In order to compare the genomic sequence data of the seven SHGs to genetic information from other ancient individuals and modern-day groups, data were merged with shotgun sequence data and SNP capture data from six published Mesolithic individuals from Motala in central Scandinavia, and 47 published Stone Age (Upper Paleolithic, Mesolithic, and Early Neolithic) individuals from other parts of Eurasia (S6 Text) [17–22,26,27,29,35–38], as well as with a world-wide set of 203 modern-day populations [18,32,39]. All 13 SHGs—regardless of geographic sampling location and age—display genetic affinities to both WHGs and EHGs (Fig 1A and 1B, S6 Text). One individual, SF11, seems to be a slight genetic outlier in the principal component analysis (PCA), which could be due to the lower coverage or driven by nuclear contamination (Table 1, S6 Text). Generally, the pattern of dual ancestry is consistent with a scenario in which SHGs represent a mixed group tracing parts of their ancestry to both the WHGs and the EHGs [17–19,22,24,40].

The SHGs from northern and western Scandinavia show a distinct and significantly stronger affinity to the EHGs compared to the central and eastern SHGs (Fig 1). Conversely, the SHGs from eastern and central Scandinavia were genetically more similar to WHGs compared to the northern and western SHGs (Fig 1). Using qpAdm [19], the EHG genetic component of northern and western SHGs was estimated to 48.9% (± 5%) and differs from the 37.8% (± 3.2%) observed in eastern and south-central SHGs. The latter estimate is similar to ancestry estimates obtained for eastern Baltic hunter-gatherers from Latvia [29] (33.7% ± 4.7%, Fig 1A). Although the difference in ancestry estimates between northern and western SHG, and eastern and south-central SHG is only marginally significant (Z = 1.87, p = 0.062), this pattern is in agreement with other analyses such as ADMIXTURE and TreeMix (S6 Text). Furthermore, the direct comparison using D statistics with Chimpanzee (Chimp) as an outgroup (D(Chimp, WHG; eastern or south-central SHG, northern or western SHG) < 0, Z = −5.14 and D(Chimp, EHG; eastern or south-central SHG, northern or western SHG) > 0, Z = 1.72) show that WHG are genetically closer to eastern and south-central SHG, whereas EHG tend to share more alleles with northern and western SHGs (S2 Fig). These patterns of genetic affinity within SHGs are in direct contrast to the expectation based on geographic proximity with EHGs and WHGs.

From about 11,700 cal BP, consistent archaeological evidence of human presence exists in southern Scandinavia following the retreat of the ice sheet [6,41,42] (S1 Text). Artifacts and tools found at these sites show similarities with the Ahrensburgian tradition of northern central Europe [15,43], suggesting that these hunter-gatherers likely had a southern origin from a WHG-like gene pool as no EHG ancestry has been found in central and western Europe [18,21,24,27]. Although this genetic component would have entered from today’s northern Germany and Denmark (Fig 2, Scenario a), it remains unclear how and where the EHG component entered Scandinavia (Fig 2, Scenarios b, c and/or d). The EHG-related migration likely took place after the migration of WHGs from the south as the earliest eastern-associated pressure blade finds postdate the southwestern-associated direct blade finds in Scandinavia (S1 Text). Two migrations with admixture at different time-periods would generate a genetic gradient with the highest contribution of a source close to its geographic region of entry. The observed genetic pattern is consistent with a migration of the EHGs from the northeast moving southwards along the ice-free Norwegian Atlantic coast where the two groups started mixing (Fig 2, Scenarios a and b), which would cause more EHG ancestry in western SHGs. If the EHG migration had crossed the Baltic Sea into Scandinavia, where it would meet and mix with a WHG-like population (Fig 2, combination of Scenarios a and c), a gradient with most EHG ancestry in eastern SHGs would have been created—exactly opposite to the observed pattern. A similar pattern would be expected if the EHG migration went around the Baltic Sea along current day’s Finnish west coast and down via today’s Swedish east coast (scenario not depicted in Fig 2). An EHG migration along the southern Baltic coast (Fig 2, Scenarios a and d) should cause a related pattern to a crossing of the Baltic Sea with more EHG ancestry in central and eastern SHGs. Furthermore, such a scenario would likely also make the Latvian Mesolithic hunter-gatherers the group with most EHG ancestry, which is in stark contrast to the empirical data in which the Latvian group shows the lowest proportion of EHG ancestry (33.7% ± 4.7%), and also not consistent with chronology, as the dated settlements east of the Baltic Sea are younger than the early settlements in Scandinavia (S1 Text). Thus, the only scenario consistent with both genetic and archaeological data is a migration of a WHG-related group migrating into Scandinavia from the south, followed by an EHG-related group migrating to Scandinavia from the northeast along the Norwegian Atlantic coast. Notably, such a migration along the Norwegian coast could have been facilitated by the use of the more specialized pressure blade technique (S1 Text) [12,14]. The individuals sequenced here postdate these migrations, but a genetic east-west gradient would be maintained over time in Scandinavia and only additional large-scale migrations from different sources would alter this pattern. This observation is important as the geographic pattern still holds without the chronologically much younger Steigen individual, which might represent local continuity or later migrations into north-western Scandinavia from the east.

Interestingly, stable nitrogen and carbon isotope analysis of northern and western SHGs revealed an extreme marine diet, suggesting a pronounced maritime subsistence, in contrast to the more mixed terrestrial and aquatic diet of eastern and central SHGs (S1 Text). Mobility is difficult to trace based solely on carbon and nitrogen isotope data; however, the patterns are consistent with a migration along the Norwegian Atlantic coast relying on local resources.

By sequencing complete ancient genomes, we can compute unbiased estimates of genetic diversity, which are informative of past population sizes and population history. Here, we restrict the analysis to WHGs and SHGs because only SNP capture data are available for EHGs (S7 Text). In modern-day Europe, there is greater genetic diversity in the south compared to the north. During the Mesolithic period, by contrast, we find lower levels of runs of homozygosity (RoH) (Fig 3A) and linkage disequilibrium (LD) (Fig 3B) in SHGs compared to WHGs (represented by Loschbour and Bichon [18,35]). By using a multiple sequentially Markovian coalescent (MSMC) approach [44] for the high-coverage, high-quality genome of SF12, we find that right before the SF12 individual lived, the effective population size of SHGs was similar to that of WHGs (Fig 3C). At the time of the LGM and back to approximately 50,000 years ago, both the WHGs and SHGs go through a bottleneck, but the ancestors of SHGs retained a greater effective population size in contrast to the ancestors of WHGs who went through a more severe bottleneck (Fig 2C), which is consistent across 100 bootstrap replicates (S2 Fig). These differences in effective population size estimates may be attributed to the admixture in SHGs as migration events can have delayed effects on estimates of effective population size over time [45]. Around 50,000–70,000 years ago, the effective population sizes of the ancestors of SHGs, WHGs, Neolithic groups (represented by Stuttgart [18]), and Paleolithic Eurasians (represented by Ust-Ishim [38]) align, suggesting that these diverse groups all trace their ancestry back to a common ancestral group, which likely represents the early migrants out of Africa.

With the aim of detecting signs of adaptation to high-latitude environments and selection during and after the Mesolithic period, we employed two different approaches that utilize the Mesolithic genomic data. In the first approach, we assumed that SHGs adapted to high-latitude environments of low temperatures and seasonally low levels of light, and searched for gene variants that carried over to modern-day people in northern Europe. Modern-day northern Europeans trace limited amounts of genetic material back to the SHGs (due to the many additional migrations during later periods), and any genomic region that displays extraordinary genetic continuity would be a strong candidate for adaptation in people living in northern Europe across time. We designed a statistic, D_sel (S9 Text), that captures this specific signal and scanned the whole genome for gene variants that show strong continuity (little differentiation) between SHGs and modern-day northern Europeans while exhibiting large differentiation to modern-day southern European populations [46] (Fig 4A; S9 Text). Six of the top 10 SNPs with greatest D_sel values were located in the TMEM131 gene that has been found to be associated with physical performance [47], which could make it part of the physiological adaptation to cold [48]. This genomic region was more than 200 kbp (kilo base pairs) long and showed the strongest haplotypic differentiation between modern-day Tuscan individuals (TSIs) and modern-day Finnish individuals (FINs) across the genome (S9 Text). The particular haplotype was relatively common in SHGs, it is even more common among today’s Finnish population (S9 Text) and showed a strong signal of local adaptation (S9 Text). Other top hits included genes associated with a wide range of metabolic, cardiovascular, and developmental and psychological traits (S9 Text) potentially linked to physiological adaptation to cold environments [48].

In addition to performing this genome-wide scan, we studied the allele frequencies in three pigmentation genes (SLC24A5, SLC45A2, which have a strong effect on skin pigmentation, and OCA2/HERC2, which has a strong effect on eye pigmentation) in which the derived alleles are virtually fixed in northern Europeans today. The differences in allele frequencies of those three loci are among the highest between human populations, suggesting that selection was driving the differences in eye color, skin, and hair pigmentation as part of the adaptation to different environments [50–53]. All of the depigmentation variants at these three genes are in high frequency in SHGs in contrast to both WHGs and EHGs (Fig 4B). We conduct neutral simulations of the allele frequencies in an admixed SHG population to estimate p-values for observing these allele frequencies without selection (S9 Text). The p-values for all three SNPs are lower than 0.2; the combined p-value [54] for all three pigmentation SNPs is 0.028. Therefore, the unique configuration of the SHGs is not fully explained by the fact that SHGs are a mixture of EHGs and WHGs, but could rather be explained by a continued increase of the allele frequencies after the admixture event, likely caused by adaptation to high-latitude environments [50,52].

By combining information from climate modeling, archaeology, and Mesolithic human genomes, we were able to reveal the complexity of the early migration patterns into Scandinavia and human adaptation to high-latitude environments. We disentangled two migration routes and linked them to particular archaeological patterns. We also demonstrated greater genetic diversity in Mesolithic northern Europe compared to southern and central Europe—in contrast to modern-day patterns—and showed that many genetic variants that were common during the Mesolithic period have been lost today. These findings reiterate the importance of human migration for dispersal of novel technology in human prehistory [14–20,27,40,55–58].

Genomic sequence data were generated from teeth and bone samples belonging to seven (eight, including SF13) Mesolithic SHGs (S1 Text). A detailed description on the archaeological background of the samples as well as post-LGM Scandinavia can be found in S1 Text. Additional libraries were sequenced for two previously published Neolithic hunter-gatherers, Ajvide58 and Ajvide70 [17] (S2 Text). All samples were prepared in the dedicated aDNA facilities at Uppsala University (SF9, SF11, SF12, SF13, SBj, Hum1, Hum2, Ajvide58, Ajvide70) and at Stockholm University (Steigen).

Bones and teeth were decontaminated prior to analysis by wiping them with a 1% Sodiumhypoclorite solution and DNA-free water. Furthermore, all surfaces were UV irradiated (6 J/cm² at 254 nm). After removing 1 millimeter of the surface, approximately 30–300 mg of bone was powderized and DNA was extracted following silica-based methods as in [59] with modifications as in [57,60] or as in [61] and eluted in 25–110 μl of EB buffer. Between one and 16 extractions were made from each sample and one extraction blank with water instead of bone powder was included per six to 10 extracts. Blanks were carried along the whole process until quantitative PCR (qPCR) and/or PCR and subsequent quantification.

DNA libraries were prepared using 20 μl of extract, with blunt-end ligation coupled with P5 and P7 adapters and indexes as described in [57,62]. From each extract one to five double stranded libraries were built. Because aDNA is already fragmented, the shearing step was omitted from the protocol. Library blank controls, including water as well as extraction blanks, were carried along during every step of library preparation. In order to determine the optimal number of PCR cycles for library amplification, qPCR was performed. Each reaction was prepared in a total volume of 25 μl, containing 1 μl of DNA library, 1X MaximaSYBRGreen mastermix, and 200 nM each of IS7 and IS8 [62] reactions were set up in duplicates. Each blunt-end library was amplified in four to 12 replicates with one negative PCR control per index-PCR. The amplification reactions had a total volume of 25 μl, with 3 μl DNA library, and the following in final concentrations: 1 X AmpliTaq Gold Buffer, 2.5 mM MgCl₂, 250 μM of each dNTP, 2.5 U AmpliTaq Gold (Thermo Fisher Scientific, Waltham, MA), and 200 nM each of the IS4 primer and index primer [62]. PCR was done with the following conditions: an activation step at 94°C for 10 min followed by 10–16 cycles of 94°C for 30 s, 60°C for 30 s, and 72°C for 30 s, and a final elongation step of 72°C for 10 min. For each library, four amplifications with the same indexing primer were pooled and purified with AMPure XP beads (Agencourt; Beckman Coulter, Brea, CA). The quality and quantity of libraries was checked using Tapestation or BioAnalyzer using the High Sensitivity Kit (Agilent Technologies, Cary, NC). None of the blanks showed any presence of DNA comparable to that of a sample and were therefore not further analyzed. For initial screening, 10–20 libraries were pooled at equimolar concentrations for sequencing on an Illumina HiSeq 2500 using v.4 chemistry, and 125 bp paired-end reads or HiSeqX, 150 bp paired-end length using v2.5 chemistry at the SNP & SEQ Technology Platforms at Uppsala University and Stockholm University. After evaluation of factors such as clonality, proportion of human DNA, and genomic coverage samples were selected for resequencing, aiming to yield as high coverage as possible for each library.

Based on the results of the non-damage-repair sequencing, the SF12 individual was selected for large-scale sequencing in order to generate a high-coverage genome of high quality where damages had been repaired using UDG. In addition to the 15 extracts previously prepared and used for non-damage repair libraries, another 111 extracts were made based on a variety of silica-based methods [27,57,59,60]. From these 126 extracts, a total of 258 damage-repaired double-stranded libraries were built for Illumina sequencing platforms. Libraries were built as above, except a DNA repair step in which UDG and endonuclease VIII or USER enzyme (NEB) treatment was included in order to remove deaminated cytosines [63]. qPCR was performed in order to quantify the number of molecules and the optimal number of PCR cycles prior to amplification for each DNA library. Furthermore, this step included extraction blanks, library blanks, and amplification blanks to monitor potential contamination. All of these negative controls showed an optimal cycle of amplification significantly higher to those of our aDNA libraries (>10 cycles) and they were thus deemed as negative. Our experimental results show minimal levels of contamination, which is in concordance with mt DNA and X chromosome estimates of contamination (see S4 Text and Table 1). Each reaction was done in a total volume of 25 μl, containing 1 μl of DNA library, 1 X MaximaSYBRGreen mastermix (Thermo Fisher Scientific), and 200 nM each of IS7 and IS8 [62], reactions were set up in duplicate. The PCRs were set up using a similar system as for the nondamage repair samples (in quadruplicates that were pooled prior to cleanup of the PCR products), except for using AccuPrime DNA polymerase (Thermo Fisher Scientific) instead of AmpliTaqGold (Thermo Fisher Scientific) and the following PCR conditions: an activation step at 95°C for 2 min followed by 10–16 cycles of 95°C for 15 s, 60°C for 30 s, and 68°C for 1 min, and a final elongation step of 68°C for 5 min. Blank controls, including water as well as extraction blanks, were carried out during every step of library preparation. Amplified libraries were pooled, cleaned, quantified, and sequenced in the same manner as non-damage repaired libraries. A small proportion of the libraries (n = 14) were also subjected to whole genome capture (WGC) using European MYbaits from MYcroarray, and following the manufacturers protocol as done in [64].

In order to sequence libraries to depletion, two to eight libraries were pooled together and sequenced until reaching a clonality of >50%; if sequencing was halted before reaching that clonality level, it was either because the library was classified as unproductive based on the genome coverage generated, or that the sequencing goal (>55 × coverage) was already reached and further sequencing was deemed unnecessary. Sequencing was performed as above.

Paired-end reads were merged using MergeReadsFastQ_cc.py [65]; if an overlap of at least 11 base pairs was found, the base qualities were added together and any remaining adapters were trimmed. Merged reads were then mapped single-ended with bwa aln 0.7.13 [66] to the human reference genome (build 36 and 37) using the following nondefault parameters: seeds disabled -l 16500 -n 0.01 -o 2 [17,18]. To remove PCR duplicates, reads with identical start and end positions were collapsed using a modified version, to ensure random choice of bases, of FilterUniqSAMCons_cc.py [65]. Reads with less than 10% mismatches to the human reference genome, reads longer than 35 base pairs, and reads with mapping quality higher than 30 were used to estimate contamination.

The genetic data obtained from the two bone elements SF9 and SF13 showed extremely high similarities, which suggested that the two individuals were related. Using READ [67], a tool to estimate kin-relationship from aDNA, SF9 and SF13 were classified as either identical twins or the same individual. Therefore, we merged the genetic data for both individuals and refer to the merged individual as SF9 throughout the genetic analysis.

All data show damage patterns indicative of authentic aDNA (S3 Text). Contamination was estimated using three different sources of data: (1) the mt genome [68], (2) the X chromosome if the individual was male [69,70], and (3) the autosomes [71]. The data mapping to the human genome can be considered largely endogenous, as the contamination estimates were low across all three methods (S4 Text).

Most population genomic analyses require a set of reference data for comparison. We compiled three different data sets from the literature and merged them with the data from ancient individuals (S6 Text). The three reference SNP panels were as follows:

These data sets were merged with ancient individuals of less than 15× genome coverage using the following approach: for each SNP site, a random read covering that site with minimum mapping quality 30 was drawn (using samtools 0.1.19 mpileup [73]) and its allele was assumed to be homozygous in the ancient individual. Transition sites were coded as missing data for individuals that were not UDG-treated, and SNPs showing additional alleles or indels in the ancient individuals were excluded from the data.

The six high-coverage ancient individuals (SF12, NE1 [27], Kotias [35], Loschbour [18], Stuttgart [18], and Ust-Ishim [38]) used in this study were treated differently, as we generated diploid genotype calls for them. First, the base qualities of all Ts in the first five base pairs of each read as well as all As in the last five base pairs were set to 2. We then used Picard [74] to add read groups to the files. Indel realignment was conducted with GATK 3.5.0 [66] using indels identified in phase 1 of the 1000 Genomes Project as reference [32]. Finally, GATK’s UnifiedGenotyper was used to call diploid genotypes with the parameters -stand_call_conf 50.0, -stand_emit_conf 50.0, -mbq 30, -contamination 0.02, and—output_mode EMIT_ALL_SITES using dbSNP version 142 as known SNPs. SNP sites from the reference data sets were extracted from the VCF files using vcftools [72] if they were not marked as low-quality calls. Plink 1.9 [75,76] was used to merge the different data sets.

We performed PCA to characterize the genetic affinities of the ancient Scandinavian genomes to previously published ancient and modern genetic data. PCA was conducted on 42 present-day west Eurasian populations from the Human Origins data set [18,39] using smartpca [77] with numoutlieriter: 0 and lsqproject: YES options. A total of 59 ancient genomes (52 previously published and 7 reported here) (S6 Text) were projected into the reference PCA space and computed from the genotypes of modern individuals. For all individuals, a single allele was selected randomly—making the data set fully homozygous. The result was plotted using the ploteig program of EIGENSOFT [77] with the–x and–k options.

popstats [78] was used to calculate D statistics to test deviations from a tree-like population topology of the shape ((A,B);(X,Y)) [39]. Standard errors were calculated using a weighted block jackknife of 0.5 Mbp. The tree topologies are balanced at zero, indicating no recent interactions between the test populations. Significant deviations from zero indicate a deviation from the proposed tree topology depending on the value. Positive values indicate an excess of shared alleles between A and X or B and Y, whereas negative values indicate more shared alleles between B and X or A and Y. Using an outgroup as population A limits the test results to depend on the recent relationships between B and Y (if positive) or B and X (if negative). Here, we used high-coverage Mota [37], Yoruba [32], and Chimp genome as (A) outgroups. popstats [78] was used to calculate f₄ statistics in order to estimate shared drift between groups. Standard errors and Z scores for f₄ statistics were estimated using a weighted block jackknife (Fig 1C).

A model-based clustering algorithm, implemented in the ADMIXTURE software [79], was used to estimate ancestry components and to cluster individuals. ADMIXTURE was conducted on the Human Origins data set [18,39], which was merged with the ancient individuals as described above. Data was pseudo-haploidized by randomly selecting one allele at each heterozygous site of present-day individuals. Finally, the data set was filtered for LD using PLINK [75,76] with parameters (--indep-pairwise 200 25 0.4), this retained 289,504 SNPs. ADMIXTURE was run in 50 replicates with different random seeds for ancestral clusters from K = 2 to K = 20. Common signals between independent runs for each K were identified using the LargeKGreedy algorithm of CLUMPP [80]. Clustering was visualized using rworldmap, ggplot2, SDMTools, and RColorBrewer packages of GNU R version 3.3.0. Starting from K = 3, when the modern samples split up into an African and eastern and western Eurasian clusters, the Mesolithic Scandinavians from Norway show slightly higher proportions of the Eastern cluster than Swedish Mesolithic individuals. This pattern continues to develop across higher values of K and it is consistent with the higher Eastern affinities of the Norwegian samples seen in the PCA and D- and f4 statistics. The results for all Ks are shown in S1 Fig.

In addition to ADMIXTURE, we assessed the admixture patterns in Mesolithic Scandinavians using a set of methods implemented in ADMIXTOOLS [39], qpWave [81], and qpAdm [19]. Both methods are based on f₄ statistics, which relate a set of test populations to a set of outgroups in different distances from the potential source populations. We used the following set of outgroup populations from the Human Origins data set: Ami_Coriell, Biaka, Bougainville, Chukchi, Eskimo_Naukan, Han, Karitiana, Kharia, and Onge. We first used qpWave to test the number of source populations for Mesolithic west Eurasians (WHG). qpWave calculates a set of statistics X(u,v) = f₄(u0, u; v0, v) where u0 and v0 are populations from the sets of test populations L and outgroups R, respectively. To avoid having more test populations than outgroups, we built four groups consisting of (1) genetically western and central hunter-gatherers (Bichon, Loschbour, KO1, LaBrana), (2) EHGs (UzOO74/I0061, SVP44/I0124, UzOO40/I0211), (3) Norwegian hunter-gathers (Hum1, Hum2, Steigen), and (4) Swedish hunter-gatherers (individuals from Motala and Mesolithic Gotland). qpWave tests the rank of the matrix of all X(u,v) statistics. If the matrix has rank m, the test populations can be assumed to be related to at least m + 1 “waves” of ancestry, which are differently related to the outgroups. A rank of 0 is rejected in our case (p = 3.13e-81), whereas a rank of 1 is consistent with the data (p = 0.699). Haak et al. [19] already showed, using the same approach, that WHG and EHG descend from at least two sources (confirmed with our data as rank 0 is rejected with p = 1.66e-86, whereas rank 1 is consistent with the data), and adding individuals from Motala does not change these observations. Therefore, we conclude that European Mesolithic populations, including Swedish and Norwegian Mesolithic individuals, have at least two source populations.

We then used qpAdm to model Mesolithic Scandinavian individuals as a 2-way admixture of WHG and EHG. qpAdm was run separately for each Scandinavian individual x, setting T = x as target and S = (EHG, WHG) as sources. The general approach of qpAdm is related to qpWave: target and source are used as L (with T being the base population), and f₄ statistics with outgroups from R (same as above) are calculated. The rank of the resulting matrix is then set to the number of sources minus one, which allows to estimate the admixture contributions from each population in S to T. The results are shown in Fig 1. We calculate a Z score for the difference between Norwegian and Swedish SHG as Z=anor-asweSEnor2+SEswe2 where a are the ancestry estimates and SE are the respective block-jackknife estimates of the standard errors.

Heterozygosity is a measurement for general population diversity and its effective population size. Analyzing the extent of homozygous segments across the genome can also give us a temporal perspective on the effective population sizes. Many short segments of homozygous SNPs can be connected to historically small population sizes, whereas an excess of long RoH suggests recent inbreeding. We restricted this analysis to the six high-coverage individuals (SF12, NE1, Kotias, Loschbour, Stuttgart, Ust-Ishim) for which we obtained diploid genotype calls and we compared them to modern individuals from the 1000 Genomes Project. The length and number of RoH were estimated using Plink 1.9 [75,76] and the parameters--homozyg-density 50,--homozyg-gap 100,--homozyg-kb 500,--homozyg-snp 100,--homozyg-window-het 1,--homozyg-window-snp 100,--homozyg-window-threshold 0.05, and--homozyg-window-missing 20. The results are shown in Fig 3A.

Similar to RoH, the decay of LD harbors information on the demographic history of a population. Long-distance LD can be caused by a low effective population size and past bottlenecks. Calculating LD for aDNA data is challenging, as the low amounts of authentic DNA usually just yields haploid allele calls with unknown phase. In order to estimate LD decay for ancient populations, we first combine two haploid ancient individuals to a pseudo-diploid individual (similar to the approach chosen for conditional nucleotide diversity, S7 Text). Next, we bin SNP pairs by distance (bin size 5 kb) and then calculated the covariance of derived allele frequencies (0, 0.5, or 1.0) for each bin. This way, we do not need phase information to calculate LD decay because we do not consider multilocus haplotypes, which is similar to the approach taken by ROLLOFF [39,82] and ALDER [83] to date admixture events based on admixture LD decay. For Fig 3B, we used two modern 1000 Genomes Project populations to scale the LD per bin. The LD between two randomly chosen PELs (modern-day Peruvian individuals) was set to 1 and the LD between two randomly chosen TSIs was set to 0. This approach is used to obtain a relative scale for the ancient populations, and we caution against a direct interpretation of the differences to modern populations because technical differences in the modern data (e.g., SNP calling or imputation) may have substantial effects.

We are using MSMC’s implementation of PSMC’ [44] to infer effective population sizes over time from single high-coverage genomes. We restrict this analysis to UDG-treated individuals (SF12, Loschbour, Stuttgart, Ust-Ishim) as postmortem damage would cause an excess of false heterozygous transition sites. Input files were prepared using scripts provided with the release of MSMC (https://github.com/stschiff/msmc-tools) and MSMC was run with the nondefault parameters--fixedRecombination and -r 0.88 in order to set the ratio of recombination to mutation rate to a realistic level for humans. We also estimate effective population size for six high-coverage modern genomes [84] (Fig 3C). We plot the effective population size assuming a mutation rate of 1.25x10e-8 and a generation time of 30 years. The curves for ancient individuals were shifted based on their average C14 date. Additionally, we used multihetsep_bootstrap.py to generate 100 bootstraps per individual. The results are shown in S4 Fig.

We scanned the genomes for SNPs with similar allele frequencies in Mesolithic and modern-day northern Europeans and contrasted it to a modern-day population from southern latitudes. Pooling all Mesolithic Scandinavians together, we obtain an allele frequency estimate for SHGs, which is compared to FINs and TSIs from the 1000 Genomes Project [32]. We use the Finnish population as representatives of modern-day northern Europeans (this sample contains the largest number of sequenced genomes from a northern European population). Tuscans are used as an alternative population, who also trace some ancestry to Mesolithic populations, but who do not trace their ancestry to groups that lived at northern latitudes in the last 7,000–9,000 years. Our approach is similar to PBS [85] and inspired by DAnc [46]. For each SNP, we calculated the statistic D_sel, comparing the allele frequencies between one ancestral and two modern populations: Dsel=|DAFSHG−DAFTSI|−|DAFSHG−DAFFIN|

This scan was performed on all transversion SNPs extracted from the 1000 Genomes Project data. Only sites with a high-confidence ancestral allele in the human ancestor (as used by the 1000 Genomes Project [32]) and with coverage for at least six ancient Scandinavians were included in the computation. More information can be found in S9 Text.