As a reviewer and now discussant, I read Martin Furholt's important article ‘Massive Migrations? The Impact of Recent aDNA Studies on our View of Third Millennium Europe’ with great interest. I fully support this crucial dialogue and hope this publication and its discussion will motivate and foster many future collaborative studies that aim to integrate archaeology, anthropology, genetics, and perhaps linguistics. In what follows, I will add a few technical points for consideration:

Martin Furholt directly engages with work done by myself and my colleagues in the ancient DNA field, writing ‘Allentoft et al. (Reference Allentoft, Sikora, Sjögren, Rasmussen, Rasmussen and Stenderup2015) have sampled additional Corded Ware individuals, some dated to between 2800 and 2600 cal bc, who show a strong affinity to the contemporary Yamnaya samples (although less so than the Esperstedt individuals presented by Haak et al., Reference Haak, Lazaridis, Patterson, Rohland, Mallick and Llamas2015)’ (p. 8).

It is important to co-analyse data from the two studies in order to make direct comparisons. As shown in Figure 1, all Corded Ware-associated individuals published to date show very similar proportions (and can be shown to form a clade to the exclusion of other ancient individuals by formal statistics). Of note, the amount of ‘early European farmer’-ancestry (orange component) also varies among the individuals from Esperstedt. For comparison, I also include data from additional Corded Ware-associated individuals from the Baltic region (Allentoft et al., Reference Allentoft, Sikora, Sjögren, Rasmussen, Rasmussen and Stenderup2015; Jones et al., Reference Jones, Zarina, Moiseyev, Lightfoot, Nigst and Manica2017). Additional data from Baltic Corded Ware individuals will be available shortly (Saag et al., Reference Saag, Varul, Scheib, Stenderup, Allentoft and Saag2017; Mittnik et al., Reference Mittnik, Wang, Pfrengle, Daubaras, Zariņa and Hallgren2017). Admixture proportions (linkage disequilibrium-pruned; k = 12) show that in both central Europe and the Baltic region, CW-associated individuals are the first group to carry ‘Yamnaya-like’ steppe ancestry (a blend of the blue and green component) and ‘early European farmer’-ancestry. The latter ancestry is varying during the time-span and geographic area covered by these individuals, which is seen both in the Baltic region as well as central Europe (Mittelelbe-Saale and Bavaria), and suggests that the period of the Corded Ware is the time of admixture of ‘Early Farmer’ and ‘Steppe’ ancestry, a process that eventually results in more balanced proportions in the subsequent Únětice-associated individuals of the Early Bronze Age.

Figure 1. ADMIXTURE plot of select ancient individuals (data from Allentoft et al., Reference Allentoft, Sikora, Sjögren, Rasmussen, Rasmussen and Stenderup2015; Haak et al., Reference Haak, Lazaridis, Patterson, Rohland, Mallick and Llamas2015; Mathieson et al., Reference Mathieson, Lazaridis, Rohland, Mallick, Patterson and Roodenberg2015; Jones et al., Reference Jones, Zarina, Moiseyev, Lightfoot, Nigst and Manica2017). CW = Corded Ware; MN = Middle Neolithic.

As Furholt continues his argument, much of his subsequent debate revolves around the term ‘migration’ and (as opposed to) ‘gene flow’ as, for example, when he writes, ‘The argument of Haak et al. (Reference Haak, Lazaridis, Patterson, Rohland, Mallick and Llamas2015) rests on the assumption that the Corded Ware represents a single distinct population and that one would need evidence of Yamnaya affinity in an earlier archaeological culture to make a case for a continuous gene flow. This model seems to exclude the possibility that such a continuous gene flow could take place within the Corded Ware, which lasts for up to 800 years’ (p. 8); and, additionally, ‘the real issue here is that the authors do not make explicit what they mean by the term migration. The suggestion that continuous gene flow would be something different from migration is not consistent with the archaeological debates on the matter’ (p. 8).

I agree that there is no clear definition of migration in our manuscript, which, as the author admits, remains an elusive term. However, the model proposed in Haak et al. is based on the possibility of distinguishing between migration and continuous gene flow, wherein the latter becomes somewhat easier to demarcate. Under the assumption of continuous gene flow between the east (here, the north Pontic steppe) and the west (here, central Europe), we would not expect such a clear distinction between the genetic profiles of both. Instead, we would expect to see a gradient of shared ancestry in which the respective proportions would be maximized on one side (here ‘Early Farmer’ ancestry in the west and ‘Iranian Neolithic’ ancestry in the east), minimized in the opposite direction, but present nonetheless. However, this is not the case, as seen from individuals that span the time frame 8000-3000 bp. Ancestry profiles remain exclusive until the time of the Corded Ware.

Of note, new data from Globular Amphorae-associated individuals from Poland and the Ukraine show no steppe ancestry, that is, they very closely resemble the Middle Neolithic farmers in Figure 1 (Mathieson et al., Reference Mathieson, Alpaslan Roodenberg, Posth, Szécsényi-Nagy, Rohland and Mallick2017, available on biorxiv: http://biorxiv.org/content/early/2017/05/09/135616), which is intriguing given the geographical proximity and contemporaneity with Yamnaya individuals. Likewise, as also seen in Figure 1, one individual associated with the Corded Ware in the Baltic region lacks ‘farmer-ancestry’ (CW Latvia from Jones et al., Reference Jones, Zarina, Moiseyev, Lightfoot, Nigst and Manica2017) and, thus, resembles the steppe ancestry profile of Yamnaya individuals.

Both observations narrow down the remaining time window for the expansion of steppe ancestry into central Europe to a few hundred years at best or perhaps five to ten generations. Given that we do not observe the signal of continuous gene flow over longer time periods (where the formation of steppe ancestry 5000–6000 years ago would pose a time constraint), we were inclined to call this process ‘migration’. Given the time window between the Globular Amphorae individuals with no ancestry and the earliest Corded Ware individuals with very large proportions, this process is still considered ‘rapid’ in biological terms and ‘massive’ in comparison.

As a further consideration, Furholt argues that, ‘this interpretation of the patterns seems to overstate the explanatory powers of the PCA. The notion of a generally closer connection of Corded Ware individuals to Yamnaya individuals than the other Late Neolithic samples is much less clear in a different study using different samples connected to Corded Ware (Allentoft et al., Reference Allentoft, Sikora, Sjögren, Rasmussen, Rasmussen and Stenderup2015)’ (p. 8). PCA and ADMIXTURE are qualitative methods that are used to characterize the ancestry profiles of prehistoric individuals. All observations from PCA and ADMIXTURE are backed by formal statistics (f- and D-statistic, etc.), which are quantitative methods and which were described in detail in the respective papers. As such, formal admixture tests were carried out to explain the genetic profiles of Corded Ware-associated individuals and the likely source populations (e.g. Haak et al., Reference Haak, Lazaridis, Patterson, Rohland, Mallick and Llamas2015: Supplementary Information 7, page 75 onwards and Supplementary Information 9, page 101 onwards). The observed ancestry components as well as the positioning of Corded Ware individuals in principal component space are reliable and remain stable in all subsequent studies, which include these datapoints (e.g. Günther & Jakobsson, Reference Günther and Jakobsson2016; Jones et al., Reference Jones, Zarina, Moiseyev, Lightfoot, Nigst and Manica2017; Mittnik et al. Reference Mittnik, Wang, Pfrengle, Daubaras, Zariņa and Hallgren2017, http://biorxiv.org/content/early/2017/03/03/113241; Saag et al., Reference Saag, Varul, Scheib, Stenderup, Allentoft and Saag2017).

Finally, I would like to address Furholt's statement that ‘for example, in their Supplementary Information 2, Haak et al. (Reference Haak, Lazaridis, Patterson, Rohland, Mallick and Llamas2015) demonstrate that three individuals connected to the Pitted Ware culture in Sweden (taken from Skoglund et al., Reference Skoglund, Malmström, Raghavan, Storå, Hall and Willerslev2012) are clearly under that eastern genetic influence’ (p. 10). Supplementary Information 2 describes the mitochondrial DNA data. Individuals associated with the Pitted Ware show high proportions of mtDNA U4 and U5 lineages (~74%), which are very common among all Holocene hunter-gatherer individuals reported so far. This mtDNA profile thus equates to the blue component of the autosomal data and not to ‘steppe ancestry’ per se.

Overall, I welcome this opportunity of interaction and open discussion. It is important that archaeologists shed a critical light on the recent findings of archaeogenetics in order to put these into a balanced and well-contextualized perspective. Likewise, I am grateful for the opportunity to clarify a few technical aspects of our genetic work, which might relativize some of Furholt's arguments.

Although this paper is focused on the Corded Ware, it makes several excellent points about aDNA data and their interpretation in archaeology generally. This is a topic of obvious interest both to researchers and to the wider public, but archaeologists have been uncertain how to react to the flood of new information and the associated interpretations. On the one hand, genetics have been enthusiastically embraced as part of a third science revolution which will finally free us from self-absorbed theorizing and mere ‘storytelling’ (e.g. Kristiansen, Reference Kristiansen2014; Gerbault et al., Reference Gerbault, Allaby, Boivin, Rudzinski, Grimaldi and Pirs2017), but alongside the explicit critical voices (see e.g. Niklasson, Reference Niklasson2014) many colleagues have preferred to remain on the sidelines of the debate.

As Furholt points out, this is largely because they feel uncomfortable with the ‘Kossinna-like’ interpretative shorthand employed in such studies (see also Heyd, Reference Heyd2017). Also, assumptions inherent in the methodologies are often difficult to pinpoint and critique for those not familiar with statistical or genetic terminology. For instance, the closedness of the ‘populations’ under study, their internal homogeneity, and the timings and speed of gene flow are all far from proven (as Furholt recognizes), although they are written about with considerable assertiveness. Sometimes, the number of individuals taken as representative for a given ‘culture’ is extremely low and/or from a restricted area; and it is not yet possible to investigate trends over the whole duration of often long-lived cultural phenomena. As a result, we seem to be re-creating the internally homogenous and static ‘cultures’ which then need a revolutionary event to be transformed—the population revolution which goes with our science revolution in an increasingly hyperbolic rhetoric.

Furholt's paper takes an important and necessary step in highlighting the potential archaeological contribution to the mobility and migration debate. This is especially so because he does not stop at criticism, but sketches plausible alternatives to the scenarios proposed on the basis of genetic work. These can now be researched further. In particular, the idea that more mobile communities will be internally more heterogeneous and, therefore, materially more uniform is interesting and deserves to be compared with other case studies making similar points, for instance for the LBK (Hofmann, Reference Hofmann2016) or the lake village horizon (Ebersbach et al., Reference Ebersbach, Doppler, Hofmann and Whittle2017), and probably well beyond the Neolithic, too.

But there remains a general sense of dissatisfaction with how archaeological interpretations are generated by those outside the discipline. Even in times of inter- and increasingly trans- or even meta-disciplinarity, communication does not appear to be working terribly well, at least not at the scale beyond individual research projects (see e.g. Bánffy et al., Reference Bánffy, Brandt and Alt2012). Indeed, as social/‘soft’ and natural/‘hard’ scientists, we have caricatures of each other firmly in mind: one lot are fluffy storytellers, obsessed with details, who only claim to be worried about new results because they don't understand the maths, the other lot are boors, unaware of their own inbuilt subjectivity, who just want the fame of solving an age-old mystery, ideally on the front page of the right magazine. I'll leave you to figure out who's who.

Thus, although the entrenched oppositions between the humanities and sciences have been declared over (e.g. Robb, Reference Robb, Whittle and Bickle2014), the truce seems a little uneasy in places. This may not be a bad thing. Disagreements are, after all, fertile ground for new research endeavours. For the purposes of the present discussion, two aspects deserve to be drawn out.

First, to work together better, we need to find common concerns and vocabularies. From an archaeological perspective, if our theoretically aware models have been ignored, we are a little bit to blame ourselves. It is not just that, as Furholt outlines, some theoretically less enthusiastic archaeologists have continued to use cultures as an all-too-convenient shorthand. There has also been a tendency among some of those who do enjoy theorizing to remain aloof with regard to scientific approaches and to refrain from ‘big questions’ concerning ‘origins’, widespread material culture patterns, or convergent social trends at the continental or global scale. These topics brush over local nuance, which so many of us are accustomed to put centre-stage. Because geneticists, partly by training and partly due to the available data, tend to look at broad timescales and large regions, there is a mismatch of scales here.

This is only a problem if the genetic data as a palimpsest of timescales and regions are interpreted in terms of short-term ‘events’, but with a sketchy grasp of the details, or, indeed, if the increasingly detailed material entanglements archaeologists write about disregard a wider and potentially unsettling context. As Furholt points out, it should be possible for geneticists to write about scenarios other than an implicitly bloodthirsty replacement of one set of populations by another. Yet, by the same token, it should be possible to write narratives of power imbalance, exploitation, and upheaval within symmetrical, network, and similar approaches. As yet, the overwhelming majority of these (and I must admit this is largely an outsider's perspective) seem to prefer a cosier view. We have moved away from debates in which we passionately argued about the differences between people, things, and practices to writings in which all capacity for action is diffused across very complex but ultimately similar networks (or meshworks, etc.), largely ignoring the social constellations supporting them, including institutions, norms, and power relations (as criticized e.g. in Strathern, Reference Strathern1996; Glørstad, Reference Glørstad, Glørstad and Hedeager2008; Burmeister, Reference Burmeister2013). This lends itself most easily to narratives of sedate paces and steady flows, as for instance in Neolithisation debates (e.g. Cummings & Harris, Reference Cummings and Harris2011; Jones & Sibbesson, Reference Jones, Sibbesson, Alberti, Jones and Pollard2013) and recreates human actors as the ‘faceless blobs’ long critiqued in feminist writing (Tringham, Reference Tringham, Gero and Conkey1991: 94). It is good to have this comfort challenged, also to reveal the full potential of these theoretical approaches.

Second, power differentials are not just part of the pasts we study, but also of the research contexts within which we work. There is no point denying that, in the current climate, archaeologists feel very much like the junior partner, with funding and fame on the side of the geneticists. Joining in the debate more actively, therefore, holds the promise of considerable gains; but this does not mean that we have to act as mere sample providers and ‘culture consultants’. Instead, we must be genuinely interested in outcomes, find a vocabulary that makes sense to others and brings our concerns across clearly, and also stand by those concerns, even if they are temporarily unfashionable. Indeed, this kind of debate is something several archaeogeneticists explicitly value (e.g. see Haak's comments on this article).

One can only agree with Niklasson (Reference Niklasson2014: 59) that we need to question and critique the reasons archaeogenetics are so popular right now, and why these ‘facts’ are happily accepted within an otherwise allegedly facts-hostile climate. We must also continue to challenge the idea that greater simplification always makes better explanations (Gerbault et al., Reference Gerbault, Allaby, Boivin, Rudzinski, Grimaldi and Pirs2017; for criticism see e.g. Mizoguchi, Reference Mizoguchi2017: 20). As we are no longer in a position in which choosing a bottom-up instead of a top-down approach will gain anything, we have to argue clearly why diversity and internal complexity is the more fascinating question, at whatever scale (local community or ‘culture’) we are seeking the answer.

Judging from the controversies surrounding other newly introduced techniques (for instance, ¹⁴C-dating or strontium isotopes), we can expect that, after an initial phase of unbridled enthusiasm, it will become clear that the new technique does not serve easy answers up on a plate. That is the point at which common ground can be found, and it is a process we can actively initiate and shape. Papers like Furholt's are key first steps. My hope is that this will inspire more people from across the theoretical spectrum to incorporate the results of genetics explicitly into their own writings, identifying and working through alternative perspectives and scenarios. Then we'll have plenty to talk about.

In the present manuscript, the author revisits the contribution of recent ancient DNA studies to the knowledge of third millennium cal bc societies in Europe while stressing their main conceptual flaws. The main critique revolves around the equation of archaeological cultures and biological/genetic population distinctiveness, and three main aspects are highlighted: a) the (lack of) representativeness of the studied samples; b) the lack of biological/genetic homogeneity of the members of a particular archaeological culture; and c) the ambiguous use of the term migration in those publications.

I find this paper both timely and necessary. It comes at a time when the popularity of ancient DNA studies has transcended the scientific community to seize the holders of popular media in a time of economic and political instability, where the debate on immigration and its subsequent ramifications are on the table. Hopefully, this manuscript will serve as inspiration for a constructive dialogue between geneticists and archaeologists in the search for a more holistic and realistic interpretation of the dynamics of prehistoric populations.

One of the practices criticized by the author of this manuscript is the use of a handful of samples as representative of a whole period or archaeological culture, and he cites the four individuals from Esperstedt that signify the whole Corded Ware culture in Haak et al. (Reference Haak, Lazaridis, Patterson, Rohland, Mallick and Llamas2015) as an example. While this is a widespread practice in ancient DNA studies, it should be seen as a result of the limitations imposed by the small working sample size. It is important to highlight at this point that ancient DNA results are heavily constrained firstly by the availability of suitable samples and, ultimately, by their bio-molecular preservation. While this bias is insurmountable, it is our responsibility to recognize the limitations of the data, and I agree with the author that some of the cited papers have failed in adequately integrating the obtained genetic data with the evidence from other sources.

Turning into other sources of evidence to fill in the gaps and using the author's words ‘engagment with archaeological and anthropological theory’ (p. 4) is undoubtedly the right path to follow; however, I feel that much more can be done from the genetics side itself. Even with a limited sample size, two independent teams have reported that a new genetic component nearly absent in the preceding European populations appears in several individuals belonging to the Corded Ware culture, thus indicating an exogenous genomic influence during the third millennium cal bc (Allentoft et al., Reference Allentoft, Sikora, Sjögren, Rasmussen, Rasmussen and Stenderup2015; Haak et al., Reference Haak, Lazaridis, Patterson, Rohland, Mallick and Llamas2015). The questions to be answered are: 1) how much of the original genetic diversity that existed in these cultures has been captured by the studied samples; and 2) if a pan-cultural pattern can be inferred, as defended by the authors of these studies.

Ultimately, this leads us to the question of how the resolution of these studies can be improved. In my opinion, in a time where ancient genomic studies have gained considerable success due to new technical advances and a targeted sampling of certain skeletal elements, we should aim for a more complete chronological and geographical genetic dissection of the different cultural/populational sub-units as a way to assess the genetic substructure of these big cultural units (e.g. Corded Ware or Yamnaya). This can only be achieved through a combined effort of archaeologists and geneticists towards an informed sampling protocol followed by a holistic interpretation of the data.

During the time of revision of the present paper, interesting additions to the debate have been published. The most significant one is the work of Kristiansen et al. (Reference Kristiansen, Allentoft, Frei, Iversen, Johannsen and Kroonen2017) in Antiquity. In this paper, some of the authors of Allentoff et al. (Reference Allentoft, Sikora, Sjögren, Rasmussen, Rasmussen and Stenderup2015) re-theorize their original ‘massive migration’ hypothesis towards an integrative model that places more emphasis onto ‘social’ factors rather than on migration and assimilation to explain the observed connections between the Yamnaya and the Corded Ware people. This reworked version of the original paper incorporates some of the lacking “cultural and social elements to explain population history” and is more in line with the views of the author of this manuscript about a constant genetic flow between both cultural units, explained by Kristiansen et al. (Reference Kristiansen, Allentoft, Frei, Iversen, Johannsen and Kroonen2017) through a pattern of female exogamy.

However, the most revealing paragraph brings up a point that is also central to the present manuscript, the recognition that ‘the exact source [referring to the eastern genetic component found in the studied Corded Ware individuals] could have been another, yet unsampled group of people’ (Kristiansen et al., Reference Kristiansen, Allentoft, Frei, Iversen, Johannsen and Kroonen2017: 335). This illustrates very well some of the limitations of genetic data as a single predictor of past population movements. Ultimately, human population genetics needs to feed more strongly on other disciplines to be able to disentangle the biological, social, and cultural mechanisms behind the observed genetic patterns.

Hardly a single week seems to pass without the publication of another aDNA paper on later European prehistory, bringing its sense of repetition in terms of methods and, most worryingly, results and limited archaeological contextualization. And yet, despite the magnitude of this data-cascade, archaeological reactions remain comparatively limited and subdued (but see Hofmann, Reference Hofmann2014; Vander Linden, Reference Vander Linden2016). From this point of view, this important contribution by Martin Furholt, and the decision by the EJA editorial team to attach to it a full discussion, must be applauded. Obviously, the relevance of Furholt's piece reaches well beyond its mere existence and lies first and foremost in its intrinsic quality and the key points it raises.

Furholt rightly stresses the uncomfortable position of archaeologists regarding aDNA. On the one hand, here is a method which demonstrates exquisite technical refinements, but, on the other hand, its interpretations are plagued, at least to the archaeologist's trained eye, by an outdated framework which treats migrations as securely identified historical events to be mapped and documented, rather than explained and understood. Even if these papers are published in the highest-ranking journals, one is left with the uneasy feeling that, in archaeological terms, very little has actually been learned. Whether for the Early or the Late European Neolithic, the existence of migrating populations has indeed been long suspected; although, as any student of our discipline knows all too well, their exact role in explaining change in past human societies has been systematically minimized since the 1960s.

The point is simple. As processual archaeology rose from the ashes of the pyre it had set on migration, the topic became, until relatively recently, a no-go area for most archaeologists. Furholt might be able to invoke several key papers when advocating a more complex take on migration, but the field remains in its infancy. Likewise, the excessive liberty taken by geneticists with archaeological cultures reflects, in a distorted way, the unease of our discipline with this core concept and, beyond that, how poor we generally are at describing material variability, let alone interpreting it (see Shennan, Reference Shennan2013). All in all, Furholt's outlook reflects the state of uncertainty where the discipline has been lingering for too long.

In many respects, thus, we created a void waiting to be filled, which geneticists did on the back of undeniable technical prowess. This being said, it is obvious that geneticists do not engage that much with archaeology and archaeologists, the latter often appearing as passive sample providers rather than active intellectual contributors in these publications. At the core of the problem lies the assumed identity between biological populations and archaeological cultures, both considered as expressions of coherent, self-bounded units, a fallacy denounced fifteen years ago when modern DNA was hailed as revolutionary (e.g. MacEachern, Reference Maceachern2000). Two simple points, also made by Furholt, demonstrate the negative impact of this simplistic and false assumption.

Firstly, aDNA papers often stem from a limited number of samples, from which any pattern is then generalized across the entire geographical and temporal extent of the corresponding archaeological culture. The nature of aDNA data partly overcomes this problem (Li & Durbin, Reference Li and Durbin2011) and further—hopefully more systematic—sampling will by definition improve the resolution. However, the limitations of this approach are obvious as the narrow range of samples does not allow one to explore possible differences within the geographical and temporal lapse of a given archaeological culture. Secondly, the question of relatedness between populations is central to the genetic entreprise, and reflected in ADMIXTURE and PCA graphs which provide statistically-informed depictions of this measure. The reasons for this preference lie deeply in the project of describing and understanding the variation of the modern Europe genetic variation. The difficulty lies when one attempts to translate biological relatedness in social terms, materialized by archaeological artefacts. This tension is well exemplified when genetic relations between central and eastern European third millennium bc samples are linked to corresponding material affinities between the Yamnaya and Corded Ware complexes while, as Furholt elegantly reminds us, the latter is pretty much typologically-related to all archaeological cultures before, after, and around it.

The above remarks arguably stem from a genuine lack of archaeological sophistication in most aDNA papers, in many ways repeating and prolonging the mistakes made by archaeologists for several decades. Are we thus in a theoretical impasse? Or is it that aDNA can only provide information with which we cannot do much? Most surely not. The bulk of the work has, so far, been carried out in a deceptively empirical way, taking advantage of a so-called golden phase where each sample is bound to tell us something that we by definition did not know about the genetic make-up of past populations. This strategy, while efficient in the short term, is hardly sustainable. The only viable alternative lies in complex hypotheses, informed and tested by several categories of evidence, all considered on equal footings.

Population history, including migration, provides a robust framework for such hypotheses to be elaborated. Indeed, the main result gained from aDNA, as well as from other studies, is that Neolithic populations were in constant flux, as suggested by ever-changing levels of admixture. This simple observation opens countless possibilities for future research. For instance, reading the literature, one can be left with the impression that the Early and Late Neolithic migration events were interchangeable, while they obviously happened under different demographic regimes, under different logistics, that is, in fundamentally different ways. Were small or large groups moving? Did the migration involve all categories of people, or were they sex-biased? Both questions can partly be answered by bioinformatic treatments of the data (e.g. Pemberton et al., Reference Pemberton, Absher, Feldman, Myers, Rosenberg and Li2012; Goldberg et al., Reference Goldberg, Günther, Rosenberg and Jakobsson2017). Further fine-grained structure in these migrations will, without doubt, be unravelled by re-examining in parallel the aDNA and wider archaeological records. However, when doing so, and as hinted at by Furholt, we need to drive away from our implicit will to align neatly all signals to write simple, elegant, yet inherently faulty narratives. Genes and material culture, in their own complexity, do not operate in the same spheres of action, nor do they unfold upon the same spatial and temporal scales. We need to take advantage of their respective complexity to test alternative hypotheses, and get towards a more textured representation of the past.

To conclude, aDNA is, without any doubt, a fantastic technique, whose amazing potential we only begin to grasp. It is, however, worth remembering that this potential only applies to a narrow part of the archaeological agenda (e.g. Kintigh et al., Reference Kintigh, Altschul, Beaudry, Drennan, Kinzig and Kohler2014) and will only be unfolded by testing proper hypotheses, rather than chasing ghosts of our discipline's past. Of all social sciences, archaeology has assuredly the best track record at inter-disciplinarity and, thus, at overcoming a range of responses from extreme confidence to total disenchantment with new techniques. In this sense, the difficulties we encounter with aDNA are hardly new. Let us just not forget that any improvement will not simply come from ‘us’ teaching ‘them’, but also from us giving a hard look at ourselves in the mirror.

The comments from two archaeologists and two geneticists represent a spectrum of critique, approval, and extension of the main issues discussed in my article, and will hopefully help to push forward the necessary interdisciplinary dialogue. Wolfgang Haak defends his view that the data indicate a rather rapid migration process that would coincide with the beginning of the Corded Ware, arguing that the ever-increasing number of samples has now confirmed that all individuals connected to Corded Ware so far analysed have steppe ancestry, while those connected to the slightly earlier Globular Amphora Complex do not. Of course, it is not impossible that the first appearance of steppe ancestry in central Europe coincides sharply with the first appearance of Corded Ware, and I have no problem with this interpretation, as long as it is empirically proven. What I criticize in my paper is the presupposition of a biological similarity of individuals connected to specific units of archaeological material. This is a premise that derives from and feeds into an unholy reification and biologisation of cultures as closed and homogeneous social units. More importantly, it is empirically false. Looking at the clusters of samples on the PCA in Figure 2 (i.e. the Early/Middle Neolithic cluster or the Late Neolithic/Steppe ancestry cluster), one can see that they contain a mix of samples associated to different archaeological cultures. This is even more obvious in the newer, updated versions of the same PCA (i.e. Mathieson et al., Reference Mathieson, Alpaslan Roodenberg, Posth, Szécsényi-Nagy, Rohland and Mallick2017: fig. 1). These clusters represent units in space and time (i.e. sixth to fourth millennia bc in southern and central Europe, or third and second millennia bc in central Europe); they do not differentiate between archaeological cultures. Clearly, by the third millennium cal bc, a major change in the genetic pool of central Europe has taken place; but the data do not, at present, suggest a very rapid, event-like process. Nine individuals from two sites connected to Globular Amphora from Poland and Ukraine without steppe ancestry do not adequately represent the entire pre-Corded Ware situation in Europe. As I argue in the article, and as was recently stressed by Volker Heyd (Reference Heyd2017) archaeologically, steppe influence, which is visible in burial rites among other practices, can be traced back to the fifth millennium cal bc in south-eastern Europe and the Carpathian basin; and it clearly played an important role during the fourth millennium cal bc in different parts of Europe. The study Haak mentions (Mathieson et al., Reference Mathieson, Alpaslan Roodenberg, Posth, Szécsényi-Nagy, Rohland and Mallick2017) also presents two individuals from Bulgaria who date to the fifth millennium cal bc (Varna I and Smyadovo) and show a stronger steppe ancestry component in the ADMIXTURE plot. All this indicates the possibility of a deeper, longer-term history of interaction, characterized by regular and repeated human movement between the steppes and south-eastern and central Europe, instead of a rapid, massive migration event.

However, to move forward it is not enough to dissect the details of every data point and archaeological observation. It is about creating a better interdisciplinary discussion. Daniela Hofmann's commentary broadens the perspective of the scientific and social context in which this discussion should be viewed. She targets the apparent opposition between broad-stroke narratives and detailed critiques. The assessment of regional and diachronic patterns should go hand in hand with the exploration of local and historical variability. I agree with her argument that both the top-down and the bottom-up perspectives would profit from a more direct engagement with real social processes, which involve active individuals, social norms, institutions, and power relations. Without such an engagement ‘migration’ will remain a hollow phrase. This resonates well with Marc Vander Linden's call for more elaborated migration scenarios, testing of complex hypotheses, and the exploration of the social consequences of mobility for prehistoric communities. Vander Linden rightly warns us against the tendency to choose the simplest possible explanation of a set of data.

However, as Eva Fernández-Domínguez makes clear, the geneticists also have to deliver in order to enable a more sophisticated interdisciplinary discussion, be more aware of the limitations of their datasets, and take seriously the conceptual pitfalls—sample size, the reification of cultures, ambiguous use of the term migration—and work on ways to avoid them through a more intensive collaboration across disciplinary borders. She positively evaluates the new paper by Kristiansen et al. (Reference Kristiansen, Allentoft, Frei, Iversen, Johannsen and Kroonen2017) as an example of a more elaborated re-theorization of the Allentoft et al. (Reference Allentoft, Sikora, Sjögren, Rasmussen, Rasmussen and Stenderup2015) migration narrative. This new scenario—Corded Ware being formed as a consequence of migration of individuals with steppe ancestry into central Europe, followed by interaction with local individuals, adaptation, admixture, and hybridization—is a hypothesis that can be tested against the biomolecular and archaeological datasets. For example, in such a scenario, we should expect to find steppe ancestry in central Europe connected to pre-Corded Ware archaeological complexes. Yet, to return again to Hofmann's and Vander Linden's commentaries, although Kristiansen et al. (Reference Kristiansen, Allentoft, Frei, Iversen, Johannsen and Kroonen2017) provide an appealing broad-stroke narrative, and propose concrete social mechanisms (female exogamy), it is a one-size-fits-all approach that should be elaborated by incorporating a stronger acknowledgement of and emphasis on local variability and potentially different social mechanisms that are strongly suggested by the variability visible in the archaeological record.

Although discussions of these topics are already gaining speed, we still have a long way to go until we will have developed an anthropologically informed integration of bio-molecular and archaeological data, yielding an identification of realistic social processes. While a stronger bottom-up component is surely crucial, we should also explore a broader range of anthropologically studied mechanisms of mobility, migration, and population circulation, and systematically explore the ways in which such phenomena are discernible by studying the archaeological record and genetic datasets.