Directly modelling population dynamics in the South American Arid Diagonal using ¹⁴ C dates

Abstract

Large anthropogenic 14 C datasets are widely used to generate summed probability distributions (SPDs) as a proxy for past human population levels. However, SPDs are a poor proxy when datasets are small, bearing little relationship to true population dynamics. Instead, more robust inferences can be achieved by directly modelling the population and assessing the model likelihood given the data. We introduce the R package ADMUR which uses a continuous piecewise linear (CPL) model of population change, calculates the model likelihood given a 14 C dataset, estimates credible intervals using Markov chain Monte Carlo, applies a goodness-of-fit test, and uses the Schwarz Criterion to compare CPL models. We demonstrate the efficacy of this method using toy data, showing that spurious dynamics are avoided when sample sizes are small, and true population dynamics are recovered as sample sizes increase. Finally, we use an improved 14 C dataset for the South American Arid Diagonal to compare CPL modelling to current simulation methods, and identify three Holocene phases when population trajectory estimates changed from rapid initial growth of 4.15% per generation to a decline of 0.05% per generation between 10 821 and 7055 yr BP, then gently grew at 0.58% per generation until 2500 yr BP. This article is part of the theme issue ‘Cross-disciplinary approaches to prehistoric demography’.

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

“…Furthermore, because such an approach effectively implies as many observation points as the number of years in the window of analyses, the actual number of radiocarbon samples is not formally taken into consideration. The ultimate consequence is that statistical measures such as standard errors of fitted parameters, p-values, and likelihood estimates (and derived statistics such as AIC) are biased [10] .…”

“…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].…”

“…As others have already recently noted [10,31] this is unwarranted, as it simultaneously ignores sampling error and calibration effects. This paper presents a new approach that addresses these concerns by considering the problem to be similar to the objectives and principles of Bayesian phase modelling [44][45][46].…”

Archaeology, demography and life history theory together can help us explain past and present population patterns

“…The so-called 'Cologne Protocol' developed by Zimmermann and colleagues and represented here by the papers of Schmidt et al [3] and Lundström et al [25] takes a rigorously defined spatial approach at different scales, producing successive snapshots of scaledependent population patterns that aim to estimate absolute and not just relative population densities. Moreover, like Timpson et al [35], Schmidt et al provide the computational tools to make their methods available; it can be anticipated that they will be widely taken up.…”

“…McLaughlin et al's study of Atlantic Iberia provides a very good example of this, using a variety of lines of evidence to show how a series of environmental fluctuations was linked to lagged population changes, while the formation of new maritime environments after 8.2 kya provided productive resources that had not previously existed, whose exploitation led to major population growth [31]. In a similar vein, Timpson et al show that the phase of rapid population growth in the South American Arid Diagonal was associated with expansion into a new niche [35]. The following phase, on the other hand, corresponds to an effective equilibrium lasting 4000 years.…”