: Supplemental

Supplemental Figure 2: Alternative oligonucleotide sequences targeted against dynamin or caveolin also block syndecan-4-induced endocytosis. Arf6 is not responsible for syndecan-4-regulated reduction in cell avidity, but mediates recycling of 5 1 integrin, related to Fig. 3. Supplemental Figure 3: An alternative oligonucleotide sequence targeted against RhoG also blocks syndecan-4-induced endocytosis, related to Fig. 5.

Recent archaeogenomic studies have revealed a number of interesting observations on the gene pools in Southwest Asia and the East Mediterranean, which we summarise and discuss below. We also discuss why certain population genetic observations (e.g. decreasing FST over time) can be interpreted as indicating inter-regional admixture and mobility. Finally, we discuss how we may reconcile historical observations on increasing mobility with previously observed population genetics patterns that hint at reduced mobility. a) Within-population genetic diversity: Diversity levels were low in the early Holocene, but appear to have increased following the Neolithic transition S2-S7 . This is compatible with increasing admixture within the studied populations. Meanwhile, local population growth without admixture would not explain this observation. This is because diversity in at least some of these studies S5,S8 was measured using SNPs ascertained in populations from Africa, representing outgroups to present-day Eurasians. These variants, therefore, arose earlier than the separation among the Eurasian populations under study. Any de novo variants that could accumulate in growing populations and that would normally increase diversity would be invisible to such analysis. Likewise, our observation of increasing diversity in Southwest Asia cannot be explained by de novo variants. This leaves mobility behind. b) Inter-population genetic differentiation: FST is a commonly used measure of population differentiation, roughly comparing population divergence with total diversity (including withinpopulation diversity). FST values calculated among West Eurasian human groups before the Neolithic were high, but dropped sharply during the Neolithic and Chalcolithic periods S3,S4,S9 . Low genetic diversity and high FST observed by the late Pleistocene and early Holocene suggest population isolation in earlier periods. During the Neolithic period, especially with the westward and eastward Neolithic expansions around 9,000 Before Present (BP), there appears to have occurred rapid admixture and consequent genetic homogenization across the region. Importantly, inter-population differentiation (average FST) appears to have strongly decreased from early-tomid-Holocene S3,S4,S9 . A drop in FST between two groups is compatible with inter-population admixture, which would cause shorter coalescence times S10 . c) Ancestry components: Ancestry components can be inferred using qpAdm analysis S11 , where a genome is explained as a mixture of source genomes. Such analysis can reveal potential admixture events if the sources include earlier populations from the same region, and under the assumption of limited population structure within a region. If this is the case, any change in ancestry components over time should be caused by admixture.
In Southwest Asia, qpAdm analyses on genomes from the Holocene have yielded a number of important insights. The foremost for our study is widespread inter-regional admixture from the Neolithic to the Bronze Ages, especially between eastern (Iran and South Caucasus) and western (Anatolia and Levant) Southwest Asia, and also extending into the Aegean S4,S7,S9,S12-S21 . For instance, by the Early Bronze Age, Anatolian groups carried approximately 50% ancestry of eastern origin (related to early Holocene South Caucasus/Iran), while Zagros populations carried approximately 50% ancestry of western origin (related to early Holocene Anatolia) S19,S20 .
During the Bronze Age, Steppe-or West Siberia-related gene flow is also observed in the broad region, albeit at lower levels and not ubiquitously S9,S12,S13,S16,S19-S21 . Importantly, changes in admixture components appear to be more modest in the period between the Bronze Age period and the present-day. Analysing past and extant populations of present-day Iran S22 of the Levant S15,S16,S23 , of the Caucasus S21,S24 , and of present-day Greece have suggested limited or even no observable change in ancestry components over the last 3,000-4,000 years S13,S18 .
While singular ancient genomes with non-local ancestry (often dubbed "outliers") are occasionally discovered, these mobility events appear to not have left substantial traces in the local gene pools from the Bronze Age onwards S16,S19,S20,S25 .
We next discuss the signal of decreasing FST (differentiation) and increasing stability (lower change) in ancestry components in the latter half of the Holocene. On the surface, these observations may seem to imply a decrease in mobility with the Bronze Ages. But this would be at odds with rich archaeological, historical and linguistic evidence for inter-regional human movements in the same period, from the establishment of trade colonies to forced population transfers (see Table I in Document Z1). A number of non-exclusive explanations could be conceived to reconcile expected inter-regional mobility and the observed genetic stability pattern: 1) Even if migration continued, the large size of resident agricultural populations that emerged by the Bronze Age may have diluted the genetic impact of immigrants S3,S16 .
2) Low amounts of gene flow simultaneously emerging from diverse external sources may not be visible in qpAdm analyses and may not cause an increase in FST, thus producing the wrong impression of reduced mobility.
3) The relative homogenization among regional gene pools in Southwest Asia in the early Holocene may have rendered later mobility events within Southwest Asia less visible to qpAdm analyses. Specifically, after an initial bout of admixture e.g. during the Neolithic, further admixture between the same groups e.g. during the Bronze Age may be difficult to detect via qpAdm.
4) The post-Bronze Age samples from the region may not be sufficiently representative of demographic changes in this period [for instance, an analysis of a relatively rich temporal sample from the Levant S15 reported subtle admixture from the Iron Age to the Ottoman Period from external regions (the Steppe, Africa, South Asia, and Central Asia) not observed earlier]. Nevertheless, the largely consistent patterns of ancestry change observed using genomes from different sites from each region, including the new genomes presented here (Figure 3), overall suggest that insufficient sampling is not a major issue. 5) FST may not be the optimal statistic to gauge rates of inter-population migration, as it is influenced by within-population diversity. For instance, FST is sensitive to population size reduction, which can cause an increase in FST without admixture (see Figure VII in Document Z1).

B. Discussion on interpretation of ancestry proportion estimations
In our qpAdm analyses we specifically model the population of each period with the earlier period as sources from the region. More precisely, we attempt to explain regional populations A or B at time T+1 ("target"), as mixtures of populations of the same regions A and B at time T ("sources").
This analysis revealed that, in a number of instances, we need additional ancestry sources to explain the later-coming genome sample (e.g. the post-Neolithic Zagros sample needing Anatolian ancestry in addition to the earlier Zagros Neolithic ancestry). This would be compatible with inter-regional mobility. Still, there remain some significant limitations in interpreting qpAdm results: • The appearance of an ancestry component related to population B at time T in population A at time T+1 does not mean a movement from B to A. To avoid such overinterpretation, we use "population X-related" to describe putative admixture events. • There is the possibility of a hidden and strong population structure that confounds temporal change. If intra-regional genetic differences (differences within region A) are larger than inter-regional differences (between A and B), this would render the inference of mobility invalid. But if we can assume that strong population structure is not common (which is usually, though not always, the case at the time scales we use; see Figure 1 and 3), changing ancestry sources in qpAdm could be interpreted as mobility. • High genetic similarity between the target and source populations can introduce high noise in qpAdm analysis. For instance, in our analyses, we found a wide range of possible Anatolian contributions (0-42%) in Levant genomes (Table S4). This is likely caused by high affinity between Anatolia and Levant populations in the early Holocene. The pre-Neolithic Anatolian gene pool itself is thought to have arisen from admixture between Levant and European pre-Neolithic groups, and the Neolithic Anatolians are thought to have descended from this gene pool S25,S26 . As a consequence, when the source populations share high drift (common ancestry), qpAdm modelling has difficulty in precisely estimating the proportion of admixture. • qpAdm-estimated proportions are sometimes treated as migration rate estimates, but they cannot be interpreted as such unless the direct sources are known. • Multiple models may explain the same data and may be similarly valid. In Figure 3 we chose to represent only one, following the criteria explained in the STAR Methods. Meanwhile, using alternative models (e.g. with similar but slightly different sources, such as CHG vs. Iran Neolithic) would yield the same qualitative conclusions about putative admixture-events.

C. Discussion on the possible effects of heterogeneous datasets on the results
The fact that we are using a heterogeneous dataset comprises a wide spectrum of whole genome coverage values (from 0.1X to 11.5X for shotgun samples and from 0.0007X to 0.50X for 1240K capture) and different protocols (shotgun sequencing versus SNP capture) requires additional consideration: 1) Low depth of coverage: This can lead to false negative results (missing subtle admixture signals) and it may introduce noise in f3 statistics.
Meanwhile, low coverage is not expected to cause a bias in f3 statistics (i.e. systematically higher affinity towards one population over another). Consequently, our main observations involving temporal changes (increasing diversity over time, the pattern of reduced and later increased interregional differences, and the sex-bias effect) are not expected to be influenced by heterogeneity in the coverage, as we explain below: 1a) We find that when we use all the data (ancient shotgun and SNP capture, and presentday genomes), there is a correlation between time and coverage (Spearman's rho = -0.16, p=0.0005). This appears to be driven by modern-day genomes (~30X coverage per genome), and also by having genomes produced by using two different protocols within the dataset (shotgun sequencing versus SNP capture). However, within the two ancient genome datasets produced by these protocols, we do not find a correlation between time and coverage (Spearman's rho = -0.05, p=0.34 in the 1240K data; Spearman's rho = 0.06, p=0.47 in the shotgun data). This is important because when we analyse the two (shotgun and capture) datasets separately, we find the same results again ( Figure XIX and Figure  XX in Document Z1).
1b) The outgroup-f3 comparisons can be affected by the number of SNPs used in the calculation (i.e. very low SNPs may introduce strong noise). In our original analyses we had used > 2,000 SNPs as cutoff for calculations for autosomal SNPs and > 1,000 SNPs for X chromosome SNPs (see STAR Methods). When we repeat our main observations involving temporal changes (increasing diversity over time, the pattern of reduced and later increased inter-regional differences, and the sex-bias effect) by using 10K (Figure X in Document Z1) and 50K SNPs ( Figure XI in Document Z1) cutoff calculations for autosomal SNPs, we observe the same patterns.
2) Combining data produced by different laboratories runs the risk of technical effects (related to laboratory protocols or data processing) confounding biological signals. To minimize this risk we took two measures: • We processed all ancient genome BAM files from external sources through the same pipeline as the newly generated data (STAR Methods). • For our main novel observations, we repeated the analyses separately using shotgun sequencing and SNP capture-based datasets (Figures XV, XVI in Document Z1).