Ancient human genome-wide data from a 3000-year interval in the Caucasus corresponds with eco-geographic regions

Archaeogenetic studies have described the formation of Eurasian ‘steppe ancestry’ as a mixture of Eastern and Caucasus hunter-gatherers. However, it remains unclear when and where this ancestry arose and whether it was related to a horizon of cultural innovations in the 4th millennium BCE that subsequently facilitated the advance of pastoral societies in Eurasia. Here we generated genome-wide SNP data from 45 prehistoric individuals along a 3000-year temporal transect in the North Caucasus. We observe a genetic separation between the groups of the Caucasus and those of the adjacent steppe. The northern Caucasus groups are genetically similar to contemporaneous populations south of it, suggesting human movement across the mountain range during the Bronze Age. The steppe groups from Yamnaya and subsequent pastoralist cultures show evidence for previously undetected farmer-related ancestry from different contact zones, while Steppe Maykop individuals harbour additional Upper Palaeolithic Siberian and Native American related ancestry.


Supplementary Note 1 Ecological and archaeological background of the Caucasus region
Ecological background The mountain ranges of the Greater Caucasus and the southern Lesser Caucasus form a bridge linking the mountainous zones of the Near East to Eurasia. The South Caucasus river systems are connected to the upper Euphrates and Tigris drainage, and the mountain passes of the Great Caucasus offer a number of passages to the steppe landscapes to the north. However, the most important ecological demarcation is the interface of mountain and steppe ecozones in the North Caucasian foothills, a mid-altitude zone of hills and narrow plateaus and the slightly hilly piedmont steppe 3 . Intermediate biospheres, known as ecotones, which are micro-environmental patches between larger vegetation zones, are characterized by higher biodiversity and provide fodder-rich landscapes ideal for pastoralism but also for basic agriculture 4 . This demarcation and the correlated ecotones fluctuated considerably during the Bronze Age. For instance, the 6 to 5 ky rapid climate change event placed Maykop sites in a much more steppe-like environment than it is today, while the 4.2 ky event put a halt to the exploitation of the steppe zone for several hundred years due to severe aridisation 5 . The ecological division separates mountain-and steppe-based economies despite the fact that both used biologically highly diverse environments with rich pastures ideal for mobile and semi-sedentary pastoralists, but which are traditionally shared by groups practising such economies. At a local level, the Caucasus is therefore characterized by a large variety of specific economic and social adaptations. These are reflected in a large degree of cultural and linguistic diversity, and complex networks of interaction within and between the Caucasus and the adjacent regions.

Archaeological background
The geographical dichotomy of the mountain and steppe-based economies in the Caucasus is also reflected in the high diversity of archaeological cultural phenomena 6,7,8 . Our study includes representatives of all major Bronze Age groups in the North Caucasus. They reflect affiliations with either mountain-associated cultural groups such as the Darkveti-Meshoko Eneolithic (4700-3500 calBCE) 9 , the Maykop phenomenon (3900-2900 calBCE) 7 , communities of a Northern variant of the Kura-Araxes culture (3600-2500 calBCE) 10 , the North Caucasian cultural formation or the mountain groups of the post-Catacomb grave horizon 11 , or to large-scale cultural phenomena of the steppe such as the Don-Kaspi Steppe Eneolithic (4300-4100 calBCE) 12 , the Yamnaya (3300-2600/2500 calBCE), the Catacomb cultural communities (2800-2200 calBCE) 5 and the post-Catacomb Lola formation (2200-1700 calBCE) 13 . To represent the South Caucasus Kura-Araxes culture 6 (3600-2500 calBCE), we also included individuals from the Kaps site in present-day Armenia. Each of these formations is outlined by particular sets of artefacts, settlement and burial practices, or adaptations to specific environments. However, the chronological overlap of sites within the same territory, regional variations in artefact spectra and a high frequency of elements crossing over blur the delineation of clear cut 'archaeological cultures'. Consequently, the applied terms must in their specific time frames be understood as operational tools rather than social entities that represent uniform and coherent peoples.  12 , but they are related to a much larger supra-regional network linking elites of the steppe zone between the Balkans and the Caspian Sea 18 . These groups introduced the so-called kurgan, a specific type of burial monument, which soon spread across the entire steppe zone. The Maykop 'culture' or cultural formation is the first Early Bronze Age culture in the Caucasus. This enigmatic phenomenon exhibits the first gigantic burial mounds with splendid 'royal' tombs 6,7 containing exquisite burial gifts in gold, silver and bronze that reveal an entire spectrum of technological innovations in metallurgy (among others). Maykop plays a key role in the transfer of technological innovations and social alterations to the West. An increase in sites, the expansion of territories, the enlargement of burial mounds as well as large groupings of mounds in cemeteries indicate a prospering culture and population growth. The economy seems to have been based on an agro-pastoral to pastoral subsistence with a focus on cattle herding, but detailed economic data are largely missing. Judging by the artefact spectrum, the early phase of this phenomenon appears closely linked to northern Mesopotamia 19 . A specific component of the Maykop phenomenon is found in sites located in the modern steppe zone. We refer to them here as Steppe Maykop (cf. 5 ). These burials share elements of mortuary practices and artefacts with piedmont Maykop groups but at the same time reveal Eneolithic and autonomous components from the steppe. Both Maykop-related phenomena develop in parallel. The Maykop individuals in the present study come from a variety of sites related to both Steppe and piedmont and date to an earlier (3900-3500 calBCE) and later chronological phase (3500-2900 calBCE), respectively. A more detailed chronology can be found in the cited literature. Some sites in the steppe-zone might be affected by a radiocarbon reservoir effect 20 5 . Yamnaya interments of the South Russian and North Caucasus plain share specific burial practices with other regional variants of this far-reaching supra-regional cultural network. They differ however in the quantity of burial goods they use. Complete or dismantled wooden wagons are frequently found in Yamnaya and related graves. Like those from the Volga region, the North Caucasian steppe complexes belong to the earliest representatives of the Yamnaya phenomenon in the Eurasian steppe. Stable isotope and palynological evidence argue for a mobile lifestyle based on pastoralism for these groups, but with rather limited mobility radii. The Velikent site at the coast of the Caspian Sea is a representative for a northern variant of the Kura-Araxes culture, although it is considerably different from the primary variant, which warrants its own Early Bronze Age designation (3300-2400/2200 calBCE). The site is over 30 ha in size and is comprised of several settlement and cemetery mounds 10,23 . Velikent and related sites are important for this study as they represent comprehensive agro-pastoral economies. The Caucasian Middle Bronze Age is represented by the Catacomb grave formation (2800-2200 calBCE) mostly found in the steppe and by the North Caucasian cultural groups (2800-2400 calBCE) and Catacomb culture in the piedmont zone. Both represent economies that were based on mobile pastoralism. The first is one of several variants of the supra-regional Catacomb grave phenomenon, which split into even smaller regional components in the North Caucasus and the Caspian steppe. With the Catacomb horizon, the number of mounds and burials increases exponentially in the steppe. The North Caucasian formation in the piedmont and mountain zone likewise witness a fragmentation into smaller regional units with a rather heterogeneous artefact spectrum. However, the occupation of all ecological niches including the various steppe zones as well as the high mountains indicates, like in the Catacomb area, a considerable intensification of human activity. In particular, the mountain groups must have intensified mining as well, since burials dating to this period frequently contain metal artefacts, e.g. the complex of Lysogorskaya 6 in this study. After 2400 calBCE, Catacomb complexes first overlap with those of the North Caucasian groups and then seem to replace them. The climatic deterioration of the 4.2 ky event led to a dissolution of both the Catacomb and the North Caucasian cultural formations, replacing them in the steppe and piedmont steppe by cultures of the post-Catacomb horizon or Late Bronze Age 1 (2200-1700 calBCE) 13 . The number of sites decreases rapidly. By 1700 calBCE the steppe including the zones directly at the foothills of the mountains are abandoned. Interments like those of Rasshevatskiy 4 and Nevinnomyskiy represent some of the late Bronze Age complexes. However, the mountain communities reorganized themselves in a final stage of North Caucasian traditions, as seen in complexes from Kabardinka or Kudachurt. These paved the way for a renewed intensification of a semi-mobile pastoral economy at high altitudes, which peaked as a highly efficient combined mountain agricultural system during the Late Bronze Age 2 (1700-1100/1000 calBCE) 24 .

Supplementary Note 2 Archaeological context of sites and newly reported individuals
Relative and absolute dates We provide dates either as relative dates or in the form of absolute dates, i.e. radiocarbon-dated samples. Relative dates are reported based on archaeological context in the form "5500-5000 BCE". Radiocarbon dates are given in the format "95.4 % CI calibrated radiocarbon age (noncalibrated radiocarbon years, laboratory number Sites and individuals (in alphabetical order) After the general site descriptions, we provide short profiles of each ancient individual for whom we produced ancient genome-wide data. Where possible, the attributed archaeological culture is given in italics. The sampled individuals stem from this first mound phase. The first interments in the mound, grave 8 and 8a, were found in a massive stone box covered by a cairn-like stone package. It was surrounded by a large circle of vertical stone slabs, some of which had collapsed to the interior. Graves 9, 15 and 16 were added inside the circle, and some were covered by collapsed stones of the stone circle. The entire constructing was then filled with a layer of topsoil. It was covered by a stone shell and an earthen mound-shell (shell 1). The remaining 12 graves date chiefly to the Middle and Late Bronze Age and are associated with the North Caucasian cultural formation (graves 4, 10), the Catacomb cultural formation (graves 7, 12-12) and a late or post-Catacomb horizon (graves 1, 3, 11, 12). Graves 2, 5 and 6 are uncertain in date. The Maykop individuals were part of a paleoanthropological study 26 and investigated with regards to their radiocarbon and stable isotope composition 27 . Paired radiocarbon dates on human and animal bones, chiefly herbivores, revealed radiocarbon off-sets for some bones (see comments below), but confirm a mid to late Maykop date for all graves. The particularities of inventories and grave construction together with the location of the site in the grass-steppe zone associate these complexes with our Steppe-Maykop cultural formation. Two sampled individuals from the Maykop complexes produced genome-wide data.

Aygurskiy 2, Russia
• AY2003.A0101.TF1 (BZNK-289/1), kurgan 22, grave 9, was the burial of a 1.5-yearold child in an oval burial pit covered by stones and associated with two ceramic vessels, a flint flake and an astragalus 25  The mound belongs to a number of mid-size and larger mounds in the vicinity of the village of Baksanyonok. These were excavated over the course of several years in various rescue archaeology projects. One individual produced genome-wide data: • I1720, kurgan 2, grave 5, a Maykop burial from a mid-size burial mound. No further information is available.

Beliy Ugol 2, Russia
The site of Beliy Ugol 2 is a burial mound cemetery situated in the North Caucasian foothills near the city of Essentuki, directly at the opening of a narrow gorge into the mountain valleys. The site is situated in a forest steppe to forest environment, which belongs to the Caucasian mountain vegetation zones 3 . The largest mound, mound 1, was excavated during rescue excavations, and parts of the burials had been seriously damaged. Before destruction, the mound had a diameter of approximately 40 m and a height of 3.7 m. In the barrow, 37 burials were excavated. 31 of the burials date to the North Caucasian cultural formation, but the complex stratigraphy suggests at least three major building phases that can be subdivided further. Grave 11 is the central grave of the fourth mound-shell, yet probably not the earliest interment in this phase. Genome-wide data was recovered from the individual buried in grave 11. Mound-shell 4 represents the final stage of the first construction phase. The second and third construction phases (mound-shell 5-7) likewise date to the North Caucasian epoch, yet three interments were catacomb graves. Mound-shells 2, 5 and 6 were surrounded by stone circles built with mid-and large-sized river pebbles. Three later graves were Sarmatian (Late Iron Age) and Medieval and several others could not be securely dated. One individual from the earlier North Caucasian construction produced genome-wide data: • BU2001.A0101.TF1 (BZNK-305/1), kurgan 1, grave 11 was a poorly preserved inhumation in a wooden chamber inside of a classical North Caucasus grave pit. The grave inventory included a bronze weapon, bronze pins and ornaments as well as a collection of stone beads. The site of Goryachkevodsky 2 near the city of Pyatigorsk is situated in the North Caucasian foothills neighboring a hilly landscape formed by volcanic activity. The Konstantinov plateau where the site is situated is well known for dense clusters of burial mounds, which are chiefly found at the watersheds between smaller creeks. The vegetation zone is forest steppe environment 3 . The location of the site is at the right side of the Podkumok river, approximately 25 km downstream from Beliy Ugol 2. The site consisted of at least five mounds, severely affected by agricultural activities. Mound 3 was excavated in 1999 prior to road construction by the Institute of Archaeology of the Caucasus 28 . It was severely damaged but formerly had a diameter of at least 45 m and was still 1.7 m high. This mound was one of the smaller features of this cemetery. The first construction in the mound consisted of three late Maykop burials (graves 4, 5, 6), which were placed in the centre in parallel rectangular pits and covered by a long, rectangular stone package. Graves 4 and 5 were dug into the ground after grave 6, which was situated on the former ground level. Grave 5 is one of the few dendrochronologically dated complexes in the North Caucasus. It is 2 years younger than grave 12 from Marinskaya 5 29 . The late Maykop grave 3 was placed directly on top of the central grave 6. Graves 8 and possibly 7 also belong to the late Maykop phase. The Maykop mound was bordered by a stone circle. A series of interments (graves 2, 9, 10) attributed to the North Caucasus formation were inserted into this circle, partly destroying the Maykop construction. The last construction on this mound was a series of four or five graves of the post-Catacomb horizon. Several graves from this site were subjected to analyses of isotope composition and radiocarbon reservoir effects 27 . The paired samples from grave 5 (grave 9 in 27 ) produced reproducible dates suggesting no reservoir offset 27 . Two individuals produced genome-wide data: The big mound of Ipatovo (Ipatovo 3, mound 2) was part of a series of linear alignments of mounds that run west-east crossing the system of the Kalaus river. Today the slightly hilly zone around the site is part of the North Caucasian herb and grass-steppe zone, while the Kalaus valley itself is part of the desert-steppe 3 . However, the vegetation likely shifted between desert and grass steppe in prehistory. During the construction of the mound, the climate was generally warmer and more humid than it is today and the landscape was more forested. Mound 2 was the largest in a group of at least eleven mounds visible from aerial images. It was excavated due to construction work and yielded a total number of 195 burials in 11 construction phases 30 . 151 of the interments were part of a Nogay cemetery dating to the 18 th century. One grave held the burial of a splendidly furnished Sarmatian woman 31 . The mound construction and 34 graves were assigned to a Bronze Age date and published in a monograph. Several of the Catacomb epoch interments were accompanied by wooden wagons 32 . The first three mound-shells are associated with graves that belong to an Eneolithic or Steppe-Maykop tradition. Grave 187, which is part of this study and has produced genome-wide data, is the founding grave of the entire mound. It was attributed to a local Eneolithic tradition in the monograph 30 . After reevaluation of the data, we would now rather group it with the Steppe Maykop complexes. This individual produced genome-wide data: • The tombs of Kaps are located on the southern and eastern slopes of a ridge on the left bank of the Akhuryan River. Out of four stone-chamber tombs found only one (2 x 2 x 1m) with a double-burial had remained untouched. The entrance of the chamber was located in the eastern wall. There are three synchronous burials in this chamber. Two human skeletons lying on their right side were found directly beside the western wall, whereas the third burial was documented behind the immobile entrance stone. The head of the latter skeleton was oriented towards to the east. Early Bronze Age Red-Black-ceramic vessels and bronze objects were found in these chambers. A synchronous settlement was documented near the burial ground, including portable fire-installations and ceramics. However, the settlement had been damaged during construction works. The archaeological site of Kaps is dated to the second stage of the Early Bronze Age (EBA; 4 th -3 rd millennium). The core area of the EBA Kura-Araxes culture is in Mesopotamia between the Kura and Araxes rivers. EBA cultural remains dating from the end of the 4 th millennium to 3 rd millennium BCE have been documented in the south-western regions of the highlands, in the north-western part of the Iranian plateau, and in the North Caucasus (intermediate zone). The peripheral zone of the Kura-Araxes culture extends to northern Syria and the Levant. Chronologically, Kura-Araxes extends to the last quarter of the 3 rd millennium BCE. The Kura-Araxes culture represents a period in which complex societies were formed in the South Caucasus, which was later succeeded by a period of early statehood, which represents a new archaeological culture. Two individuals produced genome-wide data: The burial mound cemetery Rasshevatskiy 1 is one of several groups of mounds that run in long lines from West to East. The vegetation today is an herb-steppe with larger patches of forest steppe vegetation 3 . The actual cemetery included 27 mounds and extended across 2 km, with distances between mounds varying from 30 to 130 m. Mound 21 with an oval to ogival shape was 110 m long, 85 m wide and 6 to 6,4 m high 37,38,39 . It was excavated during rescue excavation in 2000 and is one of the two largest mounds in the group. The mound was built in five construction layers or mound-shells of different forms and earth compositions. Moundshell 1 was constructed from dark-brown and brown loamy substrate in an egg-shaped form with an axis running North-South. It is associated with the Steppe Maykop formation, the founding burial is grave 14. Mound-shell 2, still egg-shaped, was built over the empty burial pit 3 in the Yamnaya period; graves 9, 11 and 13 were inserted into this shell and are also associated with the Yamnaya epoch. Two of the individuals from this epoch were sampled and produced genome-wide data, grave 11 revealed the oldest evidence of an early form of Yersinia pestis 40 . The second mound was entirely covered by a thin layer of light grey river-clay. The third mound-shell is associated with Novotitorovskaya groups. Its founding burial was grave 7, which was accompanied by a dismantled wagon. Graves 15, 17, 18 and probably 19 are associated with mound-shell 3. By this time, the mound was transformed into an oval construction with a flat top. Mound-shell 4, a construction of several layers among them darkand light brown loamy substrates, is associated with North Caucasus grave 16. Grave 21 of the same cultural formation possibly also belongs to shell 4. This was the third individual that produced genome-wide data. After that, the mound was considerably enlarged and had a flat top-platform, but its axis was still running North-South. The construction of mound-shell 5 included a considerable enlargement and a turn of the main axis from North-South to East-West. The founding burial, grave 8, is dated to the early Catacomb period with three wagons standing beside the grave pit (labelled initially 'grave 6'). Graves 2, 4, 12, the sacrificial pit 'grave' 1, and possibly grave 20 are also associated with the late Catacomb phase.  The site of Vonyuchka 1 also belongs to the groups of burial mounds located on the Konstantinov plateau near the town or Pyatigorsk. The mounds are situated near a small creek, at the right side of river Podkumok. The site is close to Goryachevodsky 2 (1.5 km) and Lysogorskaya 6 (22 km), respectively. Thus, like the others, Vonyuchka 1 is situated in the North Caucasian piedmont steppe in a forest steppe-herb steppe environment 3 . Mound 1, which was excavated in a rescue excavation, had a diameter of 40 m and was up to 2 m high and contained beside the studied founding grave 8 other Bronze Age burials. One individual produced genome-wide data: • VJ1001.B0101+D0101 (BZNK-3112+114/2), kurgan 1, grave 8, the founding grave in the mound discovered in a catacomb like construction. The bones were very badly preserved, but samples were taken directly after excavation. The entire skeleton was packed in a thick layer of dark-red ochre. Grave goods consisted of a ceramic vessel, a long flint blade, a flint scraper and a stone object. The skull of the individual revealed a partly healed trepanation 36

Supplementary Note 3 Ancient DNA authenticity and Kinship analysis
We performed X-chromosomal contamination tests for the male samples following an approach introduced by Rasmussen et al. 48 and implemented in the ANGSD software suite 49 . We applied the "MoM" (Methods of Moments) and "ML" (Maximum Likelihood) estimate from the "Method 1" likelihood computations (Supplementary Table 20). We note that the estimates of the highlighted individuals in are considered non-informative because of fewer than 200 Xchromosomal SNPs covered by at least two sequence reads. The estimated contamination rates for the other individuals are very low.
Supplementary Table 20. X-chromosomal contamination estimates for male samples based on ANGSD. "MoM" and "ML" are the estimated contamination rates using "Method 1" statistical approaches. "SE(MoM)" and "SE(ML)" are the standard errors. The estimates of the highlighted samples are not informative because of fewer than 200 SNPs covered by at least two sequences in these two samples. We only show the results generated using the new_llh version of ANGSD.

Sample
We used two methods lcMLkin 50 and READ 51 to determine genetic kinship. We identified two pairs (ARM003 and ARM002, VEK007 and VEK009) as the same individual or identical twins. We also found several pairs of first or second-degree relatives and removed them from most of the population genetic analyses (except for PCA and ADMIXTURE) to avoid bias resulting from a defined population consisting of too many closely related individuals.
An interesting finding is that three individuals SIJ001, SIJ002 and SIJ003 are suggested to be first-degree relatives while the pairs SIJ002-SIJ003 and SIJ001-SIJ003 are estimated to have a parent/offspring relationship (Supplementary Table 21 and 22).

Sex determination
We determined the sex of the newly reported samples in this study by counting the number of reads overlapping with the targets of 1240k capture reagent as discussed in Fu et al. 52 . We extracted the reads of high base and mapping quality (samtools depth -q30 -Q37) using samtools v1.3.1 53 . We calculated the ratios of the numbers of reads mapped on X chromosome or Y chromosome compared with that mapped on autosomes (X-rate = xCov/autCov and Y-rate = yCov/autCov). We observed two clusters in the X-rate to Y-rate scatterplot (Supplementary Figure 10), which we interpreted as a clear separation between males and females. We have identified 45 individuals (including 7 independent replicates in the library preparation) with an X-rate < 0.42 and a Y-rate > 0.26 as males and 20 individuals (including 1 independent replicate in the library preparation) with an X-rate > 0.68 and a Y-rate < 0.02 as females. We have one individual I2057 having an intermediate sex ratio, for which we could not reliably determine the genetic sex (Supplementary Table 23).

Supplementary Note 6 Admixture Graph modelling
In previous analyses, we defined two genetic clusters within the Greater Caucasus region, correlating to the Caucasus groups of the northern foothills and Steppe groups of the bordering steppe regions. In this section, we use the method qpGraph 56 , as implemented in ADMIXTOOLS 57 to test models of possible phylogenetic relationships for the two genetic clusters with reported representatives of ancient West Eurasians. qpGraph assesses the fit of Admixture Graph models to data by computing f2-, f3-and f4-statistics measuring allele sharing among pairs, triples, and quadruples of populations and evaluating fits based on the maximum |Z|-score comparing predicted and observed values of these statistics. We use the newly generated Maykop and Yamnaya_Caucasus data to represent the above two clusters, respectively. We also add Eneolithic_Steppe into the graph as a potential source for the Steppe groups.
We started with a skeleton phylogenetic tree consisting of Mbuti, Loschbour, and MA1 without admixture (Supplementary Figure 11), which could be fitted in the graph without outliers: Supplementary Figure 11. Skeleton Admixture Graph without admixture edges. Fit to genetic data with no f-statistics more than |Z|>3 different between model and expectation. The Z-score of the worst f-statistic (Mbuti, MA1; MA1, Loschbour) = -0.078. The drift along edges (number next to the arrows) is multiplied by 1000.
We then added Globular_Amphora as a representative of European farming populations to all possible edges in the graph of Supplementary Figure 11. We obtained one tree topology that fitted with no outliers and one additional admixture event implying that Globular_Amphora derived ancestry from Loschbour and a basal lineage branching off earlier than the split of MA1 and Loschbour (Supplementary Figure 12), which is consistent with a previous study that reported that Early European Farmers (EEF) had basal Eurasian ancestry 58 .
The model in which Globular_Amphora is admixed, which is a fit to the data in the sense that there are no f-statistics more than |Z|>3 different between model and expectation. The Z-score of the worst f-statistic (MA1, Loschbour; MA1, Globular_Amphora) = 0.075.
We continued to add EHG into the graph in Supplementary Figure 12 but failed to get fitted models with no additional admixture event. We got four fitted models with one additional admixture event: The model b0.c1 in which EHG are admixed deriving ancestry from MA1 and Loschbour related lineages, which is a fit to the data in the sense that there are no f-statistics more than |Z|>3 different between model and expectation. The Z-score of the worst f-statistic (Mbuti, Globular_Amphora; Loschbour, Globular_Amphora) = 0.051.
We then added CHG into the above 3 graphs b0.c1, b0.c3, and b0.c5 with low Z-scores and likelihood scores. We were not able to fit CHG into the graphs without invoking an additional admixture event, but got 17 fitted models with one additional admixture event: b0.c1-c2  Figure 14. Adding CHG. The model b0.c1-c4.d1, in which CHG are admixed deriving ancestry from basal Eurasian and Loschbour related lineages, which is a fit to the data in the sense that there are no f-statistics more than |Z|>3 different between model and expectation. The Z-score of the worst f-statistic (Mbuti, CHG; Loschbour, EHG) = 1.264.
We continued to add Eneolithic_Steppe onto the model b0.c1-c4.d1 ( Figure SF3.4) because this model has the lowest Z-score and likelihood score. We obtained only one graph topology fitted with no outliers, which models Eneolithic_Steppe as an admixture with one source of ancestry EHG-related, and the other lineage from the basal Eurasian side that also contributed to CHG (Supplementary Figure 15).
We continued to add Yamnaya_Caucasus into the graph in Supplementary Figure 15 and got two fitted models with one additional admixture event: d6.e4-c5.f6: the Z-score of the worst f-statistic = -2.823, likelihood score = 13469.860; d6.e4-c6.f6: the Z-score of the worst f-statistic = -2.044, likelihood score = 7733.921 (Supplementary Figure 16). We continued to add Maykop into the above two models but failed to get fitted models with no additional admixture event or with only one additional admixture event. The best model is shown in Supplementary Figure 17, suggesting that Maykop derives ancestry from CHG and Globular_Amphora related lineages, but it is not a good fit to the data in the sense that there is one f-statistics outlier: the Z-score of f (MA1, Maykop; EHG, Eneolithic_Steppe) = -3.369. The outlier could be interpreted as suggesting unmodeled affinity between the pair of MA1 and Eneolithic_Steppe or Maykop and EHG. We then manually added an admixture event from MA1 to Eneolithic_Steppe in the graph in Supplementary Figure 18 and an admixture event from EHG to Maykop in the graph in Supplementary Figure 19.
The model in which Eneolithic_Steppe are admixed deriving ancestry from CHG related basal Eurasian and EHG related lineages, which is a fit to the data in the sense that there are no fstatistics more than |Z|>3 different between model and expectation. The Z-score of the worst fstatistic (MA1, Loschbour; EHG, Eneolithic_Steppe) = -1.815. Figure 16. Adding Yamnaya_Caucasus.

Supplementary
The model d6.e4-c6.f6, in which Yamnaya_Caucasus are admixed deriving ancestry from Eneolithic_Steppe and Globular_Amphora related lineages, which is a fit to the data in the sense that there are no f-statistics more than |Z|>3 different between model and expectation. The Zscore of the worst f-statistic (MA1, Loschbour; EHG, Eneolithic_Steppe) = -2.044.
The best model by fitting Maykop deriving ancestry from CHG and Globular_Amphora related lineages, which is not a fit to the data in the sense that there is one f-statistic outlier: the Z-score of f (MA1, Maykop; EHG, Eneolithic_Steppe) = -3.369.

Supplementary Note 7 Phenotypic variants and marker under selection
We also explored a set of SNPs that has been shown to be under selection in West Eurasia over the last 8000 years of human history 59 (Supplementary Table 24). We observe an almost complete lack of the derived allele at the LCT locus, which codes for lactase persistence, i.e. the ability to digest milk sugar in adulthood. Only one 4000-year-old individual from the Late North Caucasus site of Kabardinka is heterozygous for the derived allele. The SNPs at SLC24A5 and SLC45A2 are associated with lighter skin pigmentation and HERC2 with lighter eye colour. The great majority of individuals from both main clusters likely had lighter skin colour, while the eye colour varied within each cluster. Interestingly, one of the Steppe Maykop individuals carried the derived allele at the EDAR 370A locus, which was shown to be at high frequency in East Asia thus associated with straighter, thicker hair and shovel-shaped incisors. This finding is consistent with the ancestral East Asian/Siberian affinity shown above.