End-to-end Bayesian analysis of¹⁴C dates reveals new insights into lowland Maya demography

Abstract

<jats:title>ABSTRACT</jats:title><jats:p>Archaeologists and demographers increasingly employ aggregations of published radiocarbon (<jats:sup>14</jats:sup>C) dates as demographic proxies summarizing changes in human activity in past societies. Presently, summed probability densities (SPDs) of calibrated radiocarbon dates are the dominant method of using <jats:sup>14</jats:sup>C dates to reconstruct demographic trends. Unfortunately, SPDs are incapable of converging on their true generating distributions even as the number of observations gets large. To overcome this problem, we propose a more principled alternative that combines finite mixture models and Bayesian inference to identify the generating distribution of a set of radiocarbon dates. Numerical simulations and an assessment of the statistical identifiability of our method demonstrate that it correctly converges on the generating distribution. We apply this novel end-to-end Bayesian approach to reconstruct prehistoric Maya demographic growth using a recently compiled Mesoamerican radiocarbon database. Our results show that the Maya Lowlands experienced a century of rapid growth rates (1%) during the Late Classic, followed by a rapid decrease in population during the Terminal Classic, and a subsequent more-modest resurgence in population during the Postclassic. Additionally, a detailed population reconstruction of the important political center of Tikal verifies that slow population growth between the Preclassic and Early Classic gave pace to rapid growth starting around AD 500 and peaking at the beginning of the eight century. Our proposed method verifies previous reconstructions based on settlement patterns and ceramics, but with far more precise time-resolution and characterization of uncertainty than has been possible.</jats:p>

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

“…Many of these applications directly utilise SPDs as a dependent variable, and as such estimates do not account for sampling error or calibration effects, potentially leading to biased estimates particularly when dealing with smaller sample sizes and shorter time intervals. As for the Monte-Carlo NHST approaches, off-the-shelf solutions are hardly applicable in these cases, and bespoke solutions are required [10,11,88]. [37] introduces a trade-off where one needs to sacrifice any evidence of inter-site size variation [8].…”

“…A second approach to SPD analysis involves the direct reconstruction of the shape of the underlying time-frequency distribution through non-parametric Bayesian models. Examples of this category are Bayesian KDE [7] and Gaussian mixture approaches [11] (see also BchronDensity function in the Bchron R package [53]). While these examples differ in key details, they fundamentally share the same objective of inferring the shape of the underlying population distribution whilst acknowledging the uncertainty associated with sampling and calibration.…”

“…The main advantage is that no explicit hypotheses and assumptions are required, and the resulting output can replace the visual assessment of SPDs. While some parameters, such as growth rates for user-defined intervals, can be extracted from the model [11], these approaches are limited if one wishes to examine the impact of covariates [15] or compare alternative growth models derived from explicit theoretical principles [40,43].…”

“…Radiocarbon dates have been used as a proxy for studying past human population dynamics for over 30 years, but the last few years saw an exceptional increase in the number of studies thanks to the broader availability and accessibility of large collection 14 C dates (e.g. [1][2][3][4][5][6]) as well as dedicated software packages enabling the use of an array of new statistical approaches [7][8][9][10][11][12]. The opportunities offered by this growth are unquestionable [13]; we are no longer constrained by the arbitrary limits of regional relative chronologies, we can test the supposed role of climate change on demographic processes [14][15][16][17][18][19][20][21] and pursue comparative studies at continental [22][23][24][25][26] or even global scales [27].…”

“…More formal statistical treatment of radiocarbon dates are clearly necessary for proper inference, and while there have been a substantially large number of studies, time-frequency of radiocarbon dates have been generally analysed in three ways: 1) using Monte-Carlo simulation or random permutation techniques to carry out basic null hypothesis significance testing [22,37,38]; 2) fitting Bayesian non-parametric models to reconstruct the underlying 'shape' of the probability distribution of the 14 C dates [7,11] ; and 3) employing conventional statistical methods (e.g. correlation and regression analyses, information-criterion based model comparison, etc.)…”