We thank K. Magnussen, L. Petersen, C. Mortensen and A. Seguin-Orlando at the Danish National Sequencing Centre for producing the analysed sequences; P. Reimer and S. Hoper at the 14Chrono Center Belfast for providing accelerator mass spectrometry dating; S. Hackenbeck for discussing palaeodietary reconstructions; D. Christiansen Appelt, B. Heyerdahl, the Explico Foundation team, J. Isakova, B. Daulet, A. Tairov, N. Abduov, B. Tudiyarov, V. Volkov, M. Akchurin, I. Baimukhan, N. Namdakov, Y. Yusupov, E. Ramankulov, A. Nurgaziyev and A. Kusaev for important assistance in fieldwork; J. Stenderup, P. V. Olsen and T. Brand for technical assistance in the laboratory; all involved archaeologists, historians and geographers from Kazakhstan: A. Suslov, I. Erofeeva, E. Nurmaganbetov, B. Kozhakhmetov, N. Loman, Y. Parshin, S. Ladunskiy, M. Bedelbaeva, A. Marcsik, O. Gábor, M. Půlpán, Y. Kubeev, R. Zhumashev, K. Omarov, S. Kasymov and U. Akimbayeva; P. Rodzianko for creating the initial contact between P.d.B.D., S.E. and E.U.; and S. Jacobsen and J. O’Brien for translating and proofreading Russian contributions. E.W. thanks St. John’s College, Cambridge for support and for providing an environment facilitating scientific discussions. B.Boldg. thanks the Taylor Family-Asia Foundation Endowed Chair in Ecology and Conservation Biology. The project was funded by the Danish National Research Foundation (E.W.), the Lundbeck Foundation (E.W.) and KU2016 (E.W.).

Reviewer information

Nature thanks T. Higham, D. Anthony, B. Shapiro, R. Dennell and the other anonymous reviewer(s) for their contribution to the peer review of this work.