In contrast with these possible explanations, we note that a growth rate of 0

Increased sedentism has also been proposed as an explanation for this late phase of growth , and while a decrease in residential mobility has been proposed in the Atacama desert of northern Chile around 7 kyr BP coinciding with our observed population growth at 7055 yr BP, there also appears to be much regional heterogeneity in mobility and, for instance, there is little to no evidence of increased sedentism in large areas of the SAAD at this time, including Patagonia [50,82].

58% per generation (95% CI = 0.42–0.81) is not unusually high, and is instead broadly consistent with (indeed slightly lower than) the global estimates of 1% per generation (0.04% per year) for broadscale background Holocene population growth . Zahid et al. proposed that this background growth rate is a global phenomenon occurring irrespective of the local environment or subsistence strategy and is, therefore, intrinsic to our species, arguing that it is likely to be related to the global climate and/or endogenous biological factors.

14. Conclusion

While current SPD simulation methods provide a robust statistical framework to test a single null hypothesis, successfully rejecting the null offers the researcher little in the way of drawing an inference about true population dynamics, and this inferential vacuum is often filled with overinterpretation of peaks and troughs in SPDs. Furthermore, rejection of the simple exponential model of constant background growth has become so common that it is no longer tenable to use a classical hypothesis test that heavily favours this null. Instead, we argue that a model selection approach is more appropriate. By including the exponential in the model selection process, there is still the opportunity for this model to be selected, but unlike current simulation methods that can only reject (or fail to reject) an ‘assumed correct’ model, CPL modelling automatically provides a best explanation. The structure of the CPL model provides meaningful and useful date estimates of historic events, relative population levels and growth rates, avoids overfitting, and the GOF test quantitively checks if the data are reasonable, given the model. Together, these methods provide a solid inferential framework for evaluating prehistoric population dynamics from 14 C datasets of any size, and naturally avoids the overinterpretation that is common with SPD analysis.

Our SAAD case study provides a demonstration of the need for this more robust inferential methodology. A substantial body of literature has grown to support a claim of mid-Holocene population fluctuations, based on the misinterpretation of the available 14 C data and the misappropriation of a significant p-value when using SPD simulation methods. We show that based on the current data, this inference is unjustified, and that a steady population trajectory during this period is a better explanation of the data. Directly modelling population dynamics provides robust, justified and reasonable inferences. Our findings should not be misinterpreted as a claim that, in reality, there were no population fluctuations. Future larger datasets have the potential to support models of much greater complexity, and CPL modelling provides the basis and flexibility of fitting any number of hinges, offering detailed population histories of key events.

Data accessibility

To enable full transparency of our methods and aid other researchers in applying and further developing these methods, we provide an accompanying package in R called ADMUR: Ancient Demography Modelling Using Radiocarbon. We refer users to the vignette ‘Guide’ from which provides details of installation and use. All analysis and plots in this paper can be exactly replicated using the vignette ‘Replicating results’.

Authors’ contributions

A.T. devised the methodology, performed the analyses, generated plots and co-wrote the paper. R.B., M.G.T., C.M. and KM co-wrote the paper.

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