Summed radiocarbon calibrations as a population proxy: a critical evaluation using a realistic simulation approach

Abstract

The logic of using summed radiocarbon (14C) calibrations (cumulative probability density functions for large numbers of calibrated 14C dates) as proxies for past populations rests on the presumption of a proportional relationship between population size and the production, and subsequent preservation, recovery, and analysis, of 14C-datable material. Critiques of this approach have generally focused on the various problems that may undermine the validity of this assumption.Here, instead, we presume a perfect correspondence between population size and the quantity of datable material produced at any given time, and explore the question of how well summed 14C calibrations can track demographic changes under such ideal circumstances. We introduce a method of generating a random sample of simulated 14C determinations, from a specified distribution, with variable data densities and measurement errors. In other words, we generate a random sample of 14C dates not from an ideal statistical distribution but rather using a defined population curve to determine the probability distribution from which the calendar dates of the simulated 14C samples are drawn. We generate simulated 14C ages for these samples, calibrate them, and sum those calibrations. We compare the resulting proxy population curve to the known population distribution from which it was generated, to see whether known population fluctuations are unambiguously visible on a proxy curve derived from 14C data sets that are realistic in terms of the number and precision of the 14C determinations included.Results highlight 1) the critical role played by the magnitude and duration of any population fluctuation, and 2) the importance of sample size, and the reality that the numbers of samples required to detect significant population changes are generally far higher than those available to researchers proposing demographic reconstructions on the basis of literature searches for radiocarbon dates. We conclude that even if archaeological 14C data sets could be corrected for taphonomic filters and research biases, demographic signals would be difficult to distinguish from statistical noise in summed probability distributions. We suggest that simulation studies should be integral components of any attempt to reconstruct prehistoric demography from 14C dates.