a b s t r a c tIn a previous study we presented a new method that used summed probability distributions (SPD) of radiocarbon dates as a proxy for population levels, and Monte-Carlo simulation to test the significance of the observed fluctuations in the context of uncertainty in the calibration curve and archaeological sampling. The method allowed us to identify periods of significant short-term population change, caveated with the fact that around 5% of these periods were false positives. In this study we present an improvement to the method by applying a criterion to remove these false positives from both the simulated and observed distributions, resulting in a substantial improvement to both its sensitivity and specificity. We also demonstrate that the method is extremely robust in the face of small sample sizes. Finally we apply this improved method to radiocarbon datasets from 12 European regions, covering the period 8000e4000 BP. As in our previous study, the results reveal a boom-bust pattern for most regions, with population levels rising rapidly after the local arrival of farming, followed by a crash to levels much lower than the peak. The prevalence of this phenomenon, combined with the dissimilarity and lack of synchronicity in the general shapes of the regional SPDs, supports the hypothesis of endogenous causes.

Recent advances in the use of summed probability distribution (SPD) of calibrated 14C dates have opened new possibilities for studying prehistoric demography. The degree of correlation between climate change and population dynamics can now be accurately quantified, and divergences in the demographic history of distinct geographic areas can be statistically assessed. Here we contribute to this research agenda by reconstructing the prehistoric population change of Jomon hunter-gatherers between 7,000 and 3,000 cal BP. We collected 1,433 14C dates from three different regions in Eastern Japan (Kanto, Aomori and Hokkaido) and established that the observed fluctuations in the SPDs were statistically significant. We also introduced a new non-parametric permutation test for comparing multiple sets of SPDs that highlights point of divergences in the population history of different geographic regions. Our analyses indicate a general rise-and-fall pattern shared by the three regions but also some key regional differences during the 6th millennium cal BP. The results confirm some of the patterns suggested by previous archaeological studies based on house and site counts but offer statistical significance and an absolute chronological framework that will enable future studies aiming to establish potential correlation with climatic changes.

The last decade has seen the development of a range of new statistical and computational techniques for analysing large collections of radiocarbon (14C) dates, often but not exclusively to make inferences about human population change in the past. Here we introduce rcarbon, an open-source software package for the R statistical computing language which implements many of these techniques and looks to foster transparent future study of their strengths and weaknesses. In this paper, we review the key assumptions, limitations and potentials behind statistical analyses of summed probability distribution of 14C dates, including Monte-Carlo simulation-based tests, permutation tests, and spatial analyses. Supplementary material provides a fully reproducible analysis with further details not covered in the main paper.

Summary In this study we compare the genetic ancestry of individuals from two as yet genetically unstudied cultural traditions in Estonia in the context of available modern and ancient datasets: 15 from the Late Bronze Age stone-cist graves (1200–400 BC) (EstBA), and 6 from the Pre-Roman Iron Age tarand cemeteries (800/500 BC–50 AD) (EstIA). We also included 5 Pre-Roman to Roman Iron Age Ingrian (500 BC–450 AD) (IngIA) and 7 Middle Age Estonian (1200–1600 AD) (EstMA) individuals to build a dataset for studying the demographic history of the northern parts of the Eastern Baltic from the earliest layer of Mesolithic to modern times. Our findings are consistent with EstBA receiving gene flow from regions with strong Western hunter-gatherer (WHG) affinities, and EstIA from populations related to modern Siberians. The latter inference is in accordance with Y chromosome (chrY) distributions in present-day populations of the Eastern Baltic, as well as patterns of autosomal variation in the majority of the westernmost Uralic speakers [1–5]. This ancestry reached the coasts of the Baltic Sea no later than the mid-first millennium BC; i.e. in the same time window as the diversification of west Uralic/Finnic languages [6]. Furthermore, phenotypic traits often associated with modern Northern Europeans like light eyes, hair and skin as well as lactose tolerance can be traced back to the Bronze Age in the Eastern Baltic.

Summed probability distributions of radiocarbon dates are an increasingly popular means by which to reconstruct prehistoric population dynamics, enabling more thorough cross-regional comparison and more robust hypothesis testing, for example with regard to the impact of climate change on past human demography. Here we review another use of such summed distributions -to make spatially explicit inferences about geographic variation in prehistoric populations. We argue that most of the methods proposed so far have been strongly biased by spatially varying sampling intensity, and we therefore propose a spatial permutation test that is robust to such forms of bias and able to detect both positive and negative local deviations from pan-regional rates of change in radiocarbon date density. We test our method both on some simple, simulated population trajectories and also on a large real-world dataset, and show that we can draw useful conclusions about spatio-temporal variation in population across Neolithic Europe. Highlights• Spatial analyses of radiocarbon dates are reviewed.• A new method for detecting hot-spots and cold-spots in the temporal change of radiocarbon density is proposed. • The method is tested with simulated data and a case study from Neolithic Europe.• Results of the case study depict a front of sharp demographic growth linked to the expansion of farming. • The method is available as part of the R statistical package rcarbon.