A Bayesian approach for fitting and comparing demographic growth models of radiocarbon dates: A case study on the Jomon-Yayoi transition in Kyushu (Japan)

Abstract

Large sets of radiocarbon dates are increasingly used as proxies for inferring past population dynamics and the last few years, in particular, saw an increase in the development of new statistical techniques to overcome some of the key challenges imposed by this kind of data. These include: 1) null hypothesis significance testing approaches based on Monte-Carlo simulations or mark permutations; 2) non-parametric Bayesian modelling approaches, and 3) the use of more traditional techniques such as correlation, regression, and AIC-based model comparison directly on the summed probability distribution of radiocarbon dates (SPD). While the range of opportunities offered by these solutions is unquestionably appealing, they often do not consider the uncertainty and the biases arising from calibration effects or sampling error. Here we introduce a novel Bayesian approach and nimbleCarbon, an R package that offers model fitting and comparison for population growth models based on the temporal frequency data of radiocarbon dates. We evaluate the robustness of the proposed approach on a range of simulated scenarios and illustrate its application on a case study focused on the demographic impact of the introduction of wet-rice farming in prehistoric Japan during the 1st millennium BCE.

Bayesian analyses question the role of climate in Chulmun demography

“…0.06% and -0.05% in the coastal region. The rate of past population changes in both regions is within the range of changes seen in other case studies on past populations 22 , 38 , 42 .

Figure 2 Marginal posterior distribution of growth rates r 1 and r 2 and change-point c for the inland and coastal radiocarbon dates.

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“…We fitted a truncated double-exponential growth model 22 using the nimbleCarbon package 37 to estimate the growth rates and identify the start-point of the decline in the density of 14 C dates between 7,000 and 3,000 cal. BP.…”

“…One such issue is the intrinsic uncertainty associated with these curves that arises from a combination of different errors, namely, sampling, radiometric measurement, and calibration. As a result, it has been noted that visual inspections of SPD values should be carried out with caution, and more importantly, ‘direct’ statistical analyses of SPD values should be avoided as they do not account for the different forms of uncertainties associated with the 14 C data 19 , 21 , 22 .…”

“…We consider the possibility that the mobile hunter-gathering tradition, prevalent in the coastal regions before the Middle Chulmun, may have lingered and contributed to regional variations in the population decline pattern toward the Late/Final phase. To check this possibility, we fit a truncated double-exponential hierarchical Bayesian model 22 to the 14 C frequency data of the two regions. Fitted parameters of the double-exponential model provide the estimated rates of growth in the two regions, as well as the timing of when the population trend reversed from positive to negative growth rates.…”

The spread of agriculture in Iberia through Approximate Bayesian Computation and Neolithic projectile tools

“…Focusing on the chronological matrix, because we are working on calibrated dates, choosing one single date to represent a site can be tricky. One option is to choose an average of the calibrated date [ 53 ], while for the construction of diachronic models, more sophisticated options, such as the use of Bayesian hierarchic models have been proposed [ 91 ]. However, and accounting for the fact that in this case we are focusing on a single calibrated date per site, we have decided to sample the calibrated date from the probability distribution of the calibration of the BP date.…”