs (Serbia) † 0.030; Bulgarian † 0.036	Croatian † 0.0063; Serbs (Serbia) † 0.0074; Bulgarian † 0.0085
Cypriot † (5)	Greek (Athens) 0.039; North Italian 0.092; Greek (Thessaloniki) 0.122	Greek (Athens) 0.0069; North Italian 0.0200; Greek (Thessaloniki) 0.0284

Euclidean distance between the group means on PC1 and PC2 of the 73 groups of Table 2, in map A units (×10⁻³) and in map B units (×10⁻³ bits). † projected group.

Regional PCAs

Each region below has its own PCA, run on the same Human Origins data with only the reference groups of that region building the axes. The axes, eigenvalues and scale therefore differ from Fig. 1, and the coordinates are raw, not entropy-rescaled. Groups keep one colour within a figure. The Balkan groups of the main study are projected where they are shown.

Sardinians (n = 17)
Spanish and Basque (n = 30)
French and English (n = 22)
North Italians (n = 15)
Finnish and Russian (n = 20)
Greeks (n = 15)
Albanians and Cypriots (n = 11)
Bulgarians, Croatians, Serbs (n = 55)
Spanish and Basque
French and English
North Italians
Finnish and Russian
Bulgarians, Croatians, Serbs
All other genomes
Group centroid

185 genomes · 442,397 SNPs

Figure 2Europe. PCA of nine European reference groups with the Balkan groups projected. Reference outliers were removed (22 genomes, 6 sigma).

British Isles (n = 48)
Iceland and Norway (n = 26)
French (n = 82)
Basque (n = 48)
Central Europe (n = 33)
Baltic and Finnish (n = 29)
Belarusians, Ukrainians, Russians (n = 117)
Sardinians (n = 43)
British Isles
Iceland and Norway
French
Central Europe
Baltic and Finnish
Belarusians, Ukrainians, Russians
All other genomes
Group centroid

426 genomes · 457,849 SNPs

Figure 3Northern, Western and Central Europe. PCA of sixteen reference groups from Orkney and Iceland to Hungary, the Baltic, Ukraine and Russia, with Sardinians and Basques as southern anchors. Human Origins groups with all their persons; reference outliers were removed (6 sigma).

Iberia (n = 212)
French (n = 84)
Sardinians (n = 48)
North Italians (n = 55)
South Italy, Sicily, Malta (n = 41)
Greeks and Albanians (n = 26)
Balkans and Hungary (n = 53)
Orcadians (n = 24)
Iberia
North Italians
South Italy, Sicily, Malta
Greeks and Albanians
Balkans and Hungary
Sardinians
All other genomes
Group centroid

543 genomes · 479,234 SNPs

Figure 4Southern Europe. PCA of fifteen reference groups from Iberia to the Balkans and Malta, with Orcadians as a northern anchor. Human Origins groups with all their persons; reference outliers were removed (6 sigma).

Western Europe (n = 64)
Greeks (n = 17)
Turks (n = 14)
Caucasus (n = 39)
Iranians (n = 15)
Levant (n = 14)
Albanians and Cypriots (n = 11)
Bulgarians, Croatians, Serbs (n = 55)
Western Europe
Turks
Caucasus
Iranians
Levant
Bulgarians, Croatians, Serbs
All other genomes
Group centroid

229 genomes · 455,832 SNPs

Figure 5Southeast Europe, Anatolia, Levant and Caucasus. PCA of thirteen reference groups from western Europe to the Levant with the Balkan groups projected. Reference outliers were removed.

Turks (n = 17)
Caucasus (n = 49)
Iranians (n = 17)
Levant (n = 34)
Bedouin B (n = 17)
Egyptians (n = 17)
Turks
Caucasus
Iranians
Levant
Bedouin B
Egyptians
All other genomes
Group centroid

151 genomes · 482,792 SNPs

Figure 6Near East and Caucasus. PCA of nine reference groups of the Near East and the Caucasus.

North and East Africa (n = 46)
West Africa (n = 44)
Bantu Kenya (n = 13)
Biaka (n = 17)
Mbuti (n = 15)
Ju/'hoan (n = 10)
North and East Africa
West Africa
Bantu Kenya
Biaka
Mbuti
All other genomes
Group centroid

145 genomes · 545,695 SNPs

Figure 7Africa. PCA of ten African reference groups.

Iran and Pakistan (n = 85)
India (n = 29)
Central Asia (n = 51)
Siberia (n = 102)
Chukchi (n = 17)
Tibetans (n = 17)
East Asia (n = 76)
Southeast Asia (n = 61)
Iran and Pakistan
India
Central Asia
Siberia
East Asia
Southeast Asia
All other genomes
Group centroid

438 genomes · 472,671 SNPs

Figure 8Asia. PCA of 29 Asian reference groups.

Iranians (n = 17)
Balochi (n = 17)
Pathan (n = 17)
Kalash (n = 17)
Burusho (n = 17)
Punjabi and Gujarati (n = 29)
Hazara (n = 17)
Uzbek and Kazakh (n = 34)
Iranians
Balochi and Pathan
Kalash and Burusho
Punjabi and Gujarati
Hazara
Uzbek and Kazakh
All other genomes
Group centroid

165 genomes · 460,042 SNPs

Figure 9South and Central Asia. PCA of ten South and Central Asian reference groups.

Tuvinians (n = 17)
Buryat (n = 17)
Yakut (n = 17)
Selkup and Ket (n = 34)
Nganasan (n = 17)
Chukchi (n = 17)
Eskimo (n = 14)
Mongola and Han (n = 28)
Tuvinians
Buryat
Yakut
Selkup and Ket
Nganasan
Eskimo
All other genomes
Group centroid

161 genomes · 437,905 SNPs

Figure 10Siberia and the Arctic. PCA of ten Siberian and Arctic reference groups.

Han (n = 17)
Japanese and Korean (n = 24)
Miao and Yi (n = 24)
Mongola (n = 11)
Tibetans (n = 17)
Dai (n = 15)
Hmong and Kinh (n = 27)
Malay and Kankanaey (n = 19)
Han
Japanese and Korean
Miao and Yi
Tibetans
Dai
Hmong and Kinh
All other genomes
Group centroid

154 genomes · 425,525 SNPs

Figure 11East and Southeast Asia. PCA of twelve East and Southeast Asian reference groups.

Eskimo (n = 14)
Chukchi (n = 17)
Pima (n = 16)
Mixe (n = 13)
Maya (n = 17)
Karitiana (n = 17)
Surui (n = 10)
Pima
Mixe
Maya
Karitiana and Surui
Eskimo
Chukchi
All other genomes
Group centroid

104 genomes · 405,075 SNPs

Figure 12Americas. PCA of seven reference groups of the Americas and the Arctic.

Papuan (n = 17)
Nasioi (n = 13)
Australian (n = 10)
Kankanaey (n = 10)
Malay (n = 9)
Papuan
Nasioi
Australian
Kankanaey and Malay
All other genomes
Group centroid

59 genomes · 426,883 SNPs

Figure 13Oceania. PCA of five reference groups of Oceania and Island Southeast Asia.

What the maps do not show

Positions, not ancestry. A position on a map describes how a group's genomes relate to the other groups on these axes. It gives no ancestry share, no direction of gene flow and no date; a share needs qpAdm with a fitting model.

Few persons. Greek (Athens), Serbs (Bosnia), Serbs (Croatia) and the Cypriots have five persons each, and their means carry wide uncertainty. Two persons of the Serb samples (18-646-21 and 18-646-39) have metadata in which the population label and the locality do not match; they are shown under the label used in the run. The Serb samples are male only in the source.

Projected groups. The eight projected groups did not build the axes. Their positions are placements on axes built by the reference groups, so a structure particular to them cannot appear on the axes.

PC3 and PC6. The Ju/'hoan group carries both axes, and they do not describe contrasts between regions.

Coverage. Human Origins has gaps: South Asia, Ethiopia and East Africa (Somali only), North America (Pima and Naukan Yupik only), and the Pacific beyond Papuan, Nasioi and Aboriginal Australian. Slovenes and Macedonians are absent.

Data and methods: Human Origins SNP set (564,989 SNPs), shrinkmode, six components, smartpca fancy normalisation, least-squares projection of the projected groups, no outlier removal, no LD pruning; platform PCA run 7bbdaf39 (1,034 persons: 968 reference, 66 projected). The platform normalises each axis over all returned persons; dividing by the norm of the reference persons restores the scale of the earlier world run 77cd2a60, whose eigenvalues are identical, and every reference person reproduces its coordinates there (largest difference below 10⁻¹⁵). Fig. 1 is drawn by the platform from run 7bbdaf39. Tables 2 to 4 are computed from the person-level coordinates of the run with the formulas above.

Regional runs (Human Origins, shrinkmode unless noted): Europe fa7f6221-6fc2-47a3-88ad-231c49a5489b (no shrinkage, outlier removal); Northern, Western and Central Europe 63077396-355d-41ec-b884-7bf3bdd6ae47 and Southern Europe a19b5fcc-c6f8-4a1c-b4a6-ee508ae106d1 (no shrinkage, outlier removal, all persons of each Human Origins group); Southeast Europe 4243b502-031c-4b0b-b5c6-26933eea87c6 (no shrinkage, outlier removal); Near East 898ccfa6-eb3f-4337-83bc-ebb91e940f32; Africa 52e54606-6a91-446a-b41c-a86fbe70ed2c; Asia 60102929-7de1-46a8-b895-e5d34777ef7f; South and Central Asia 71912151-e167-40d4-a4b1-e3a52d8e0885; Siberia d2122ce2-6496-48c8-9622-7f0ad284818b; East and Southeast Asia ac5cb3e5-a535-4ce8-aab9-7b29eb99a6c5; Americas d6edc9c7-f41f-4d83-aac9-9feafa62a468; Oceania 79f3567d-6319-4d90-ade5-19bd475a1c37.

Taleb, N. N. et al. Informational rescaling of PCA maps with application to genetic distance. Comput Struct Biotechnol J 27, 48–56 (2025); arXiv:2303.12654.

Patterson, N. et al. Ancient admixture in human history. Genetics 192, 1065–1093 (2012).

Patterson, N., Price, A. L. & Reich, D. Population structure and eigenanalysis. PLoS Genet 2, e190 (2006).

Magnus Albertus Papers · @AlbertusMvagnus · 2026

Every article

qpAdm54 min read
Slavic, Anatolian and Mycenaean sources in qpAdm models of Modern Greeks
Replications of posted models, a pre-declared grid of 191 qpAdm models and a robustness check of the Old Hittite (Kaman) fits: a Slavic-type and an Anatolian-type source are needed, the Mycenaean share is not identified.
Mvagnus AlbertusNovember 1, 2026
MWII0136 min read
MWII01, a low-coverage femur from the Abbey Church of Middelburg: ancestry fit against medieval, Roman and Iron Age references
MWII01, a low-coverage femur from Middelburg Abbey, fitted with qpAdm, f-statistics and entropy-rescaled PCA distances: a Netherlands Medieval Saxon source fits, no Slavic source adds anything, and only 4 of 104 two-source models are precise.
- PCA
Mvagnus AlbertusOctober 31, 2026
England13 min read
Bronze Age England: Where Do the Closest Genomes Lie?
Three methods on the same 20 Beaker-period and 25 Middle Bronze Age persons from England: Gaussian-process match maps, entropy-rescaled PCA distances and qpAdm.
- PCA
- qpAdm
Mvagnus AlbertusOctober 30, 2026

Design of the run

The world on PC1 and PC2

Group means on the rescaled maps

Southeast Europe on the first two axes

Regional PCAs

What the maps do not show

Keep reading

Slavic, Anatolian and Mycenaean sources in qpAdm models of Modern Greeks

MWII01, a low-coverage femur from the Abbey Church of Middelburg: ancestry fit against medieval, Roman and Iron Age references

Bronze Age England: Where Do the Closest Genomes Lie?