The Great Hungarian Plain was a crossroads of cultural transformations that have shaped European prehistory. Here we analyse a 5,000-year transect of human genomes, sampled from petrous bones giving consistently excellent endogenous DNA yields, from 13 Hungarian Neolithic, Copper, Bronze and Iron Age burials including two to high (~22 × ) and seven to ~1 × coverage, to investigate the impact of these on Europe’s genetic landscape. These data suggest genomic shifts with the advent of the Neolithic, Bronze and Iron Ages, with interleaved periods of genome stability. The earliest Neolithic context genome shows a European hunter-gatherer genetic signature and a restricted ancestral population size, suggesting direct contact between cultures after the arrival of the first farmers into Europe. The latest, Iron Age, sample reveals an eastern genomic influence concordant with introduced Steppe burial rites. We observe transition towards lighter pigmentation and surprisingly, no Neolithic presence of lactase persistence.

The importance of chronology is reasserted as a means to achieving history and a sense of temporality. A range of current methods for estimating the dates and durations of archaeological processes and events are considered, including visual inspection of graphs and tables of calibrated dates and the summing of the probability distributions of calibrated dates. These approaches are found wanting. The Bayesian statistical framework is introduced, and a worked example presents simulated radiocarbon dates as a demonstration of the explicit, quantified, probabilistic estimates now possible on a routine basis. Using this example, the reliability of the chronologies presented for the five long barrows considered in this series of papers is explored. It is essential that the ‘informative’ prior beliefs in a chronological model are correct. If they are not, the dating suggested by the model will be incorrect. In contrast, the ‘uninformative’ prior beliefs have to be grossly incorrect before the outputs of the model are importantly wrong. It is also vital that the radiocarbon ages included in a model are accurate, and that their errors are correctly estimated. If they are not, the dating suggested by a model may also be importantly wrong. Strenuous effort and rigorous attention to archaeological and scientific detail are inescapable if reliable chronologies are to be built. The dates presented in the following papers are based on models. ‘All models are wrong, some models are useful’ (Box 1979, 202). We hope readers will find them useful, and will employ ‘worry selectivity’ to determine whether and how each model may be importantly wrong. The questions demand the timetable, and our prehistories deserve both.

Community differentiation is a fundamental topic of the social sciences, and its prehistoric origins in Europe are typically assumed to lie among the complex, densely populated societies that developed millennia after their Neolithic predecessors. Here we present the earliest, statistically significant evidence for such differentiation among the first farmers of Neolithic Europe. By using strontium isotopic data from more than 300 early Neolithic human skeletons, we find significantly less variance in geographic signatures among males than we find among females, and less variance among burials with ground stone adzes than burials without such adzes. From this, in context with other available evidence, we infer differential land use in early Neolithic central Europe within a patrilocal kinship system.

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Perhaps nowhere in European prehistory does the idea of clearly-defined cultural boundaries remain more current than in the initial Neolithic, where the southeast–northwest trend of the spread of farming crosses what is perceived as a sharp divide between the Balkans and central Europe. This corresponds to a distinction between the Vinča culture package, named for a classic site in Serbia, with its characteristic pottery assemblage and absence of longhouses, and the Linearbandkeramik (LBK), with equally diagnostic but different pottery, and its apparently culturally-diagnostic longhouses, extending in a more northerly belt through central Europe westward to the Dutch coast. In this paper we question the concept of such a clear division through a presentation of new data from the site of Szederkény-Kukorica-dűlő. A large settlement in southeast Transdanubia, Hungary, excavated in advance of road construction, Szederkény is notable for its combination of pottery styles, variously including Vinča A, Ražište and LBK, and longhouses of a kind otherwise familiar from the LBK world. Formal modelling of its date establishes that the site probably began in the later 54th century cal BC, lasting until the first decades of the 52nd century cal BC. Occupation, featuring longhouses, pits and graves, probably began at the same time in the eastern and western parts of the settlement, starting a decade or two later in the central part; the western part was probably the last to be abandoned. Vinča pottery is predominantly associated with the eastern and central parts of the site, and Ražište pottery with the west. Formal modelling of the early history of longhouses in the LBK world suggests their emergence in the Formative LBK of Transdanubia c. 5500 cal BC followed by rapid dispersal in the middle of the 54th century cal BC, associated with the ‘earliest’ (älteste) LBK. The adoption of longhouses at Szederkény thus appears to come a few generations after the start of this ‘diaspora’. Rather than explaining the mixture of things, practices and perhaps people at Szederkény with reference to problematic notions such as hybridity, we propose instead a more fluid and varied vocabulary, encompassing combination and amalgamation, relationships and performance in the flow of social life, and networks; this makes greater allowance for diversity and interleaving in a context of rapid change.