Two co-authored articles in Nature (Haak et al., 2015; Allentoft et al., 2015) caused a sensation. They revealed genetically the mass migration of steppe Yamnaya culture people in the Early Bronze Age to central and northern Europe. The authors considered this event as the basis of the spread of Indo-European languages. In response, the Russian archaeologist, Leo S. Klejn, expresses critical remarks on the genetic inference, and in particular its implications for the problem of the origins of Indo-European languages. These remarks were shown to the authors and they present their objections. Klejn, however, has come to the conclusion that the authors’ objections do not assuage his doubts. He analyses these objections in a further response.

The concept of a temporal phylogenetic network is a mathematical model of evolution of a family of natural languages. It takes into account the fact that languages can trade their characteristics with each other when linguistic communities are in contact, and also that a contact is only possible when the languages are spoken at the same time. We show how computational methods of answer set programming and constraint logic programming can be used to generate plausible conjectures about contacts between prehistoric linguistic communities, and illustrate our approach by applying it to the evolutionary history of Indo-European languages.