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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 Albertus · Popualtion Geneticist

Published 54 min read

Public qpAdm models of Modern Greeks combine a Slavic, a Mycenaean and one Anatolian source and are used to argue about the size of the Aegean share and about which Anatolian proxy is valid. We rebuilt the posted models with proxies from the Nexju base (Human Origins v66 ext 3) and ran a pre-declared grid of 191 models for Modern Greeks (Athens, n=17; Thessaloniki, n=14): the Slavic proxy (Poland Early Medieval, n=46) plus one of 17 Anatolian-type sources, with and without Mycenaeans (n=7), on two right panels. Of the four posted Mycenaean-containing models, only the Old Hittite (Kaman, n=2) model fits, with different weights (Mycenaeans 19 instead of 32 %); the Roman-era, Alalakh and Arslantepe models are rejected. No model without a Slavic source (0 of 34) and no model without an Anatolian source (0 of 4) fits. Without Mycenaeans, 10 two-source models fit; 6 of them become infeasible when Mycenaeans are added. Only 2 of 68 three-source models are strict fits, and both use the same source of two persons (Old Hittite, Kaman). A second pre-declared block (116 models and 4 sensitivity analyses) tested these two fits. Removing one of the two persons leaves a rejected model (p = 0.040 for Athens, 0.029 for Thessaloniki), raw instead of reduced counts of two right populations reject the Athens fit (p = 0.037), and the fit depends on the right panel. By the pre-declared rule the Kaman three-source fits are INVALID: they are not used as evidence about Greeks. This does not show them to be false. The Mycenaean share is not identified: passing models with a Kaman-site source give 5.3 to 50.2 %.

Introduction

qpAdm1 tests whether the allele frequencies of a target population can be reproduced as a mixture of a set of source populations, relative to a set of right (outgroup) populations. A model is not rejected when the p-value of the fit is not below 0.05. That is the absence of rejection with the power of the data, not evidence of descent.2

A public discussion about modern Thessalonians and Athenians uses qpAdm models with three sources: a Slavic-type source (Early Medieval Central and Eastern Europe), a Mycenaean or Aegean Bronze Age source, and one Anatolian-type source. The posted models differ in the Anatolian source (Roman-era, Alalakh, Arslantepe, Old Hittite). The arguments around them are (i) that the Aegean share of Greeks is large (“well over 35 %”), (ii) that Alalakh and Arslantepe are valid proxies of post-Chalcolithic Anatolian ancestry whereas Old Hittite or Early Bronze Age Anatolians do not fit, and (iii) that, when closer West-Anatolian Bronze Age sources are used, the drift goes to them and not to the Mycenaean source.

This study asks four questions. (Q1) Can the posted models be reproduced with the sources of the Nexju base? (Q2) How do fit, weights and the Mycenaean share react when the Anatolian source is changed, and does a model need a Slavic, an Anatolian and a Mycenaean source? (Q3) What is the evidence for the Old Hittite (Kaman) models, the only strict three-source fits? (Q4) Does that evidence survive checks that were fixed before the runs? The rules for all comparisons were written down before the runs of each block and were not changed afterwards.

Data and methods

Data and targets. All models use the Nexju base (Human Origins v66 ext 3, with individual labels that follow the Allen Ancient DNA Resource3), qpAdm with allSnps false unless stated, α = 0.05. The targets are the Modern Greek groups Greek_WGA (Athens, n=17) and Greek_Thessaloniki (n=14). The Slavic proxy (SP) is Poland Early Medieval Slavs (n=46); the Mycenaean source (MY) is a group of seven Mycenaean individuals (n=7). The 17 Anatolian-type sources X are nine Roman-era groups, two Byzantine and one Ottoman group, Alalakh (n=5), Arslantepe (n=16), Old Hittite from Kalehöyük, Kaman (n=2; KAM2: MA2200, 1,021,939 SNPs, and MA2203, 317,679 SNPs), and two West-Anatolian Bronze Age groups. Table 14 lists every group with its code and members. Several of these groups are small (n=1 to 5) or have fewer than 500,000 SNPs; this is stated where it matters.

Right panels. Two panels are used. RB13 (13 rights) is built from the base populations that correspond to the 13 outgroup classes of the posted models; R10 (10 rights) is the panel of earlier Nexju blocks. Both are proxies of the posted panels, not identical ones. R14 is R10 plus four populations of the Anatolian and Levantine side. Two right populations hold fewer individuals in the datasets of block 1 than their base label suggests (Turkey_N 43 instead of 68 on RB13, Crete 5 instead of 34); this is tested in the check V6.

Fit rule. A model is a fit if p ≥ 0.05, every weight lies in [0,1], and every weight standard error is below 0.10. A model with p ≥ 0.05 and feasible weights but a standard error of 0.10 or more is imprecise; with a weight outside [0,1] it is infeasible. A published-style pass needs only p ≥ 0.05 and weights in [0,1]. The fits to the posted models M1–M4 use allSnps true, as in the posts. allSnps true stretches the models artificially and distorts p-values, so the p-values of M1–M4 are not comparable with the allSnps false results of the other blocks.

Record check. Every model is a single qpAdm run with exactly the sources of the model on the left, stored with its analysis id; every record was checked (sources and right count as declared, degrees of freedom = rights − sources, weights sum to 1, p reproduced from χ² and degrees of freedom). The tables are generated from the records. Each model in the tables and appendices carries a link to its public Nexju result page.

Pre-declared blocks and checks

Two blocks were run. Block 1 (191 single models): replications of the posted models M1–M4 (Papadopoulos) and CA1–CA3 (Antoniou), the grid SP + X (+ MY) for the 17 sources X on both panels and both targets (136 models), models without a Slavic source (34), without an Anatolian source (4), and a test of the replications on raw counts (7). Block 2 (116 single models and 4 sensitivity analyses): the checks of the Kaman fits (Table 1). The rules, the groups, the control pairs (drawn with a fixed random seed) and the expectations were written down before the runs of each block; counts and verdicts below are computed by those rules. Nothing was re-ranked afterwards, and nothing was corrected for multiplicity.

The verdict rule is: INVALID if V1 is fragile for at least one target, or V2 is fragile for at least one target, or V6 does not hold, or (V4 is “none” and V5 is not discriminating for at least one target). Otherwise valid for Kaman only if V4 is “none”, or V5 is weak or not discriminating, or V2 is mixed for at least one target. Otherwise robust. “Invalid” means that the fit is not used as evidence for any statement about Greeks; it stays in the record as a result of this source and this panel.

Table 1Checks V1–V6 fixed before the Kaman block

Check

Question

Rule (per target)

V1

Is the fit carried by one person?

Slavs + MA2200 + MY and Slavs + MA2203 + MY (RB13) must both be published-style passes; otherwise fragile.

V2

Does it survive other right sets?

14 variants of Slavs + KAM2 + MY (12 drop-one-right, panels R10 and R14): stable if at least 12 are not rejected, mixed if 10 or 11, fragile if 9 or fewer.

V3

Is the Mycenaean source needed?

Slavs + KAM2 rejected in at least 12 of its 14 variants and the drop-source variant rejected: required.

V4

Does an independent source fit too?

Strict three-source fit on RB13 with Kaman Assyrian Colony (n=3), Kaman Iron Age (n=2), Oylum Höyük (n=6) or Harmanoğlu (n=3): corroborated.

V5

Is a pass specific to this pair?

Eight control pairs of persons from pools rejected as whole groups: 0 or 1 pass = discriminating, 2 = weak, 3 or more = not discriminating.

V6

Does it depend on two right counts?

Slavs + KAM2 + MY with raw counts (Turkey_N 68, Crete 34) is a published-style pass for both targets: holds.

Replication of the posted models

Table 2 compares the posted models with the Nexju versions (target Thessaloniki, RB13). The Slavic weight is reproduced in M2–M4 (within 2.3 points), but the split between Mycenaean and Anatolian weight is not. M1 (Roman-era plus Ottoman, four sources) is rejected and infeasible (the two Anatolian weights are 123 and −118 %). M2 (Alalakh) and M3 (Arslantepe) are rejected (p = 2 × 10⁻⁵ and 2 × 10⁻¹¹), although they are the models presented as fitting. M4 (Old Hittite, Kaman) fits (p = 0.071 against the posted 0.164) with Mycenaeans at 19 % instead of 32 %. The models of Antoniou (CA1, CA2) pass, but they rest on 27,781 and 12,701 SNPs with one Aydın individual (82,389 SNPs) and the standard errors exceed the weights; a source this poor fits almost anything, so these passes carry little information. The replication is not exact: tool, SNP set, individuals and right populations differ from the posts. The fit of M1–M4 does not change when the raw counts of Turkey_N and Crete are used (largest weight change 3.6 points; models RZ in Appendix D).

Table 2Posted models and their replication with Nexju proxies, target Thessaloniki (n=14), RB13

Model

Target

p posted

p ours

Result

Largest weight difference (points)

SNPs

Weights % (SE)

Link

M1 Roman-era + Ottoman

Thessaloniki

0.427

4 × 10⁻⁵ †

rejected (infeasible)

n/a (infeasible)

468,442

MY 73.0 (20.5), Q10 123.4 (58.3), SP 21.2 (9.8), OTT5 −117.6 (67.1)

link

M2 Alalakh

Thessaloniki

0.384

2 × 10⁻⁵ †

rejected

11.6

468,442

MY 26.5 (5.0), ALA5 28.4 (4.3), SP 45.0 (1.5)

link

M3 Arslantepe

Thessaloniki

0.389

2 × 10⁻¹¹ †

rejected

1.8

468,442

MY 33.8 (6.3), ARS16 21.1 (5.1), SP 45.2 (1.8)

link

M4 Old Hittite (Kaman)

Thessaloniki

0.164

0.071 †

fit

14.9

468,442

MY 19.4 (6.0), KAM2 39.0 (5.8), SP 41.6 (1.8)

link

CA1 Lazarides LBA + Aydın BA

Thessaloniki

0.448

0.653

pass, imprecise

6.7

27,781

LAZ4 11.4 (480.9), LEB 4.6 (68.2), CZ 34.7 (82.9), AYD1 49.3 (630.2)

link

CA2 Lazarides EBA + Aydın BA

Thessaloniki

0.461

0.959

pass, imprecise

31.6

12,701

LAZ1 13.8 (8.9), LEB 28.5 (16.6), CZ 43.0 (8.9), AYD1 14.7 (26.6)

link

† allSnps true, as in the posts. It stretches the models and distorts p-values, so these p-values are not comparable with allSnps false results. The CA models use allSnps false. “Largest weight difference” is in percentage points against the posted figure. Codes as in Table 14.

Which sources a fit needs

Table 3 summarizes the 191 models of block 1 by class. Three results hold in all cells that were run.

  1. A Slavic-type source is needed. None of the 34 models X + Mycenaeans fits; 28 of the 34 are infeasible.

  2. An Anatolian-type source is needed. Slavs + Mycenaeans is rejected on all four cells (p at most 3 × 10⁻¹¹).

  3. Strict three-source fits are rare. Of 68 models Slavs + X + Mycenaeans only 2 are fits, both with X = Kaman (RB13). The same sources without Mycenaeans give 10 fits.

Table 3Number of models of block 1 by class and result

Class

Models

Fit

Imprecise

Infeasible, p ≥ 0.05

Rejected

Slavs + X + Mycenaeans (17 X, 2 targets, 2 panels)

68

2

4

6

56

Slavs + X (no Mycenaeans)

68

10

1

0

57

X + Mycenaeans (no Slavic source)

34

0

0

2

32

Slavs + Mycenaeans (no Anatolian source)

4

0

0

0

4

Fit = strict rule; imprecise and infeasible = p ≥ 0.05 but not a fit; rejected includes rejected and infeasible.

Fits without a Mycenaean source. Table 4 lists the 10 strict two-source fits. All involve small groups: Aydın Bronze Age (n=1), Turkey Imperial Roman (n=4), Roman-era QW2 (n=2) and QPW5 (n=5, assembled after the first results, hence post hoc), and Roman-era QP3 (n=3). Adding Mycenaeans raises p in 56 of 68 pairs (a free parameter is added) but turns the strict fits into: 6 infeasible (negative Mycenaean weight −1 to −22 %), 1 rejected (QP3, Athens, Mycenaean 0.7 %) and 3 imprecise (Aydın, n=1). The Slavic weight is stable in the models that are not rejected: 27 to 34 % for Athens and 37 to 42 % for Thessaloniki (Aydın models left out).

Table 4The strict fits without a Mycenaean source (Slavic proxy + one Anatolian group)

Target

Anatolian source (with Slavs)

Panel

p

Weights % (SE)

SNPs

Link

Thessaloniki

Aydın Bronze Age (n=1)

R10

0.448

SP 35.9 (10.0), AYD1 64.1 (10.0)

31,719

link

Thessaloniki

Turkey Imperial Roman (n=4)

R10

0.522

SP 36.7 (2.9), O4 63.3 (2.9)

333,884

link

Thessaloniki

Turkey Roman-era QPW5 (n=5)

R10

0.060

SP 40.6 (2.2), QPW5 59.4 (2.2)

424,172

link

Thessaloniki

Turkey Roman-era QW2 (n=2)

R10

0.068

SP 41.3 (2.6), QW2 58.7 (2.6)

407,319

link

Thessaloniki

Aydın Bronze Age (n=1)

RB13

0.864

SP 26.1 (6.1), AYD1 73.9 (6.1)

30,599

link

Athens

Turkey Imperial Roman (n=4)

R10

0.254

SP 27.0 (3.1), O4 73.0 (3.1)

333,884

link

Athens

Turkey Roman-era QPW5 (n=5)

R10

0.138

SP 31.4 (2.2), QPW5 68.6 (2.2)

424,172

link

Athens

Turkey Roman-era QW2 (n=2)

R10

0.199

SP 34.0 (2.6), QW2 66.0 (2.6)

407,319

link

Athens

Aydın Bronze Age (n=1)

RB13

0.809

SP 17.8 (6.9), AYD1 82.2 (6.9)

30,599

link

Athens

Turkey Roman-era QP3 (n=3)

RB13

0.057

SP 32.4 (1.9), QP3 67.6 (1.9)

395,400

link

allSnps false. Codes as in Table 14.

Sources of the grid. The p-values of the whole grid are in Tables 5 and 6; every model with weights and link is in Appendix D. Roman-era Anatolian groups give no three-source fit: they are rejected or, in six cells, feasible only with a negative Mycenaean weight. Alalakh and Arslantepe are rejected in the three-source models on both targets, with p of 9 × 10⁻⁶ and 2 × 10⁻¹³ (Athens) and 4 × 10⁻⁵ and 3 × 10⁻⁹ (Thessaloniki). The Mycenaean weight of the 52 feasible three-source models runs from 0.7 to 65 % depending on the Anatolian source. Of the 12 three-source models with p ≥ 0.05, six are infeasible, four imprecise and two are fits.

Table 5Grid p-values, Modern Greeks (Athens, n=17)

Source X

RB13 Slavs + X

RB13 + MY

R10 Slavs + X

R10 + MY

Turkey Roman-era (n=10)

<1e-16 R

7e-11 R

2e-14 R

3e-6 R

Turkey Roman-era QI5 (n=5)

7e-8 R

3e-5 R

6e-5 R

3e-4 R

Turkey Roman-era QL5 (n=5)

<1e-16 RX

1e-12 R

<1e-16 RX

3e-6 R

Turkey Roman-era QP3 (n=3)

0.057 F

0.031 R

0.045 R

0.039 RX

Turkey Roman-era QB3 (n=3)

<1e-16 RX

7e-16 R

<1e-16 RX

1e-5 RX

Turkey Roman-era QW2 (n=2)

5e-9 R

9e-6 R

0.199 F

0.265 X

Turkey Roman-era QS2 (n=2)

1e-16 R

4e-6 R

1e-7 R

8e-5 R

Turkey Roman-era QPW5 (n=5)

0.018 R

0.024 R

0.138 F

0.217 X

Turkey Imperial Roman (n=4)

0.006 R

0.008 RX

0.254 F

0.396 X

Byzantine West Anatolia early (n=21)

2e-12 R

3e-12 RX

1e-4 R

2e-4 RX

Byzantine West Anatolia late (n=8)

1e-13 R

3e-14 R

6e-6 R

9e-6 RX

Turkey Ottoman (n=5)

<1e-16 R

1e-13 R

5e-8 R

8e-7 R

Alalakh MLBA (n=5)

3e-10 R

9e-6 R

2e-8 R

8e-7 R

Arslantepe LC–EBA (n=16)

<1e-16 R

2e-13 R

8e-12 R

5e-11 R

Kaman (Old Hittite, n=2)

0.018 R

0.128 F

0.045 R

0.047 R

Yassitepe BA (n=2)

2e-9 R

0.004 RX

4e-9 R

0.003 RX

Aydın Bronze Age (n=1)

0.809 F

0.714 I

0.625 I

0.547 I

Each cell: p and result (F fit, I imprecise, X infeasible with p ≥ 0.05, R rejected, RX rejected and infeasible). Per panel, the pair is Slavs + X without and with Mycenaeans (+ MY). allSnps false.

Table 6Grid p-values, Modern Greeks (Thessaloniki, n=14)

Source X

RB13 Slavs + X

RB13 + MY

R10 Slavs + X

R10 + MY

Turkey Roman-era (n=10)

<1e-16 R

4e-8 R

<1e-16 R

1e-5 R

Turkey Roman-era QI5 (n=5)

3e-8 R

1e-4 R

4e-7 R

7e-5 R

Turkey Roman-era QL5 (n=5)

<1e-16 R

2e-9 R

<1e-16 RX

1e-5 R

Turkey Roman-era QP3 (n=3)

0.036 R

0.023 R

0.019 R

0.027 R

Turkey Roman-era QB3 (n=3)

<1e-16 RX

5e-11 R

<1e-16 RX

2e-5 R

Turkey Roman-era QW2 (n=2)

5e-10 R

9e-5 R

0.068 F

0.059 X

Turkey Roman-era QS2 (n=2)

<1e-16 R

8e-6 R

5e-11 R

5e-6 R

Turkey Roman-era QPW5 (n=5)

6e-4 R

0.005 R

0.060 F

0.065 X

Turkey Imperial Roman (n=4)

0.005 R

0.004 R

0.522 F

0.497 X

Byzantine West Anatolia early (n=21)

3e-11 R

1e-9 R

4e-6 R

3e-6 R

Byzantine West Anatolia late (n=8)

3e-13 R

9e-10 R

1e-7 R

2e-7 R

Turkey Ottoman (n=5)

<1e-16 R

7e-9 R

1e-9 R

8e-6 R

Alalakh MLBA (n=5)

9e-12 R

4e-5 R

2e-11 R

5e-6 R

Arslantepe LC–EBA (n=16)

<1e-16 R

3e-9 R

3e-13 R

4e-9 R

Kaman (Old Hittite, n=2)

0.006 R

0.083 F

0.002 R

0.003 R

Yassitepe BA (n=2)

1e-7 R

0.010 RX

3e-8 R

0.001 RX

Aydın Bronze Age (n=1)

0.864 F

0.859 I

0.448 F

0.339 I

Cells as in Table 5. allSnps false.

The Kaman (Old Hittite) models

The Kaman three-source models are declared INVALID by the pre-declared rule of this study (see the verdict below). They are shown here because they are the only strict three-source fits; they are not used as evidence for any statement about Greeks.

The strict fits are Slavs + Kaman + Mycenaeans on RB13: Athens p = 0.128 (Slavs 31.3 %, Kaman 47.2 %, Mycenaeans 21.5 %, SE 6.7) and Thessaloniki p = 0.083 (Slavs 41.8 %, Kaman 35.3 %, Mycenaeans 22.8 %, SE 6.5). Table 7 shows the neighbouring models. On R10 the same model is rejected (Athens p = 0.047, a hair under the line; Thessaloniki p = 0.003); without Mycenaeans it is rejected on both panels (RB13: 0.018 and 0.006; R10: 0.045 and 0.002). The Kaman group is two persons, one of them with 318,000 SNPs.

Table 7Kaman (Old Hittite, n=2) three-source models and their neighbours

Target

Model

Panel

p

Result

SNPs

Weights % (SE)

Link

Athens

Slavs + Kaman + Mycenaeans

RB13

0.128

fit

369,507

SP 31.3 (1.9), KAM2 47.2 (6.3), MY 21.5 (6.7)

link

Athens

Slavs + Kaman + Mycenaeans

R10

0.047

rejected

387,656

SP 32.7 (2.7), KAM2 55.3 (8.1), MY 12.0 (8.1)

link

Athens

Slavs + Kaman

RB13

0.018

rejected

373,260

SP 33.0 (2.4), KAM2 67.0 (2.4)

link

Athens

Slavs + Kaman

R10

0.045

rejected

389,918

SP 33.2 (3.1), KAM2 66.8 (3.1)

link

Athens

Slavs + Kaman + Mycenaeans, raw counts of Turkey_N and Crete

RB13

0.037

rejected

371,818

SP 32.7 (2.0), KAM2 49.9 (6.8), MY 17.5 (7.2)

link

Thessaloniki

Slavs + Kaman + Mycenaeans

RB13

0.083

fit

369,507

SP 41.8 (1.8), KAM2 35.3 (6.2), MY 22.8 (6.5)

link

Thessaloniki

Slavs + Kaman + Mycenaeans

R10

0.003

rejected

387,656

SP 40.8 (2.6), KAM2 45.0 (8.7), MY 14.2 (8.5)

link

Thessaloniki

Slavs + Kaman

RB13

0.006

rejected

373,260

SP 43.4 (2.3), KAM2 56.6 (2.3)

link

Thessaloniki

Slavs + Kaman

R10

0.002

rejected

389,918

SP 41.2 (3.0), KAM2 58.8 (3.0)

link

Thessaloniki

Slavs + Kaman + Mycenaeans, raw counts of Turkey_N and Crete

RB13

0.155

fit

371,818

SP 42.5 (1.8), KAM2 34.3 (6.1), MY 23.2 (6.3)

link

SP Slavs, KAM2 Kaman (n=2), MY Mycenaeans. allSnps false.

Checks of the Kaman fits

V1: one person at a time (Table 8). Without MA2200 (the person with 1,021,939 SNPs) the model Slavs + MA2203 + MY passes (Athens p = 0.348, Thessaloniki p = 0.314). Without MA2203 it is rejected: Slavs + MA2200 + MY gives p = 0.040 for Athens and 0.029 for Thessaloniki, with Mycenaeans at about 20 %. MA2203 alone has only 114,164 SNPs on the panel (in the three-source model), and Slavs + MA2203 passes even without Mycenaeans (p 0.128 and 0.062). The pair passes more easily than its better-covered member (speculation, not tested: the poorly covered person widens the standard errors of the group frequencies). V1 is fragile for both targets.

Table 8V1: the Kaman model with both persons, with MA2200 only and with MA2203 only (RB13)

Target

Model

Panel

p

Result

SNPs

Weights % (SE)

Link

Athens

Slavs + Kaman (both persons) + Mycenaeans

RB13

0.128

fit

369,507

SP 31.3 (1.9), KAM2 47.2 (6.3), MY 21.5 (6.7)

link

Athens

Slavs + MA2200 + Mycenaeans

RB13

0.040

rejected

359,242

SP 32.1 (2.2), K00 47.7 (7.6), MY 20.2 (8.1)

link

Athens

Slavs + MA2203 + Mycenaeans

RB13

0.348

fit

114,164

SP 30.2 (2.9), K03 46.8 (8.3), MY 23.0 (8.6)

link

Athens

Slavs + MA2200

RB13

0.014

rejected

362,904

SP 33.7 (2.6), K00 66.3 (2.6)

link

Athens

Slavs + MA2203

RB13

0.128

fit

115,179

SP 32.1 (3.8), K03 67.9 (3.8)

link

Thessaloniki

Slavs + Kaman (both persons) + Mycenaeans

RB13

0.083

fit

369,507

SP 41.8 (1.8), KAM2 35.3 (6.2), MY 22.8 (6.5)

link

Thessaloniki

Slavs + MA2200 + Mycenaeans

RB13

0.029

rejected

359,242

SP 42.2 (2.0), K00 35.9 (7.6), MY 21.9 (8.0)

link

Thessaloniki

Slavs + MA2203 + Mycenaeans

RB13

0.314

fit

114,164

SP 39.7 (2.7), K03 34.3 (8.5), MY 26.0 (8.7)

link

Thessaloniki

Slavs + MA2200

RB13

0.007

rejected

362,904

SP 43.9 (2.5), K00 56.1 (2.5)

link

Thessaloniki

Slavs + MA2203

RB13

0.062

fit

115,179

SP 41.6 (3.6), K03 58.4 (3.6)

link

K00 Kaman person MA2200 (1,021,939 SNPs), K03 Kaman person MA2203 (317,679 SNPs). allSnps false.

V2: right populations (Table 9; every variant in Appendix C). Athens: the base fit is not rejected in 11 of 14 variants (mixed); it is rejected when Ukraine_EIA_Scythian is dropped (p = 0.034), under R10 (p = 0.047) and under R14 (p = 0.001). Thessaloniki: not rejected in 12 of 14 (stable), rejected under R10 (p = 0.003) and R14 (p = 2 × 10⁻⁴). Inside RB13 the Mycenaean split is stable (15.9 to 23.1 % in the 11 Athens variants and 18.6 to 25.0 % in the 12 Thessaloniki variants); the change comes with the other panels.

V3: Mycenaean source needed in the Kaman model. Slavs + Kaman without Mycenaeans is rejected in 12 of 14 right-panel variants for Athens and in 14 of 14 for Thessaloniki; the drop-source variant is rejected (p = 0.018 and 0.006). Inside this model the Mycenaean source is required. This does not carry over to other sources (Tables 5 and 6).

Table 9V2 and V3: the Kaman model against the right populations (14 variants per model)

Target

Model

Variants not rejected

Rejected variants (p)

Mycenaean % in the not-rejected variants

Drop-source variants (p)

Athens

Slavs + Kaman + Mycenaeans

11 of 14 (mixed)

Ukraine_EIA_Scythian dropped (0.034), R10 (0.047), R14 (0.001)

15.9 to 23.1

no Slavs 1 × 10⁻¹⁵ (infeasible); no Kaman < 1 × 10⁻¹⁶; no Mycenaeans 0.018

Thessaloniki

Slavs + Kaman + Mycenaeans

12 of 14 (stable)

R10 (0.003), R14 (2 × 10⁻⁴)

18.6 to 25.0

no Slavs 1 × 10⁻¹⁶ (infeasible); no Kaman 3 × 10⁻¹¹; no Mycenaeans 0.006

Athens

Slavs + Kaman

2 of 14 (Croatia_MLBA dropped 0.097, Estonia_LBA_StoneCistGraves dropped 0.125)

the other 12

–

no Slavs < 1 × 10⁻¹⁶; no Kaman < 1 × 10⁻¹⁶

Thessaloniki

Slavs + Kaman

0 of 14

all 14

–

no Slavs < 1 × 10⁻¹⁶; no Kaman < 1 × 10⁻¹⁶

The 14 variants are the 12 drop-one-right variants of RB13 and the panels R10 and R14. allSnps false.

V4: other Kaman-site and Anatolian groups (Table 10). Kaman Iron Age (n=2; 194,713 SNPs) gives a strict fit for both targets (Athens p = 0.173, Thessaloniki p = 0.146), so V4 is corroborated. The composition differs strongly from the Old Hittite fit: Mycenaeans 50.2 and 46.9 % (SE 3.6 and 3.1) against about 22 %, and the Slavic weight 17 and 33 %. So a second Kaman-site group can also produce a fit with a Mycenaean source, but not the same weights. Kaman Iron Age is rejected for Athens on R10 (p = 0.033). Kaman Assyrian Colony (n=3) is rejected on RB13 (p = 0.014 and 0.037) and fits on R10 with Mycenaeans at 5.3 and 11.2 %. Oylum Höyük (n=6) and Harmanoğlu (n=3) are rejected on both panels (Oylum p = 1 × 10⁻⁵ down to 1 × 10⁻⁸). All seven Kaman individuals together (not independent of KAM2) fit for Athens (RB13 p = 0.052) and are rejected for Thessaloniki (p = 0.024).

Table 10V4: Slavs + other Kaman-site group + Mycenaeans, both panels

Target

Model

Panel

p

Result

SNPs

Weights % (SE)

Link

Athens

Slavs + Kaman Iron Age (n=2) + Mycenaeans

RB13

0.173

fit

194,713

SP 17.2 (2.8), KIA2 32.6 (5.1), MY 50.2 (3.6)

link

Athens

Slavs + Kaman Iron Age (n=2) + Mycenaeans

R10

0.033

rejected

203,370

SP 12.2 (4.1), KIA2 38.7 (5.0), MY 49.1 (3.4)

link

Thessaloniki

Slavs + Kaman Iron Age (n=2) + Mycenaeans

RB13

0.146

fit

194,713

SP 33.2 (2.8), KIA2 19.9 (4.7), MY 46.9 (3.1)

link

Thessaloniki

Slavs + Kaman Iron Age (n=2) + Mycenaeans

R10

0.084

fit

203,370

SP 27.8 (3.9), KIA2 28.4 (4.8), MY 43.8 (3.0)

link

Athens

Slavs + Kaman Assyrian Colony (n=3) + Mycenaeans

RB13

0.014

rejected

303,961

SP 32.7 (1.8), AC3 42.4 (5.8), MY 24.9 (6.5)

link

Athens

Slavs + Kaman Assyrian Colony (n=3) + Mycenaeans

R10

0.122

fit

318,702

SP 37.2 (2.6), AC3 57.5 (6.8), MY 5.3 (7.5)

link

Thessaloniki

Slavs + Kaman Assyrian Colony (n=3) + Mycenaeans

RB13

0.037

rejected

303,961

SP 43.2 (1.8), AC3 32.7 (5.5), MY 24.0 (6.1)

link

Thessaloniki

Slavs + Kaman Assyrian Colony (n=3) + Mycenaeans

R10

0.065

fit

318,702

SP 45.0 (2.4), AC3 43.8 (6.0), MY 11.2 (6.5)

link

Athens

Slavs + Kaman all periods (n=7) + Mycenaeans

RB13

0.052

fit

396,446

SP 28.6 (1.4), KAL7 41.7 (4.4), MY 29.7 (4.4)

link

Athens

Slavs + Kaman all periods (n=7) + Mycenaeans

R10

0.064

fit

416,864

SP 29.7 (2.0), KAL7 53.0 (4.9), MY 17.2 (4.7)

link

Thessaloniki

Slavs + Kaman all periods (n=7) + Mycenaeans

RB13

0.024

rejected

396,446

SP 40.0 (1.5), KAL7 31.4 (4.4), MY 28.6 (4.6)

link

Thessaloniki

Slavs + Kaman all periods (n=7) + Mycenaeans

R10

0.006

rejected

416,864

SP 39.3 (2.0), KAL7 39.6 (4.8), MY 21.1 (4.6)

link

Athens

Slavs + Oylum Höyük MBA (n=6) + Mycenaeans

RB13

1 × 10⁻⁵

rejected

398,364

SP 34.9 (1.5), OYL6 32.6 (4.1), MY 32.5 (5.0)

link

Athens

Slavs + Oylum Höyük MBA (n=6) + Mycenaeans

R10

1 × 10⁻⁸

rejected

419,646

SP 37.1 (1.8), OYL6 39.8 (4.3), MY 23.1 (4.9)

link

Thessaloniki

Slavs + Oylum Höyük MBA (n=6) + Mycenaeans

RB13

8 × 10⁻⁵

rejected

398,364

SP 44.2 (1.6), OYL6 22.6 (3.8), MY 33.2 (4.6)

link

Thessaloniki

Slavs + Oylum Höyük MBA (n=6) + Mycenaeans

R10

1 × 10⁻⁶

rejected

419,646

SP 44.3 (1.8), OYL6 26.9 (3.6), MY 28.8 (4.1)

link

Athens

Slavs + Harmanoğlu–Göndürle EBA (n=3) + Mycenaeans

RB13

4 × 10⁻⁹

rejected (infeasible)

395,104

SP 61.0 (25.0), HAR3 238.9 (201.7), MY −199.9 (225.8)

link

Athens

Slavs + Harmanoğlu–Göndürle EBA (n=3) + Mycenaeans

R10

3 × 10⁻⁷

rejected (infeasible)

418,542

SP 40.2 (3.8), HAR3 94.4 (21.2), MY −34.6 (23.2)

link

Thessaloniki

Slavs + Harmanoğlu–Göndürle EBA (n=3) + Mycenaeans

RB13

2 × 10⁻⁹

rejected (infeasible)

395,104

SP −0.7 (259.4), HAR3 −359.3 (2172.3), MY 460.0 (2431.3)

link

Thessaloniki

Slavs + Harmanoğlu–Göndürle EBA (n=3) + Mycenaeans

R10

7 × 10⁻⁹

rejected (infeasible)

418,542

SP 46.2 (3.4), HAR3 65.9 (26.3), MY −12.1 (28.3)

link

allSnps false. Codes as in Table 14.

V5: do generic pairs pass? (Table 11). None of the eight control pairs (persons of Roman-era Anatolia and Arslantepe, groups rejected as wholes) passes Slavs + pair + Mycenaeans on RB13 for either target (p from 1 × 10⁻¹⁵ to 0.020). A pass is therefore not a generic property of two-person groups on this panel. The controls come from pools that were already rejected as whole groups, which makes them a conservative control in the direction of “discriminating”. On R10 without Mycenaeans, 2 of 8 pairs pass for Athens and 1 of 8 for Thessaloniki, so small groups can pass the two-source model on R10.

Table 11V5: eight control pairs (n=2 each), Slavs + pair + Mycenaeans on RB13 and Slavs + pair on R10

Target

Model

Panel

p

Result

SNPs

Weights % (SE)

Link

Athens

Slavs + CQ1 + Mycenaeans

RB13

8 × 10⁻⁵

rejected

373,765

SP 31.5 (1.7), CQ1 45.5 (8.8), MY 23.1 (9.1)

link

Thessaloniki

Slavs + CQ1 + Mycenaeans

RB13

8 × 10⁻⁵

rejected

373,765

SP 41.4 (1.5), CQ1 29.9 (8.1), MY 28.7 (8.5)

link

Athens

Slavs + CQ2 + Mycenaeans

RB13

0.020

rejected

380,744

SP 32.8 (2.3), CQ2 62.8 (12.0), MY 4.4 (12.7)

link

Thessaloniki

Slavs + CQ2 + Mycenaeans

RB13

0.008

rejected

380,744

SP 43.0 (2.1), CQ2 45.1 (11.0), MY 11.9 (11.6)

link

Athens

Slavs + CQ3 + Mycenaeans

RB13

9 × 10⁻⁶

rejected

379,530

SP 34.9 (1.7), CQ3 34.7 (6.6), MY 30.4 (7.5)

link

Thessaloniki

Slavs + CQ3 + Mycenaeans

RB13

9 × 10⁻⁵

rejected

379,530

SP 43.3 (1.6), CQ3 23.4 (5.6), MY 33.3 (6.3)

link

Athens

Slavs + CQ4 + Mycenaeans

RB13

1 × 10⁻¹⁵

rejected

401,630

SP 21.7 (3.5), CQ4 9.8 (3.2), MY 68.5 (1.7)

link

Thessaloniki

Slavs + CQ4 + Mycenaeans

RB13

6 × 10⁻¹¹

rejected

401,630

SP 37.1 (3.4), CQ4 4.7 (3.1), MY 58.2 (1.7)

link

Athens

Slavs + CR1 + Mycenaeans

RB13

8 × 10⁻⁵

rejected (infeasible)

335,134

SP 42.7 (3.6), CR1 65.8 (16.7), MY −8.5 (19.7)

link

Thessaloniki

Slavs + CR1 + Mycenaeans

RB13

2 × 10⁻⁴

rejected

335,134

SP 49.7 (2.9), CR1 44.7 (12.4), MY 5.6 (14.7)

link

Athens

Slavs + CR2 + Mycenaeans

RB13

2 × 10⁻⁵

rejected

351,550

SP 35.9 (2.3), CR2 41.2 (9.7), MY 22.9 (11.4)

link

Thessaloniki

Slavs + CR2 + Mycenaeans

RB13

1 × 10⁻⁵

rejected

351,550

SP 43.7 (2.0), CR2 23.2 (8.8), MY 33.2 (10.2)

link

Athens

Slavs + CR3 + Mycenaeans

RB13

3 × 10⁻⁷

rejected

378,396

SP 35.3 (2.0), CR3 44.3 (11.5), MY 20.5 (12.7)

link

Thessaloniki

Slavs + CR3 + Mycenaeans

RB13

3 × 10⁻⁶

rejected

378,396

SP 43.9 (1.7), CR3 26.7 (8.1), MY 29.4 (9.0)

link

Athens

Slavs + CR4 + Mycenaeans

RB13

5 × 10⁻¹⁰

rejected

373,179

SP 33.4 (1.8), CR4 27.7 (6.7), MY 39.0 (7.8)

link

Thessaloniki

Slavs + CR4 + Mycenaeans

RB13

7 × 10⁻⁷

rejected

373,179

SP 43.2 (1.8), CR4 18.9 (5.3), MY 37.9 (6.3)

link

Athens

Slavs + CQ1

R10

0.002

rejected

401,070

SP 32.0 (2.8), CQ1 68.0 (2.8)

link

Thessaloniki

Slavs + CQ1

R10

5 × 10⁻⁶

rejected

401,070

SP 40.2 (2.7), CQ1 59.8 (2.7)

link

Athens

Slavs + CQ2

R10

0.033

rejected

402,776

SP 32.0 (3.0), CQ2 68.0 (3.0)

link

Thessaloniki

Slavs + CQ2

R10

0.013

rejected

402,776

SP 41.8 (2.9), CQ2 58.2 (2.9)

link

Athens

Slavs + CQ3

R10

0.199

fit

407,319

SP 34.0 (2.6), CQ3 66.0 (2.6)

link

Thessaloniki

Slavs + CQ3

R10

0.068

fit

407,319

SP 41.3 (2.6), CQ3 58.7 (2.6)

link

Athens

Slavs + CQ4

R10

< 1 × 10⁻¹⁶

rejected (infeasible)

424,998

SP 332.9 (43.4), CQ4 −232.9 (43.4)

link

Thessaloniki

Slavs + CQ4

R10

< 1 × 10⁻¹⁶

rejected (infeasible)

424,998

SP 281.3 (33.1), CQ4 −181.3 (33.1)

link

Athens

Slavs + CR1

R10

0.069

fit

363,488

SP 40.7 (2.3), CR1 59.3 (2.3)

link

Thessaloniki

Slavs + CR1

R10

0.034

rejected

363,488

SP 48.9 (2.2), CR1 51.1 (2.2)

link

Athens

Slavs + CR2

R10

3 × 10⁻⁴

rejected

380,371

SP 37.8 (2.7), CR2 62.2 (2.7)

link

Thessaloniki

Slavs + CR2

R10

3 × 10⁻⁶

rejected

380,371

SP 45.9 (2.5), CR2 54.1 (2.5)

link

Athens

Slavs + CR3

R10

0.003

rejected

405,549

SP 32.8 (2.7), CR3 67.2 (2.7)

link

Thessaloniki

Slavs + CR3

R10

1 × 10⁻⁵

rejected

405,549

SP 41.3 (2.7), CR3 58.7 (2.7)

link

Athens

Slavs + CR4

R10

4 × 10⁻⁷

rejected

400,500

SP 38.5 (2.4), CR4 61.5 (2.4)

link

Thessaloniki

Slavs + CR4

R10

1 × 10⁻⁹

rejected

400,500

SP 46.8 (2.4), CR4 53.2 (2.4)

link

Members of the pairs in Table 14. allSnps false.

V6: raw counts. With the raw counts of Turkey_N (68) and Crete (34) instead of 43 and 5, Slavs + Kaman + Mycenaeans is rejected for Athens (p = 0.037; Mycenaeans 17.5 %, SE 7.2) and fits for Thessaloniki (p = 0.155; Table 7). V6 therefore does not hold. The grid of block 1 was not repeated on raw counts.

Verdict on the Kaman fits

Verdict by the pre-declared rule: the Kaman three-source fits are INVALID. Two conditions of the rule are met: V1 is fragile for both targets and V6 does not hold (Athens). One such failure is decisive in the rule.

What this means. The fits Slavs + Old Hittite (Kaman) + Mycenaeans are not used as evidence for any statement about Greeks (the Mycenaean question, the claim that Old Hittite fits where Alalakh and Arslantepe do not). What it does not mean. It does not show the model to be false, and it does not show that Anatolian or Mycenaean ancestry is absent. The checks do not all point one way: V3 (Mycenaean source required), V4 (a second Kaman-site group fits) and V5 (no control pair passes) speak for the fit; V1 and V6 against it. The failures are narrow (p = 0.029 to 0.040), so the borderline calls are not stable under a small change of the data. Table 12 gives the results of the checks.

Table 12Results of the checks V1–V6

Check

Question

Athens (n=17)

Thessaloniki (n=14)

V1

remove one of the two persons

fragile: without MA2203 passes (p 0.348), without MA2200 rejected (p 0.040)

fragile: p 0.314 and 0.029

V2

drop one right or change the panel (14 variants)

mixed: not rejected in 11 of 14 (rejected: Ukraine_EIA_Scythian dropped, R10, R14)

stable: not rejected in 12 of 14 (rejected: R10, R14)

V3

is the Mycenaean source needed?

required: Slavs + Kaman without MY rejected in 12 of 14 variants, drop-source p 0.018

required: rejected in 14 of 14, drop-source p 0.006

V4

does another, independent Kaman-site group also fit?

corroborated: Iron Age Kaman (n=2) fits, p 0.173, but Mycenaeans 50.2 % (not 21 %)

corroborated: p 0.146, Mycenaeans 46.9 %

V5

do generic pairs of persons also pass?

discriminating: 0 of 8 control pairs pass

discriminating: 0 of 8

V6

raw instead of reduced counts of two right populations

does not hold: p 0.037

holds: p 0.155

K8

(descriptive) pairs passing without Mycenaeans on R10

2 of 8

1 of 8

Discussion

Which statements stand. Table 13 sets the statements that circulate against the evidence of this study. A statement is called supported only for the sources that were tested.

Table 13Statements and evidence

Statement

Evidence in this study

Status

A Slavic-type source is needed in every model

0 of 34 models without it fit; all strict fits contain it

supported (tested sources)

An Anatolian-type source is needed in every model

Slavs + Mycenaeans rejected on all four cells, p at most 3 × 10⁻¹¹

supported (tested sources)

A Mycenaean source is needed in every model

10 strict two-source fits without it (small groups; six turn infeasible with Mycenaeans). Needed only in the Kaman model, which is INVALID

not supported; absence of Aegean ancestry not shown

The Aegean share is well over 35 %

Passing models with a Kaman-site source: 5.3 to 50.2 % (12 models); Old Hittite fits 21.5 and 22.8 % (invalid); feasible three-source models 0.7 to 65 %

not identified

Old Hittite fits where Alalakh and Arslantepe do not

Alalakh and Arslantepe are rejected (p ≤ 4 × 10⁻⁵); the Old Hittite fit is INVALID

not used as evidence

Roman-era Anatolians + Slavs + Mycenaeans fit

0 of 18 cells per target (9 Roman-era groups, 2 panels); the six cells with p ≥ 0.05 are infeasible

not supported

The idea that the Kaman fits rest on one source. The objection that the fits come from one source of two persons is supported in the sense of fragility. The fit loses its better-covered person (V1), depends on two right counts (V6) and on the panel (V2). It is not supported in the sense that any two persons would fit (V5), and a second Kaman-site group can also produce a fit with another composition (V4). The Aegean share is not identified by these fits.

Limits

  • A qpAdm fit is the absence of rejection with the power of the data, not evidence of descent. The Slavic weight is the weight of a proxy; its specificity against other northern sources was not shown.

  • The posted models are replicated with proxies; tool, SNP set, individuals and right populations differ. M1–M4 use allSnps true, which distorts the models.

  • Several sources are small: Kaman (n=2), Aydın (n=1, 82,389 SNPs), Roman-era QW2 (n=2). Single persons and pairs have wide standard errors and pass more easily.

  • 191 plus 116 single models and 4 sensitivity analyses (about 310 analyses) were run without a correction for multiplicity. The decisive p-values lie close to 0.05 (0.029, 0.034, 0.037, 0.040, 0.047).

  • The control pairs come from pools rejected as whole groups, not from groups known to be unrelated to Greeks.

  • The grid was not repeated on raw counts; another Aegean source in place of the Mycenaeans was not tried; why the pair passes more easily than its member and which right population causes the panel dependence were not tested.

  • Any further control after this block is a new, post hoc block and would need its own pre-declaration.

Conclusions

  1. In these data, models need a Slavic-type and an Anatolian-type source to come near a fit; none of the tested models without either fits.

  2. A Mycenaean source is not needed in every model: 10 two-source models without it are strict fits, all with small groups. This does not show that Aegean ancestry is absent.

  3. Of the posted models, only the Old Hittite (Kaman) model fits (with other weights); the Roman-era, Alalakh and Arslantepe models are rejected.

  4. The Kaman three-source fits are INVALID by the pre-declared rule (fragile without one person; not holding on raw counts) and are not used as evidence about Greeks.

  5. The Mycenaean share is not identified: it depends on the source and on the panel.

Data and reproducibility. All models are stored as Nexju analyses; the appendices list every model with its p-value, weights and a link to its public result page. The pre-declared design and the results are in the Nexju project “nexju” of the author.

1.

Haak, W. et al. Massive migration from the steppe was a source for Indo-European languages in Europe. Nature 522, 207–211 (2015).

2.

Maier, R. et al. On the limits of fitting complex models of population history to f-statistics. eLife 12, e85492 (2023).

3.

Mallick, S. et al. The Allen Ancient DNA Resource (AADR): a curated compendium of ancient human genomes. Scientific Data 11, 182 (2024).

Appendix A: groups and codes

Table 14Groups used in the models

Code

Study name (n)

Nexju label / members

SP

Poland Early Medieval Slavs

Poland_EarlyMedieval_Slav

CZ

Czechia Early Medieval Early Slavs (n=3)

Czechia_EarlyMedieval_EarlySlav

MY

Mycenaeans (n=7)

Mycenaean_HQ7

KAM2

Old Hittite, Kaman (n=2)

Turkey_OldHittitePeriod

K00

Kaman person MA2200 (n=1)

Turkey_OldHittite_MA2200

K03

Kaman person MA2203 (n=1)

Turkey_OldHittite_MA2203

AC3

Kaman Assyrian Colony (n=3)

Turkey_Kaman_AssyrianColony3

KIA2

Kaman Iron Age (n=2)

Turkey_Kaman_IronAge2

KAL7

Kaman all periods (n=7)

Turkey_Kaman_Site7

OYL6

Oylum Höyük MBA (n=6)

Turkey_Oylum_MBA6

HAR3

Harmanoğlu–Göndürle EBA (n=3)

Turkey_Harmanoeren_EBA3

Q10

Turkey Roman-era (n=10)

Turkey_Roman_Q10

QI5

Turkey Roman-era QI5 (n=5)

Turkey_Roman_QI5

QL5

Turkey Roman-era QL5 (n=5)

Turkey_Roman_QL5

QP3

Turkey Roman-era QP3 (n=3)

Turkey_Roman_QP3

QB3

Turkey Roman-era QB3 (n=3)

Turkey_Roman_QB3

QW2

Turkey Roman-era QW2 (n=2)

Turkey_Roman_QW2

QS2

Turkey Roman-era QS2 (n=2)

Turkey_Roman_QS2

QPW5

Turkey Roman-era QPW5 (n=5)

Turkey_Roman_QPW5

O4

Turkey Imperial Roman (n=4)

Turkey_ImperialRoman

BE

Byzantine West Anatolia early (n=21)

Byz_West_Early

BL

Byzantine West Anatolia late (n=8)

Byz_West_Late

OTT5

Turkey Ottoman (n=5)

Turkey_OttomanPeriod

ALA5

Alalakh MLBA (n=5)

Turkey_MLBA_Alalakh5

ARS16

Arslantepe LC–EBA (n=16)

Turkey_LCEBA_Arslantepe16

WAB2

Yassitepe BA (n=2)

Turkey_Aegean_YassitepeBA2

AYD1

Aydın Bronze Age (n=1)

Turkey_Aegean_Aydin_BA

LAZ4

Lazarides LBA (n=4)

Greece_Lazarides_LBA

LAZ1

Lazarides EBA (n=1)

Greece_Lazarides_EBA

LEB

Lebanon MBA (n=6)

Lebanon_MBA

CQ1

control pair (n=2)

NEV020, I4530

CQ2

control pair (n=2)

BOG024, BOG020

CQ3

control pair (n=2)

I8372, I20001

CQ4

control pair (n=2)

I4529, I4531

CR1

control pair (n=2)

ART014, ART005

CR2

control pair (n=2)

ART019, ART026

CR3

control pair (n=2)

ART032, ART010

CR4

control pair (n=2)

ART027, ART022

Appendix B: the Kaman block (116 single models)

Class: KA = single Kaman person, KZ = raw counts, KS = other Kaman-site and Anatolian sources, KN = control pairs; 3 = with Mycenaeans, 2 = without. Target A Athens (n=17), T Thessaloniki (n=14). Weights in percent (SE). All allSnps false. The link opens the public result page of the model. Codes as in Table 14.

Table 15The Kaman block, models 1–58 of 116

Cl.

T

Panel

p

Result

SNPs

Weights % (SE)

Link

KA3

A

RB13

0.040

rejected

359,242

SP 32.1 (2.2), K00 47.7 (7.6), MY 20.2 (8.1)

link

KA3

T

RB13

0.029

rejected

359,242

SP 42.2 (2.0), K00 35.9 (7.6), MY 21.9 (8.0)

link

KA3

A

RB13

0.348

fit

114,164

SP 30.2 (2.9), K03 46.8 (8.3), MY 23.0 (8.6)

link

KA3

T

RB13

0.314

fit

114,164

SP 39.7 (2.7), K03 34.3 (8.5), MY 26.0 (8.7)

link

KA2

A

RB13

0.014

rejected

362,904

SP 33.7 (2.6), K00 66.3 (2.6)

link

KA2

T

RB13

0.007

rejected

362,904

SP 43.9 (2.5), K00 56.1 (2.5)

link

KA2

A

RB13

0.128

fit

115,179

SP 32.1 (3.8), K03 67.9 (3.8)

link

KA2

T

RB13

0.062

fit

115,179

SP 41.6 (3.6), K03 58.4 (3.6)

link

KZ3

A

RB13

0.037

rejected

371,818

SP 32.7 (2.0), KAM2 49.9 (6.8), MY 17.5 (7.2)

link

KZ3

T

RB13

0.155

fit

371,818

SP 42.5 (1.8), KAM2 34.3 (6.1), MY 23.2 (6.3)

link

KZ2

A

RB13

0.013

rejected

375,649

SP 34.0 (2.2), KAM2 66.0 (2.2)

link

KZ2

T

RB13

0.010

rejected

375,649

SP 44.0 (2.2), KAM2 56.0 (2.2)

link

KS3

A

R10

0.122

fit

318,702

SP 37.2 (2.6), AC3 57.5 (6.8), MY 5.3 (7.5)

link

KS3

A

RB13

0.014

rejected

303,961

SP 32.7 (1.8), AC3 42.4 (5.8), MY 24.9 (6.5)

link

KS3

T

R10

0.065

fit

318,702

SP 45.0 (2.4), AC3 43.8 (6.0), MY 11.2 (6.5)

link

KS3

T

RB13

0.037

rejected

303,961

SP 43.2 (1.8), AC3 32.7 (5.5), MY 24.0 (6.1)

link

KS3

A

R10

3 × 10⁻⁷

rejected (infeasible)

418,542

SP 40.2 (3.8), HAR3 94.4 (21.2), MY −34.6 (23.2)

link

KS3

A

RB13

4 × 10⁻⁹

rejected (infeasible)

395,104

SP 61.0 (25.0), HAR3 238.9 (201.7), MY −199.9 (225.8)

link

KS3

T

R10

7 × 10⁻⁹

rejected (infeasible)

418,542

SP 46.2 (3.4), HAR3 65.9 (26.3), MY −12.1 (28.3)

link

KS3

T

RB13

2 × 10⁻⁹

rejected (infeasible)

395,104

SP −0.7 (259.4), HAR3 −359.3 (2172.3), MY 460.0 (2431.3)

link

KS3

A

R10

0.064

fit

416,864

SP 29.7 (2.0), KAL7 53.0 (4.9), MY 17.2 (4.7)

link

KS3

A

RB13

0.052

fit

396,446

SP 28.6 (1.4), KAL7 41.7 (4.4), MY 29.7 (4.4)

link

KS3

T

R10

0.006

rejected

416,864

SP 39.3 (2.0), KAL7 39.6 (4.8), MY 21.1 (4.6)

link

KS3

T

RB13

0.024

rejected

396,446

SP 40.0 (1.5), KAL7 31.4 (4.4), MY 28.6 (4.6)

link

KS3

A

R10

0.033

rejected

203,370

SP 12.2 (4.1), KIA2 38.7 (5.0), MY 49.1 (3.4)

link

KS3

A

RB13

0.173

fit

194,713

SP 17.2 (2.8), KIA2 32.6 (5.1), MY 50.2 (3.6)

link

KS3

T

R10

0.084

fit

203,370

SP 27.8 (3.9), KIA2 28.4 (4.8), MY 43.8 (3.0)

link

KS3

T

RB13

0.146

fit

194,713

SP 33.2 (2.8), KIA2 19.9 (4.7), MY 46.9 (3.1)

link

KS3

A

R10

1 × 10⁻⁸

rejected

419,646

SP 37.1 (1.8), OYL6 39.8 (4.3), MY 23.1 (4.9)

link

KS3

A

RB13

1 × 10⁻⁵

rejected

398,364

SP 34.9 (1.5), OYL6 32.6 (4.1), MY 32.5 (5.0)

link

KS3

T

R10

1 × 10⁻⁶

rejected

419,646

SP 44.3 (1.8), OYL6 26.9 (3.6), MY 28.8 (4.1)

link

KS3

T

RB13

8 × 10⁻⁵

rejected

398,364

SP 44.2 (1.6), OYL6 22.6 (3.8), MY 33.2 (4.6)

link

KS2

A

R10

0.156

fit

320,567

SP 37.9 (2.5), AC3 62.1 (2.5)

link

KS2

A

RB13

6 × 10⁻⁴

rejected

307,060

SP 35.9 (2.0), AC3 64.1 (2.0)

link

KS2

T

R10

0.035

rejected

320,567

SP 46.4 (2.5), AC3 53.6 (2.5)

link

KS2

T

RB13

0.001

rejected

307,060

SP 46.5 (1.9), AC3 53.5 (1.9)

link

KS2

A

R10

9 × 10⁻⁹

rejected

420,614

SP 36.7 (2.3), HAR3 63.3 (2.3)

link

KS2

A

RB13

7 × 10⁻¹⁴

rejected

398,322

SP 38.4 (1.6), HAR3 61.6 (1.6)

link

KS2

T

R10

7 × 10⁻⁹

rejected

420,614

SP 45.2 (2.4), HAR3 54.8 (2.4)

link

KS2

T

RB13

5 × 10⁻¹¹

rejected

398,322

SP 48.7 (1.6), HAR3 51.3 (1.6)

link

KS2

A

R10

0.002

rejected

419,308

SP 30.5 (2.4), KAL7 69.5 (2.4)

link

KS2

A

RB13

2 × 10⁻⁷

rejected

400,484

SP 30.1 (1.8), KAL7 69.9 (1.8)

link

KS2

T

R10

2 × 10⁻⁶

rejected

419,308

SP 40.1 (2.4), KAL7 59.9 (2.4)

link

KS2

T

RB13

5 × 10⁻⁸

rejected

400,484

SP 42.0 (1.8), KAL7 58.0 (1.8)

link

KS2

A

R10

1 × 10⁻¹³

rejected (infeasible)

204,564

SP −16.8 (12.4), KIA2 116.8 (12.4)

link

KS2

A

RB13

8 × 10⁻¹⁰

rejected (infeasible)

196,653

SP −10.5 (8.2), KIA2 110.5 (8.2)

link

KS2

T

R10

8 × 10⁻¹⁵

rejected (infeasible)

204,564

SP −0.7 (11.4), KIA2 100.7 (11.4)

link

KS2

T

RB13

5 × 10⁻¹²

rejected

196,653

SP 4.5 (7.9), KIA2 95.5 (7.9)

link

KS2

A

R10

1 × 10⁻¹³

rejected

422,002

SP 41.5 (1.8), OYL6 58.5 (1.8)

link

KS2

A

RB13

6 × 10⁻¹⁴

rejected

402,224

SP 41.4 (1.2), OYL6 58.6 (1.2)

link

KS2

T

R10

< 1 × 10⁻¹⁶

rejected

422,002

SP 50.6 (1.9), OYL6 49.4 (1.9)

link

KS2

T

RB13

3 × 10⁻¹⁴

rejected

402,224

SP 50.8 (1.4), OYL6 49.2 (1.4)

link

KN3

A

R10

0.002

rejected

399,652

SP 31.8 (2.6), CQ1 60.8 (9.5), MY 7.4 (9.2)

link

KN3

A

RB13

8 × 10⁻⁵

rejected

373,765

SP 31.5 (1.7), CQ1 45.5 (8.8), MY 23.1 (9.1)

link

KN3

T

R10

1 × 10⁻⁵

rejected

399,652

SP 40.1 (2.2), CQ1 43.3 (11.2), MY 16.6 (10.6)

link

KN3

T

RB13

8 × 10⁻⁵

rejected

373,765

SP 41.4 (1.5), CQ1 29.9 (8.1), MY 28.7 (8.5)

link

KN3

A

R10

0.032

rejected (infeasible)

400,466

SP 32.3 (3.3), CQ2 72.6 (12.4), MY −4.9 (12.6)

link

KN3

A

RB13

0.020

rejected

380,744

SP 32.8 (2.3), CQ2 62.8 (12.0), MY 4.4 (12.7)

link

A Athens, T Thessaloniki. Classes as in the note above.

Table 16The Kaman block, models 59–116 of 116

Cl.

T

Panel

p

Result

SNPs

Weights % (SE)

Link

KN3

T

R10

0.017

rejected

400,466

SP 41.6 (2.8), CQ2 54.5 (11.4), MY 3.9 (11.4)

link

KN3

T

RB13

0.008

rejected

380,744

SP 43.0 (2.1), CQ2 45.1 (11.0), MY 11.9 (11.6)

link

KN3

A

R10

0.265

infeasible

405,779

SP 34.7 (3.1), CQ3 79.8 (12.0), MY −14.6 (12.2)

link

KN3

A

RB13

9 × 10⁻⁶

rejected

379,530

SP 34.9 (1.7), CQ3 34.7 (6.6), MY 30.4 (7.5)

link

KN3

T

R10

0.059

infeasible

405,779

SP 41.4 (2.7), CQ3 62.3 (11.6), MY −3.7 (11.5)

link

KN3

T

RB13

9 × 10⁻⁵

rejected

379,530

SP 43.3 (1.6), CQ3 23.4 (5.6), MY 33.3 (6.3)

link

KN3

A

R10

7 × 10⁻⁶

rejected (infeasible)

422,515

SP −25.2 (9.3), CQ4 47.9 (6.6), MY 77.3 (3.6)

link

KN3

A

RB13

1 × 10⁻¹⁵

rejected

401,630

SP 21.7 (3.5), CQ4 9.8 (3.2), MY 68.5 (1.7)

link

KN3

T

R10

4 × 10⁻⁵

rejected

422,515

SP 0.9 (8.4), CQ4 33.7 (5.9), MY 65.4 (3.2)

link

KN3

T

RB13

6 × 10⁻¹¹

rejected

401,630

SP 37.1 (3.4), CQ4 4.7 (3.1), MY 58.2 (1.7)

link

KN3

A

R10

0.170

infeasible

362,635

SP 44.5 (3.7), CR1 75.7 (12.4), MY −20.2 (14.4)

link

KN3

A

RB13

8 × 10⁻⁵

rejected (infeasible)

335,134

SP 42.7 (3.6), CR1 65.8 (16.7), MY −8.5 (19.7)

link

KN3

T

R10

0.042

rejected (infeasible)

362,635

SP 50.9 (3.2), CR1 59.5 (11.8), MY −10.3 (13.6)

link

KN3

T

RB13

2 × 10⁻⁴

rejected

335,134

SP 49.7 (2.9), CR1 44.7 (12.4), MY 5.6 (14.7)

link

KN3

A

R10

9 × 10⁻⁴

rejected

379,319

SP 36.1 (2.4), CR2 49.2 (6.8), MY 14.7 (7.4)

link

KN3

A

RB13

2 × 10⁻⁵

rejected

351,550

SP 35.9 (2.3), CR2 41.2 (9.7), MY 22.9 (11.4)

link

KN3

T

R10

8 × 10⁻⁵

rejected

379,319

SP 43.4 (2.2), CR2 35.9 (6.7), MY 20.6 (7.2)

link

KN3

T

RB13

1 × 10⁻⁵

rejected

351,550

SP 43.7 (2.0), CR2 23.2 (8.8), MY 33.2 (10.2)

link

KN3

A

R10

0.007

rejected

404,033

SP 32.0 (2.4), CR3 54.9 (7.5), MY 13.1 (7.5)

link

KN3

A

RB13

3 × 10⁻⁷

rejected

378,396

SP 35.3 (2.0), CR3 44.3 (11.5), MY 20.5 (12.7)

link

KN3

T

R10

2 × 10⁻⁴

rejected

404,033

SP 40.7 (2.2), CR3 41.5 (7.4), MY 17.8 (7.3)

link

KN3

T

RB13

3 × 10⁻⁶

rejected

378,396

SP 43.9 (1.7), CR3 26.7 (8.1), MY 29.4 (9.0)

link

KN3

A

R10

2 × 10⁻⁷

rejected

399,125

SP 37.2 (2.7), CR4 53.3 (8.9), MY 9.5 (10.1)

link

KN3

A

RB13

5 × 10⁻¹⁰

rejected

373,179

SP 33.4 (1.8), CR4 27.7 (6.7), MY 39.0 (7.8)

link

KN3

T

R10

4 × 10⁻⁸

rejected

399,125

SP 44.3 (2.1), CR4 31.8 (7.4), MY 23.9 (7.8)

link

KN3

T

RB13

7 × 10⁻⁷

rejected

373,179

SP 43.2 (1.8), CR4 18.9 (5.3), MY 37.9 (6.3)

link

KN2

A

R10

0.002

rejected

401,070

SP 32.0 (2.8), CQ1 68.0 (2.8)

link

KN2

A

RB13

6 × 10⁻⁶

rejected

375,948

SP 32.8 (2.1), CQ1 67.2 (2.1)

link

KN2

T

R10

5 × 10⁻⁶

rejected

401,070

SP 40.2 (2.7), CQ1 59.8 (2.7)

link

KN2

T

RB13

6 × 10⁻⁷

rejected

375,948

SP 43.0 (1.9), CQ1 57.0 (1.9)

link

KN2

A

R10

0.033

rejected

402,776

SP 32.0 (3.0), CQ2 68.0 (3.0)

link

KN2

A

RB13

0.041

rejected

384,556

SP 33.2 (2.2), CQ2 66.8 (2.2)

link

KN2

T

R10

0.013

rejected

402,776

SP 41.8 (2.9), CQ2 58.2 (2.9)

link

KN2

T

RB13

0.013

rejected

384,556

SP 44.0 (2.2), CQ2 56.0 (2.2)

link

KN2

A

R10

0.199

fit

407,319

SP 34.0 (2.6), CQ3 66.0 (2.6)

link

KN2

A

RB13

5 × 10⁻⁹

rejected

381,874

SP 39.0 (1.8), CQ3 61.0 (1.8)

link

KN2

T

R10

0.068

fit

407,319

SP 41.3 (2.6), CQ3 58.7 (2.6)

link

KN2

T

RB13

5 × 10⁻¹⁰

rejected

381,874

SP 47.7 (1.8), CQ3 52.3 (1.8)

link

KN2

A

R10

< 1 × 10⁻¹⁶

rejected (infeasible)

424,998

SP 332.9 (43.4), CQ4 −232.9 (43.4)

link

KN2

A

RB13

< 1 × 10⁻¹⁶

rejected (infeasible)

405,731

SP 1739.0 (1644.3), CQ4 −1639.0 (1644.3)

link

KN2

T

R10

< 1 × 10⁻¹⁶

rejected (infeasible)

424,998

SP 281.3 (33.1), CQ4 −181.3 (33.1)

link

KN2

T

RB13

< 1 × 10⁻¹⁶

rejected (infeasible)

405,731

SP 751.0 (325.9), CQ4 −651.0 (325.9)

link

KN2

A

R10

0.069

fit

363,488

SP 40.7 (2.3), CR1 59.3 (2.3)

link

KN2

A

RB13

1 × 10⁻⁴

rejected

336,417

SP 41.4 (1.7), CR1 58.6 (1.7)

link

KN2

T

R10

0.034

rejected

363,488

SP 48.9 (2.2), CR1 51.1 (2.2)

link

KN2

T

RB13

3 × 10⁻⁴

rejected

336,417

SP 50.7 (1.6), CR1 49.3 (1.6)

link

KN2

A

R10

3 × 10⁻⁴

rejected

380,371

SP 37.8 (2.7), CR2 62.2 (2.7)

link

KN2

A

RB13

5 × 10⁻⁶

rejected

353,158

SP 39.4 (1.8), CR2 60.6 (1.8)

link

KN2

T

R10

3 × 10⁻⁶

rejected

380,371

SP 45.9 (2.5), CR2 54.1 (2.5)

link

KN2

T

RB13

9 × 10⁻⁸

rejected

353,158

SP 48.7 (1.8), CR2 51.3 (1.8)

link

KN2

A

R10

0.003

rejected

405,549

SP 32.8 (2.7), CR3 67.2 (2.7)

link

KN2

A

RB13

1 × 10⁻⁸

rejected

380,748

SP 37.5 (1.8), CR3 62.5 (1.8)

link

KN2

T

R10

1 × 10⁻⁵

rejected

405,549

SP 41.3 (2.7), CR3 58.7 (2.7)

link

KN2

T

RB13

4 × 10⁻⁹

rejected

380,748

SP 47.4 (1.8), CR3 52.6 (1.8)

link

KN2

A

R10

4 × 10⁻⁷

rejected

400,500

SP 38.5 (2.4), CR4 61.5 (2.4)

link

KN2

A

RB13

5 × 10⁻¹⁴

rejected

375,269

SP 39.7 (1.7), CR4 60.3 (1.7)

link

KN2

T

R10

1 × 10⁻⁹

rejected

400,500

SP 46.8 (2.4), CR4 53.2 (2.4)

link

KN2

T

RB13

1 × 10⁻¹²

rejected

375,269

SP 49.8 (1.7), CR4 50.2 (1.7)

link

A Athens, T Thessaloniki. Classes as in the note above.

Appendix C: sensitivity analyses of the Kaman model

The right-panel variants are the 12 drop-one-right variants and the panels R10 and R14. Mycenaean weight (MY) in percent where the model has Mycenaeans. The four analyses are not single models and have no public link; each is identified by its analysis id. All allSnps false.

Table 17Slavs + Kaman + Mycenaeans, Modern Greeks (Athens, n=17)

No.

Variant

p

Result

SNPs

MY %

1

base panel RB13

0.128

not rejected

369,507

21.5

2

drop right: Russia_Samara_EBA_Yamnaya

0.094

not rejected

369,507

21.0

3

drop right: Serbia_IronGates_Mesolithic

0.235

not rejected

369,507

21.1

4

drop right: Russia_Karelia_Mesolithic

0.116

not rejected

373,836

21.3

5

drop right: Iran_GanjDareh_N

0.137

not rejected

369,885

18.6

6

drop right: Turkey_N

0.129

not rejected

369,507

23.0

7

drop right: Spain_IA_CeltIberian

0.099

not rejected

369,508

21.6

8

drop right: Greece_Crete_HgCharalambos_EMBA

0.089

not rejected

371,821

21.2

9

drop right: Croatia_MLBA

0.175

not rejected

371,572

15.9

10

drop right: Netherlands_MBA

0.140

not rejected

371,887

23.1

11

drop right: Ukraine_EIA_Scythian

0.034

rejected

401,493

18.7

12

drop right: Byz_SE_Early

0.090

not rejected

377,661

21.2

13

drop right: Estonia_LBA_StoneCistGraves

0.226

not rejected

385,574

16.8

14

panel R10

0.047

rejected

387,656

12.0

15

panel R14

0.001

rejected

386,921

13.3

16

drop source: Poland_EarlyMedieval_Slav

1 × 10⁻¹⁵

rejected (infeasible)

417,424

−241.8

17

drop source: Turkey_OldHittitePeriod

< 1 × 10⁻¹⁶

rejected

401,633

69.6

18

drop source: Mycenaean_HQ7

0.018

rejected

373,260

–

Analysis id 4582d8e2-b327-423f-a0cf-002e254e997f.

Table 18Slavs + Kaman + Mycenaeans, Modern Greeks (Thessaloniki, n=14)

No.

Variant

p

Result

SNPs

MY %

1

base panel RB13

0.083

not rejected

369,507

22.8

2

drop right: Russia_Samara_EBA_Yamnaya

0.056

not rejected

369,507

22.8

3

drop right: Serbia_IronGates_Mesolithic

0.232

not rejected

369,507

22.1

4

drop right: Russia_Karelia_Mesolithic

0.100

not rejected

373,836

23.3

5

drop right: Iran_GanjDareh_N

0.074

not rejected

369,885

20.2

6

drop right: Turkey_N

0.079

not rejected

369,507

24.6

7

drop right: Spain_IA_CeltIberian

0.070

not rejected

369,508

23.2

8

drop right: Greece_Crete_HgCharalambos_EMBA

0.153

not rejected

371,821

23.8

9

drop right: Croatia_MLBA

0.097

not rejected

371,572

18.6

10

drop right: Netherlands_MBA

0.236

not rejected

371,887

25.0

11

drop right: Ukraine_EIA_Scythian

0.066

not rejected

401,493

22.1

12

drop right: Byz_SE_Early

0.100

not rejected

377,661

21.6

13

drop right: Estonia_LBA_StoneCistGraves

0.096

not rejected

385,574

19.6

14

panel R10

0.003

rejected

387,656

14.2

15

panel R14

2 × 10⁻⁴

rejected

386,921

16.1

16

drop source: Poland_EarlyMedieval_Slav

1 × 10⁻¹⁶

rejected (infeasible)

417,424

−1,219.1

17

drop source: Turkey_OldHittitePeriod

3 × 10⁻¹¹

rejected

401,633

58.6

18

drop source: Mycenaean_HQ7

0.006

rejected

373,260

–

Analysis id 3da80129-486e-49f6-89aa-892930c2ab05.

Table 19Slavs + Kaman (no Mycenaean source), Modern Greeks (Athens, n=17)

No.

Variant

p

Result

SNPs

1

base panel RB13

0.018

rejected

373,260

2

drop right: Russia_Samara_EBA_Yamnaya

0.015

rejected

373,260

3

drop right: Serbia_IronGates_Mesolithic

0.039

rejected

373,260

4

drop right: Russia_Karelia_Mesolithic

0.017

rejected

378,399

5

drop right: Iran_GanjDareh_N

0.049

rejected

373,686

6

drop right: Turkey_N

0.012

rejected

373,260

7

drop right: Spain_IA_CeltIberian

0.012

rejected

373,261

8

drop right: Greece_Crete_HgCharalambos_EMBA

0.012

rejected

375,654

9

drop right: Croatia_MLBA

0.097

not rejected

375,844

10

drop right: Netherlands_MBA

0.011

rejected

376,176

11

drop right: Ukraine_EIA_Scythian

0.013

rejected

405,618

12

drop right: Byz_SE_Early

0.010

rejected

382,698

13

drop right: Estonia_LBA_StoneCistGraves

0.125

not rejected

389,532

14

panel R10

0.045

rejected

389,918

15

panel R14

0.001

rejected

389,046

16

drop source: Poland_EarlyMedieval_Slav

< 1 × 10⁻¹⁶

rejected

421,717

17

drop source: Turkey_OldHittitePeriod

< 1 × 10⁻¹⁶

rejected

405,734

Analysis id b2bf9833-ace4-4ae5-91f6-d6cc85c8893e.

Table 20Slavs + Kaman (no Mycenaean source), Modern Greeks (Thessaloniki, n=14)

No.

Variant

p

Result

SNPs

1

base panel RB13

0.006

rejected

373,260

2

drop right: Russia_Samara_EBA_Yamnaya

0.004

rejected

373,260

3

drop right: Serbia_IronGates_Mesolithic

0.026

rejected

373,260

4

drop right: Russia_Karelia_Mesolithic

0.007

rejected

378,399

5

drop right: Iran_GanjDareh_N

0.019

rejected

373,686

6

drop right: Turkey_N

0.003

rejected

373,260

7

drop right: Spain_IA_CeltIberian

0.004

rejected

373,261

8

drop right: Greece_Crete_HgCharalambos_EMBA

0.008

rejected

375,654

9

drop right: Croatia_MLBA

0.031

rejected

375,844

10

drop right: Netherlands_MBA

0.007

rejected

376,176

11

drop right: Ukraine_EIA_Scythian

0.009

rejected

405,618

12

drop right: Byz_SE_Early

0.007

rejected

382,698

13

drop right: Estonia_LBA_StoneCistGraves

0.031

rejected

389,532

14

panel R10

0.002

rejected

389,918

15

panel R14

6 × 10⁻⁵

rejected

389,046

16

drop source: Poland_EarlyMedieval_Slav

< 1 × 10⁻¹⁶

rejected

421,717

17

drop source: Turkey_OldHittitePeriod

< 1 × 10⁻¹⁶

rejected

405,734

Analysis id d3fcbc4d-d25b-4381-9610-5b4072ba4ffc.

Appendix D: all 191 models of block 1

Classes: TP1–TP4 posted models M1–M4 (allSnps true, marked †, Thessaloniki), CA1–CA3 Antoniou models, RZ replications on raw counts, G3 Slavs + X + Mycenaeans, G2 Slavs + X, G2b X + Mycenaeans, G2c Slavs + Mycenaeans. allSnps true (†) stretches the models and distorts p-values; all other models are allSnps false. Target A Athens (n=17), T Thessaloniki (n=14). Codes as in Table 14.

Table 21Block 1, models 1–48 of 191

Cl.

T

Panel

p

Result

SNPs

Weights % (SE)

Link

TP1

T

RB13

4 × 10⁻⁵ †

rejected (infeasible)

468,442

MY 73.0 (20.5), Q10 123.4 (58.3), SP 21.2 (9.8), OTT5 −117.6 (67.1)

link

TP2

T

RB13

2 × 10⁻⁵ †

rejected

468,442

MY 26.5 (5.0), ALA5 28.4 (4.3), SP 45.0 (1.5)

link

TP3

T

RB13

2 × 10⁻¹¹ †

rejected

468,442

MY 33.8 (6.3), ARS16 21.1 (5.1), SP 45.2 (1.8)

link

TP4

T

RB13

0.071†

fit

468,442

MY 19.4 (6.0), KAM2 39.0 (5.8), SP 41.6 (1.8)

link

CA1

T

RB13

0.653

imprecise

27,781

LAZ4 11.4 (480.9), LEB 4.6 (68.2), CZ 34.7 (82.9), AYD1 49.3 (630.2)

link

CA1

A

RB13

0.905

imprecise

27,781

LAZ4 24.2 (19.1), LEB 16.1 (9.7), CZ 27.1 (5.5), AYD1 32.6 (23.4)

link

CA2

T

RB13

0.959

imprecise

12,701

LAZ1 13.8 (8.9), LEB 28.5 (16.6), CZ 43.0 (8.9), AYD1 14.7 (26.6)

link

CA2

A

RB13

0.850

imprecise

12,701

LAZ1 16.2 (16.3), LEB 44.6 (30.7), CZ 37.4 (17.8), AYD1 1.8 (60.1)

link

CA3

T

RB13

0.838

infeasible

215,350

LAZ4 884.2 (5213.5), LEB −102.9 (745.4), CZ −49.9 (553.7), YAS2 −631.4 (3920.3)

link

CA3

A

RB13

0.845

infeasible

215,350

LAZ4 −573.6 (3621.8), LEB 110.7 (514.0), CZ 96.2 (385.4), YAS2 466.7 (2726.7)

link

RZ

T

RB13

0.748

imprecise

27,903

LAZ4 21.7 (33.3), LEB 9.2 (10.7), CZ 38.7 (6.5), AYD1 30.4 (38.7)

link

RZ

T

RB13

0.921

imprecise

12,736

LAZ1 12.9 (10.4), LEB 34.2 (19.3), CZ 46.8 (9.9), AYD1 6.1 (32.8)

link

RZ

T

RB13

0.696

infeasible

216,059

LAZ4 448.9 (1193.5), LEB −32.1 (144.7), CZ 0.0 (119.7), YAS2 −316.8 (935.7)

link

RZ

T

RB13

2 × 10⁻⁴ †

rejected (infeasible)

468,442

MY 69.9 (19.0), Q10 124.8 (55.6), SP 21.2 (9.5), OTT5 −115.9 (63.3)

link

RZ

T

RB13

4 × 10⁻⁵ †

rejected

468,442

MY 27.5 (4.6), ALA5 27.5 (4.0), SP 45.0 (1.5)

link

RZ

T

RB13

1 × 10⁻⁹ †

rejected

468,442

MY 30.2 (5.6), ARS16 23.7 (4.6), SP 46.1 (1.6)

link

RZ

T

RB13

0.056†

fit

468,442

MY 19.0 (6.1), KAM2 38.8 (5.9), SP 42.2 (1.8)

link

G3

T

R10

5 × 10⁻⁶

rejected

419,215

SP 43.9 (1.8), ALA5 31.0 (4.3), MY 25.1 (4.7)

link

G3

T

R10

4 × 10⁻⁹

rejected

422,450

SP 45.1 (1.8), ARS16 33.1 (5.3), MY 21.8 (5.8)

link

G3

T

R10

0.339

imprecise

31,573

SP 38.3 (9.7), AYD1 54.4 (29.5), MY 7.2 (23.8)

link

G3

T

R10

3 × 10⁻⁶

rejected

422,446

SP 34.2 (2.1), BE 61.7 (8.8), MY 4.1 (7.6)

link

G3

T

R10

2 × 10⁻⁷

rejected

419,083

SP 36.5 (2.3), BL 55.0 (10.2), MY 8.5 (9.1)

link

G3

T

R10

0.003

rejected

387,656

SP 40.8 (2.6), KAM2 45.0 (8.7), MY 14.2 (8.5)

link

G3

T

R10

0.497

infeasible

333,039

SP 36.7 (3.3), O4 72.3 (15.4), MY −9.0 (14.3)

link

G3

T

R10

8 × 10⁻⁶

rejected

418,180

SP 38.1 (2.0), OTT5 39.5 (5.4), MY 22.3 (4.9)

link

G3

T

R10

1 × 10⁻⁵

rejected

422,516

SP 29.1 (2.6), Q10 41.0 (4.9), MY 29.9 (3.5)

link

G3

T

R10

2 × 10⁻⁵

rejected

422,515

SP 8.9 (6.3), QB3 38.1 (6.0), MY 52.9 (2.2)

link

G3

T

R10

7 × 10⁻⁵

rejected

421,133

SP 39.4 (2.0), QI5 41.1 (5.9), MY 19.5 (5.6)

link

G3

T

R10

1 × 10⁻⁵

rejected

422,516

SP 20.4 (4.0), QL5 41.6 (5.6), MY 38.0 (2.9)

link

G3

T

R10

0.027

rejected

412,512

SP 40.1 (2.5), QP3 54.7 (9.5), MY 5.1 (9.1)

link

G3

T

R10

0.065

infeasible

421,738

SP 40.6 (2.2), QPW5 60.4 (8.4), MY −1.0 (8.2)

link

G3

T

R10

5 × 10⁻⁶

rejected

389,758

SP 39.2 (2.2), QS2 29.6 (5.4), MY 31.2 (5.0)

link

G3

T

R10

0.059

infeasible

405,779

SP 41.4 (2.7), QW2 62.3 (11.6), MY −3.7 (11.5)

link

G3

T

R10

0.001

rejected (infeasible)

299,546

SP −299.8 (36779.1), WAB2 −2041.5 (220016.6), MY 2441.3 (256794.0)

link

G3

T

RB13

4 × 10⁻⁵

rejected

397,369

SP 44.0 (1.6), ALA5 25.2 (4.6), MY 30.7 (5.3)

link

G3

T

RB13

3 × 10⁻⁹

rejected

401,507

SP 44.4 (1.9), ARS16 19.3 (5.7), MY 36.3 (7.0)

link

G3

T

RB13

0.859

imprecise

30,372

SP 27.5 (5.3), AYD1 59.3 (18.1), MY 13.2 (15.9)

link

G3

T

RB13

1 × 10⁻⁹

rejected

401,476

SP 39.7 (1.4), BE 35.1 (15.1), MY 25.2 (14.8)

link

G3

T

RB13

9 × 10⁻¹⁰

rejected

395,855

SP 41.2 (1.5), BL 24.7 (11.0), MY 34.2 (11.3)

link

G3

T

RB13

0.083

fit

369,507

SP 41.8 (1.8), KAM2 35.3 (6.2), MY 22.8 (6.5)

link

G3

T

RB13

0.004

rejected

306,512

SP 40.5 (2.1), O4 55.3 (20.5), MY 4.1 (20.6)

link

G3

T

RB13

7 × 10⁻⁹

rejected

394,423

SP 40.5 (1.5), OTT5 19.5 (6.8), MY 40.0 (7.0)

link

G3

T

RB13

4 × 10⁻⁸

rejected

401,633

SP 37.9 (1.7), Q10 19.8 (4.8), MY 42.2 (4.4)

link

G3

T

RB13

5 × 10⁻¹¹

rejected

401,631

SP 37.5 (3.2), QB3 6.0 (4.1), MY 56.5 (2.2)

link

G3

T

RB13

1 × 10⁻⁴

rejected

400,035

SP 41.9 (1.5), QI5 29.8 (5.4), MY 28.3 (5.9)

link

G3

T

RB13

2 × 10⁻⁹

rejected

401,633

SP 36.6 (2.2), QL5 13.8 (4.4), MY 49.6 (3.4)

link

G3

T

RB13

0.023

rejected

391,548

SP 42.5 (1.9), QP3 48.5 (10.3), MY 9.0 (10.8)

link

G3

T

RB13

0.005

rejected

400,574

SP 43.5 (1.6), QPW5 38.0 (6.4), MY 18.5 (6.9)

link

† allSnps true. It stretches the models and distorts p-values; these p-values are not comparable with allSnps false results.

Table 22Block 1, models 49–96 of 191

Cl.

T

Panel

p

Result

SNPs

Weights % (SE)

Link

G3

T

RB13

8 × 10⁻⁶

rejected

365,500

SP 41.5 (1.5), QS2 17.8 (4.3), MY 40.8 (4.8)

link

G3

T

RB13

9 × 10⁻⁵

rejected

379,530

SP 43.3 (1.6), QW2 23.4 (5.6), MY 33.3 (6.3)

link

G3

T

RB13

0.010

rejected (infeasible)

269,625

SP 20.6 (21.0), WAB2 −141.1 (140.1), MY 220.5 (160.5)

link

G3

A

R10

8 × 10⁻⁷

rejected

419,215

SP 36.8 (2.0), ALA5 46.0 (5.2), MY 17.2 (5.9)

link

G3

A

R10

5 × 10⁻¹¹

rejected

422,450

SP 38.7 (1.8), ARS16 50.5 (5.8), MY 10.8 (6.6)

link

G3

A

R10

0.547

imprecise

31,573

SP 29.1 (9.4), AYD1 65.6 (24.5), MY 5.3 (20.9)

link

G3

A

R10

2 × 10⁻⁴

rejected (infeasible)

422,446

SP 22.8 (1.9), BE 87.4 (7.8), MY −10.2 (7.0)

link

G3

A

R10

9 × 10⁻⁶

rejected (infeasible)

419,083

SP 25.1 (2.5), BL 82.5 (10.4), MY −7.6 (9.1)

link

G3

A

R10

0.047

rejected

387,656

SP 32.7 (2.7), KAM2 55.3 (8.1), MY 12.0 (8.1)

link

G3

A

R10

0.396

infeasible

333,039

SP 26.5 (4.1), O4 95.4 (19.0), MY −21.9 (17.5)

link

G3

A

R10

8 × 10⁻⁷

rejected

418,180

SP 28.4 (2.1), OTT5 56.1 (6.3), MY 15.5 (5.9)

link

G3

A

R10

3 × 10⁻⁶

rejected

422,516

SP 14.4 (2.7), Q10 59.8 (5.2), MY 25.8 (3.7)

link

G3

A

R10

1 × 10⁻⁵

rejected (infeasible)

422,515

SP −15.1 (6.7), QB3 55.5 (6.3), MY 59.7 (2.5)

link

G3

A

R10

3 × 10⁻⁴

rejected

421,133

SP 29.0 (2.2), QI5 58.6 (6.4), MY 12.3 (6.1)

link

G3

A

R10

3 × 10⁻⁶

rejected

422,516

SP 1.7 (4.3), QL5 61.6 (6.3), MY 36.7 (3.2)

link

G3

A

R10

0.039

rejected (infeasible)

412,512

SP 30.2 (2.8), QP3 73.6 (10.5), MY −3.8 (10.3)

link

G3

A

R10

0.217

infeasible

421,738

SP 32.0 (2.4), QPW5 79.7 (8.8), MY −11.7 (8.8)

link

G3

A

R10

8 × 10⁻⁵

rejected

389,758

SP 29.6 (2.4), QS2 44.0 (5.8), MY 26.4 (5.4)

link

G3

A

R10

0.265

infeasible

405,779

SP 34.7 (3.1), QW2 79.8 (12.0), MY −14.6 (12.2)

link

G3

A

R10

0.003

rejected (infeasible)

299,546

SP 79.4 (41.3), WAB2 275.7 (235.4), MY −255.1 (275.2)

link

G3

A

RB13

9 × 10⁻⁶

rejected

397,369

SP 34.9 (1.6), ALA5 36.3 (5.4), MY 28.8 (6.3)

link

G3

A

RB13

2 × 10⁻¹³

rejected

401,507

SP 35.4 (1.9), ARS16 28.3 (6.2), MY 36.2 (7.6)

link

G3

A

RB13

0.714

imprecise

30,372

SP 19.0 (6.4), AYD1 70.6 (21.8), MY 10.3 (18.6)

link

G3

A

RB13

3 × 10⁻¹²

rejected (infeasible)

401,476

SP 27.7 (1.6), BE 82.6 (24.5), MY −10.3 (23.5)

link

G3

A

RB13

3 × 10⁻¹⁴

rejected

395,855

SP 30.1 (1.4), BL 46.6 (26.4), MY 23.4 (26.2)

link

G3

A

RB13

0.128

fit

369,507

SP 31.3 (1.9), KAM2 47.2 (6.3), MY 21.5 (6.7)

link

G3

A

RB13

0.008

rejected (infeasible)

306,512

SP 29.6 (2.9), O4 88.9 (25.1), MY −18.5 (25.4)

link

G3

A

RB13

1 × 10⁻¹³

rejected

394,423

SP 29.8 (1.4), OTT5 28.4 (9.0), MY 41.7 (9.2)

link

G3

A

RB13

7 × 10⁻¹¹

rejected

401,633

SP 26.0 (1.5), Q10 28.8 (4.8), MY 45.1 (4.4)

link

G3

A

RB13

7 × 10⁻¹⁶

rejected

401,631

SP 22.6 (3.3), QB3 12.4 (4.3), MY 65.0 (2.2)

link

G3

A

RB13

3 × 10⁻⁵

rejected

400,035

SP 31.8 (1.4), QI5 42.7 (6.1), MY 25.5 (6.4)

link

G3

A

RB13

1 × 10⁻¹²

rejected

401,633

SP 23.4 (2.1), QL5 22.1 (4.6), MY 54.5 (3.5)

link

G3

A

RB13

0.031

rejected

391,548

SP 32.2 (2.0), QP3 67.1 (11.5), MY 0.7 (12.0)

link

G3

A

RB13

0.024

rejected

400,574

SP 34.3 (1.4), QPW5 53.6 (6.5), MY 12.1 (6.9)

link

G3

A

RB13

4 × 10⁻⁶

rejected

365,500

SP 31.4 (1.5), QS2 26.7 (4.2), MY 41.8 (4.7)

link

G3

A

RB13

9 × 10⁻⁶

rejected

379,530

SP 34.9 (1.7), QW2 34.7 (6.6), MY 30.4 (7.5)

link

G3

A

RB13

0.004

rejected (infeasible)

269,625

SP −94.5 (392.0), WAB2 −852.4 (2663.2), MY 1047.0 (3054.3)

link

G2

T

R10

2 × 10⁻¹¹

rejected

421,441

SP 48.4 (2.0), ALA5 51.6 (2.0)

link

G2

T

R10

3 × 10⁻¹³

rejected

424,908

SP 48.4 (1.7), ARS16 51.6 (1.7)

link

G2

T

R10

0.448

fit

31,719

SP 35.9 (10.0), AYD1 64.1 (10.0)

link

G2

T

R10

4 × 10⁻⁶

rejected

424,898

SP 33.9 (1.9), BE 66.1 (1.9)

link

G2

T

R10

1 × 10⁻⁷

rejected

421,222

SP 35.7 (2.2), BL 64.3 (2.2)

link

G2

T

R10

0.002

rejected

389,918

SP 41.2 (3.0), KAM2 58.8 (3.0)

link

G2

T

R10

0.522

fit

333,884

SP 36.7 (2.9), O4 63.3 (2.9)

link

G2

T

R10

1 × 10⁻⁹

rejected

420,222

SP 38.5 (2.4), OTT5 61.5 (2.4)

link

G2

T

R10

< 1 × 10⁻¹⁶

rejected

424,999

SP 21.6 (3.6), Q10 78.4 (3.6)

link

G2

T

R10

< 1 × 10⁻¹⁶

rejected (infeasible)

424,998

SP −639.9 (427.1), QB3 739.9 (427.1)

link

G2

T

R10

4 × 10⁻⁷

rejected

423,551

SP 39.9 (2.4), QI5 60.1 (2.4)

link

Table 23Block 1, models 97–144 of 191

Cl.

T

Panel

p

Result

SNPs

Weights % (SE)

Link

G2

T

R10

< 1 × 10⁻¹⁶

rejected (infeasible)

424,999

SP −18.8 (8.7), QL5 118.8 (8.7)

link

G2

T

R10

0.019

rejected

414,857

SP 40.1 (2.7), QP3 59.9 (2.7)

link

G2

T

R10

0.060

fit

424,172

SP 40.6 (2.2), QPW5 59.4 (2.2)

link

G2

T

R10

5 × 10⁻¹¹

rejected

391,144

SP 39.2 (3.3), QS2 60.8 (3.3)

link

G2

T

R10

0.068

fit

407,319

SP 41.3 (2.6), QW2 58.7 (2.6)

link

G2

T

R10

3 × 10⁻⁸

rejected

300,024

SP 50.6 (2.4), WAB2 49.4 (2.4)

link

G2

T

RB13

9 × 10⁻¹²

rejected

400,986

SP 49.4 (1.6), ALA5 50.6 (1.6)

link

G2

T

RB13

< 1 × 10⁻¹⁶

rejected

405,542

SP 51.9 (1.2), ARS16 48.1 (1.2)

link

G2

T

RB13

0.864

fit

30,599

SP 26.1 (6.1), AYD1 73.9 (6.1)

link

G2

T

RB13

3 × 10⁻¹¹

rejected

405,491

SP 39.2 (1.4), BE 60.8 (1.4)

link

G2

T

RB13

3 × 10⁻¹³

rejected

399,227

SP 41.9 (1.7), BL 58.1 (1.7)

link

G2

T

RB13

0.006

rejected

373,260

SP 43.4 (2.3), KAM2 56.6 (2.3)

link

G2

T

RB13

0.005

rejected

307,737

SP 40.5 (2.2), O4 59.5 (2.2)

link

G2

T

RB13

< 1 × 10⁻¹⁶

rejected

397,595

SP 42.6 (1.7), OTT5 57.4 (1.7)

link

G2

T

RB13

< 1 × 10⁻¹⁶

rejected

405,734

SP 36.3 (1.9), Q10 63.7 (1.9)

link

G2

T

RB13

< 1 × 10⁻¹⁶

rejected (infeasible)

405,732

SP −165.5 (48.1), QB3 265.5 (48.1)

link

G2

T

RB13

3 × 10⁻⁸

rejected

404,011

SP 44.5 (1.7), QI5 55.5 (1.7)

link

G2

T

RB13

< 1 × 10⁻¹⁶

rejected

405,734

SP 21.4 (4.1), QL5 78.6 (4.1)

link

G2

T

RB13

0.036

rejected

395,400

SP 43.2 (2.0), QP3 56.8 (2.0)

link

G2

T

RB13

6 × 10⁻⁴

rejected

404,563

SP 45.4 (1.6), QPW5 54.6 (1.6)

link

G2

T

RB13

< 1 × 10⁻¹⁶

rejected

367,671

SP 45.2 (2.1), QS2 54.8 (2.1)

link

G2

T

RB13

5 × 10⁻¹⁰

rejected

381,874

SP 47.7 (1.8), QW2 52.3 (1.8)

link

G2

T

RB13

1 × 10⁻⁷

rejected

270,218

SP 48.8 (1.7), WAB2 51.2 (1.7)

link

G2

A

R10

2 × 10⁻⁸

rejected

421,441

SP 40.0 (1.9), ALA5 60.0 (1.9)

link

G2

A

R10

8 × 10⁻¹²

rejected

424,908

SP 40.4 (1.5), ARS16 59.6 (1.5)

link

G2

A

R10

0.625

imprecise

31,719

SP 27.2 (10.2), AYD1 72.8 (10.2)

link

G2

A

R10

1 × 10⁻⁴

rejected

424,898

SP 23.9 (1.7), BE 76.1 (1.7)

link

G2

A

R10

6 × 10⁻⁶

rejected

421,222

SP 25.6 (2.2), BL 74.4 (2.2)

link

G2

A

R10

0.045

rejected

389,918

SP 33.2 (3.1), KAM2 66.8 (3.1)

link

G2

A

R10

0.254

fit

333,884

SP 27.0 (3.1), O4 73.0 (3.1)

link

G2

A

R10

5 × 10⁻⁸

rejected

420,222

SP 28.5 (2.4), OTT5 71.5 (2.4)

link

G2

A

R10

2 × 10⁻¹⁴

rejected

424,999

SP 7.3 (3.2), Q10 92.7 (3.2)

link

G2

A

R10

< 1 × 10⁻¹⁶

rejected (infeasible)

424,998

SP −543.5 (265.9), QB3 643.5 (265.9)

link

G2

A

R10

6 × 10⁻⁵

rejected

423,551

SP 29.4 (2.4), QI5 70.6 (2.4)

link

G2

A

R10

< 1 × 10⁻¹⁶

rejected (infeasible)

424,999

SP −31.9 (8.3), QL5 131.9 (8.3)

link

G2

A

R10

0.045

rejected

414,857

SP 29.9 (2.7), QP3 70.1 (2.7)

link

G2

A

R10

0.138

fit

424,172

SP 31.4 (2.2), QPW5 68.6 (2.2)

link

G2

A

R10

1 × 10⁻⁷

rejected

391,144

SP 29.8 (3.4), QS2 70.2 (3.4)

link

G2

A

R10

0.199

fit

407,319

SP 34.0 (2.6), QW2 66.0 (2.6)

link

G2

A

R10

4 × 10⁻⁹

rejected

300,024

SP 41.4 (2.5), WAB2 58.6 (2.5)

link

G2

A

RB13

3 × 10⁻¹⁰

rejected

400,986

SP 39.6 (1.5), ALA5 60.4 (1.5)

link

G2

A

RB13

< 1 × 10⁻¹⁶

rejected

405,542

SP 42.4 (1.1), ARS16 57.6 (1.1)

link

G2

A

RB13

0.809

fit

30,599

SP 17.8 (6.9), AYD1 82.2 (6.9)

link

G2

A

RB13

2 × 10⁻¹²

rejected

405,491

SP 28.0 (1.2), BE 72.0 (1.2)

link

G2

A

RB13

1 × 10⁻¹³

rejected

399,227

SP 29.2 (1.7), BL 70.8 (1.7)

link

G2

A

RB13

0.018

rejected

373,260

SP 33.0 (2.4), KAM2 67.0 (2.4)

link

G2

A

RB13

0.006

rejected

307,737

SP 29.1 (2.3), O4 70.9 (2.3)

link

G2

A

RB13

< 1 × 10⁻¹⁶

rejected

397,595

SP 31.0 (1.8), OTT5 69.0 (1.8)

link

Table 24Block 1, models 145–191 of 191

Cl.

T

Panel

p

Result

SNPs

Weights % (SE)

Link

G2

A

RB13

< 1 × 10⁻¹⁶

rejected

405,734

SP 21.3 (1.9), Q10 78.7 (1.9)

link

G2

A

RB13

< 1 × 10⁻¹⁶

rejected (infeasible)

405,732

SP −164.9 (34.0), QB3 264.9 (34.0)

link

G2

A

RB13

7 × 10⁻⁸

rejected

404,011

SP 33.8 (1.6), QI5 66.2 (1.6)

link

G2

A

RB13

< 1 × 10⁻¹⁶

rejected (infeasible)

405,734

SP −0.7 (4.0), QL5 100.7 (4.0)

link

G2

A

RB13

0.057

fit

395,400

SP 32.4 (1.9), QP3 67.6 (1.9)

link

G2

A

RB13

0.018

rejected

404,563

SP 35.5 (1.5), QPW5 64.5 (1.5)

link

G2

A

RB13

1 × 10⁻¹⁶

rejected

367,671

SP 34.9 (2.2), QS2 65.1 (2.2)

link

G2

A

RB13

5 × 10⁻⁹

rejected

381,874

SP 39.0 (1.8), QW2 61.0 (1.8)

link

G2

A

RB13

2 × 10⁻⁹

rejected

270,218

SP 39.0 (1.7), WAB2 61.0 (1.7)

link

G2b

T

R10

< 1 × 10⁻¹⁶

rejected (infeasible)

475,229

ALA5 −663.7 (794.8), MY 763.7 (794.8)

link

G2b

T

R10

< 1 × 10⁻¹⁶

rejected (infeasible)

478,950

ARS16 −194.3 (58.1), MY 294.3 (58.1)

link

G2b

T

R10

0.058

infeasible

35,365

AYD1 206.5 (102.0), MY −106.5 (102.0)

link

G2b

T

R10

< 1 × 10⁻¹⁶

rejected (infeasible)

478,950

BE 297.5 (59.3), MY −197.5 (59.3)

link

G2b

T

R10

< 1 × 10⁻¹⁶

rejected (infeasible)

475,132

BL 255.6 (43.9), MY −155.6 (43.9)

link

G2b

T

R10

4 × 10⁻¹²

rejected (infeasible)

438,833

KAM2 421.9 (218.8), MY −321.9 (218.8)

link

G2b

T

R10

1 × 10⁻⁵

rejected (infeasible)

377,375

O4 268.7 (64.2), MY −168.7 (64.2)

link

G2b

T

R10

< 1 × 10⁻¹⁶

rejected (infeasible)

474,161

OTT5 242.0 (69.7), MY −142.0 (69.7)

link

G2b

T

R10

< 1 × 10⁻¹⁶

rejected

479,024

Q10 84.7 (6.2), MY 15.3 (6.2)

link

G2b

T

R10

2 × 10⁻⁵

rejected

479,022

QB3 45.6 (2.2), MY 54.4 (2.2)

link

G2b

T

R10

< 1 × 10⁻¹⁶

rejected (infeasible)

477,413

QI5 304.6 (110.0), MY −204.6 (110.0)

link

G2b

T

R10

5 × 10⁻¹⁰

rejected

479,024

QL5 66.3 (3.3), MY 33.7 (3.3)

link

G2b

T

R10

3 × 10⁻¹²

rejected (infeasible)

467,493

QP3 340.1 (112.2), MY −240.1 (112.2)

link

G2b

T

R10

1 × 10⁻¹⁶

rejected (infeasible)

478,118

QPW5 431.7 (168.6), MY −331.7 (168.6)

link

G2b

T

R10

< 1 × 10⁻¹⁶

rejected (infeasible)

441,519

QS2 205.3 (58.8), MY −105.3 (58.8)

link

G2b

T

R10

1 × 10⁻⁹

rejected (infeasible)

459,965

QW2 433.5 (189.2), MY −333.5 (189.2)

link

G2b

T

R10

0.001

rejected (infeasible)

339,820

WAB2 −299.8 (96.6), MY 399.8 (96.6)

link

G2b

A

R10

< 1 × 10⁻¹⁶

rejected (infeasible)

475,229

ALA5 423.5 (276.2), MY −323.5 (276.2)

link

G2b

A

R10

< 1 × 10⁻¹⁶

rejected (infeasible)

478,950

ARS16 −217.6 (113.1), MY 317.6 (113.1)

link

G2b

A

R10

0.141

infeasible

35,365

AYD1 148.2 (58.1), MY −48.2 (58.1)

link

G2b

A

R10

< 1 × 10⁻¹⁶

rejected (infeasible)

478,950

BE 182.3 (20.5), MY −82.3 (20.5)

link

G2b

A

R10

9 × 10⁻¹⁴

rejected (infeasible)

475,132

BL 177.3 (19.7), MY −77.3 (19.7)

link

G2b

A

R10

2 × 10⁻¹⁰

rejected (infeasible)

438,833

KAM2 230.0 (71.8), MY −130.0 (71.8)

link

G2b

A

R10

4 × 10⁻⁴

rejected (infeasible)

377,375

O4 198.5 (39.4), MY −98.5 (39.4)

link

G2b

A

R10

< 1 × 10⁻¹⁶

rejected (infeasible)

474,161

OTT5 149.5 (24.1), MY −49.5 (24.1)

link

G2b

A

R10

3 × 10⁻¹²

rejected

479,024

Q10 79.6 (4.2), MY 20.4 (4.2)

link

G2b

A

R10

2 × 10⁻⁷

rejected

479,022

QB3 42.5 (2.1), MY 57.5 (2.1)

link

G2b

A

R10

< 1 × 10⁻¹⁶

rejected (infeasible)

477,413

QI5 158.1 (32.6), MY −58.1 (32.6)

link

G2b

A

R10

5 × 10⁻⁶

rejected

479,024

QL5 63.2 (3.0), MY 36.8 (3.0)

link

G2b

A

R10

6 × 10⁻¹⁰

rejected (infeasible)

467,493

QP3 217.1 (48.7), MY −117.1 (48.7)

link

G2b

A

R10

9 × 10⁻¹⁴

rejected (infeasible)

478,118

QPW5 249.1 (53.9), MY −149.1 (53.9)

link

G2b

A

R10

< 1 × 10⁻¹⁶

rejected (infeasible)

441,519

QS2 121.7 (24.3), MY −21.7 (24.3)

link

G2b

A

R10

5 × 10⁻⁸

rejected (infeasible)

459,965

QW2 268.9 (71.8), MY −168.9 (71.8)

link

G2b

A

R10

2 × 10⁻⁴

rejected (infeasible)

339,820

WAB2 −329.5 (139.7), MY 429.5 (139.7)

link

G2c

T

R10

< 1 × 10⁻¹⁶

rejected

422,516

SP 44.4 (2.2), MY 55.6 (2.2)

link

G2c

T

RB13

3 × 10⁻¹¹

rejected

401,633

SP 41.4 (1.7), MY 58.6 (1.7)

link

G2c

A

R10

< 1 × 10⁻¹⁶

rejected

422,516

SP 36.1 (2.4), MY 63.9 (2.4)

link

G2c

A

RB13

< 1 × 10⁻¹⁶

rejected

401,633

SP 30.4 (1.7), MY 69.6 (1.7)

link

Magnus Albertus Papers · @AlbertusMvagnus · 2026

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