Large anthropogenic ¹⁴C 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 ¹⁴C 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 ¹⁴C 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’.

大型人为¹⁴ C 数据集被广泛用于生成总概率分布 (SPD) 作为过去人口水平的代表。然而，当数据集较小时，SPD 是一个很差的代理，与真实的人口动态关系不大。相反，可以通过直接对总体建模并评估给定数据的模型可能性来实现更稳健的推断。我们介绍了 R 包 ADMUR，它使用人口变化的连续分段线性 (CPL) 模型，计算给定^{14的模型似然度}C 数据集，使用马尔可夫链蒙特卡罗估计可信区间，应用拟合优度检验，并使用 Schwarz 准则比较 CPL 模型。我们使用玩具数据证明了这种方法的有效性，表明当样本量较小时可以避免虚假动态，并且随着样本量的增加，真实的总体动态会得到恢复。最后，我们使用改进的南美干旱对角线¹⁴ C 数据集来比较 CPL 建模与当前模拟方法，并确定三个全新世阶段，当人口轨迹估计从每代 4.15% 的快速初始增长变为每代 0.05% 的下降时在 10 821 到 7055 年 BP 之间产生一代，然后以每代 0.58% 的速度缓慢增长，直到 2500 年 BP。

本文是主题问题“史前人口学的跨学科方法”的一部分。