Dataset. To explore the extent to which the European and Italian genetic variation has been shaped by ancient demographic events, we merged modern samples from FMD with 63 ancient samples selected from recent studies (data file S1) (4, 5, 8, 23, 33, 5961).

Principal component analysis (PCA). To visualize the genetic affinities of ancient and modern samples, we performed two PCAs with the EIGENSOFT (54) smartpca software and the “lsqproject” and “shrinkmode” option, projecting the ancient samples onto components inferred from modern European, West Asian, and Caucasian individuals and then only on the modern European clusters. To evaluate the potential impact of DNA damage in calling variants from aDNA samples, we repeated the PCA with the 63 ancient samples and the modern European, Caucasian, and West Asian samples by removing transition polymorphisms and recorded significant correlations for the localization of ancient samples along PC1 and PC2 (Pearson r > 0.99, P < 0.05).

ADMIXTURE analysis. We explored the genetic relationships between modern and ancient samples by projecting the ancient samples on the previously inferred ancestral allele frequencies from 10 ADMIXTURE (55) runs on modern samples (see the “Analysis of modern samples” section and the Supplementary Materials). We used CLUMPP for merging the resulting matrices and distruct for the visualization in CLUMPAK program (56).

D-statistics. We tested for admixture using the D-statistics as implemented in the qpDstat tool in the software ADMIXTOOLS v4.2 (62). We performed the D-statistics analyses evaluating the relationship of the Italian cluster with AN, ABA, and SBA. In detail, we performed the D-statistics D(Ita1,Ita2,AN/ABA/SBA,Mbuti), where Ita1 and Ita2 are the different clusters composed mainly of Italian individuals as inferred by fS.

CP/NNLS analysis. We used an approach based on the CP software (10) and a slight adaptation of the NNLS function (11, 20) to estimate the proportions of the genetic contributions from ancient population to our modern clusters. We ran CP using the unlinked mode (59) with the same Ne and θ parameters of the modern dataset, painting both modern and ancient individuals and using modern samples as donors (59, 60). We analyzed the output of CP by solving an appropriately formulated NNLS problem, reconstructing the modern clusters in terms of the ancients. We applied this combined approach on different sets of ancient samples (ultimate and proximate sources).

Goodness of fit was measured evaluating the residuals of the NNLS analysis. In detail, we focused on the proximate sources and compared the sum of squared residuals when ABA or SBA was included/excluded as putative sources. Furthermore, for the ultimate and proximate analyses, we estimated the SEs by applying a weighted jackknife bootstrap (data file S3), estimating the mixture profile removing one chromosome at time and averaging the values taking into account the total number of markers analyzed for iteration (58).

qpAdm analysis. We used the ancestral reconstruction method qpAdm, which harnesses different relationships of populations related to a set of outgroups (e.g., f4[Target, O1, O2, O3]) (1) to model the ancestry composition of modern and ancient Italian samples as different combinations of ancient sources. In detail, for each tested cluster of the FMD and HDD, we evaluated all the possible combinations of N “left” sources with N = {2..5} and one set of right/left outgroups (see the Supplementary Materials) (8).

For each of the tested combinations, we used qpWave to evaluate whether the set of chosen outgroups is able to (i) discriminate the combinations of sources and (ii) establish if the target may be explained by the sources. We used a P value threshold of 0.01. Last, we used qpAdm to infer the admixture proportions and reported it and the associated SEs in data file S4. In addition, we performed the same analysis with N = {2..4} for Iceman, Remedello, and Bell Beaker individuals from Sicily and North Italy (data file S4).

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