Rigorous Identification of Variations and Changepoints in the Observed Rates of Radiocarbon Samples Over Time 

A commonly-used approach to estimate changes in the frequency of past events or the size of populations looks at variations in the rate of archaeological and environmental samples (e.g., charcoal from fires, human/animal bones, or other evidence of occupation) found at a site over time. Time periods with large numbers of samples suggest increased activity, while those with few samples indicate a reduced level of activity. Variations and abrupt changes in the rate of observed samples might suggest the influence of important external environmental factors. This paradigm is known as “dates-as-data”. The reliability of such a “dates-as-data” approach is highly dependent upon our ability to estimate the calendar ages of the discoveries. Most archaeological/environmental dates are obtained using radiocarbon (14C). All 14C determinations need to be calibrated in order that they can be understood on the calendar scale. This introduces considerable uncertainties in the resultant calendar ages and complicates the identification of changepoints in the calendar year rates at which samples occur. In this talk, we provide a statistically rigorous approach to overcome these challenges. We model the occurrence of events (each assumed to leave a 14C sample in the archaeological/environmental record) as an inhomogeneous Poisson process, estimating the varying rate of samples using reversible-jump Markov Chain Monte Carlo. Given a set of radiocarbon samples, we aim to reconstruct how their occurrence rate varies over calendar time and identify if there are statistically significant changepoints in the rate at which the samples arise (i.e., specific times at which the rate of events abruptly changes). We will demonstrate our approach on data exploring the expansion of humans, and the parallel disappearance of megafauna, in the Yukon and Alaska in the late Pleistocene and early Holocene: investigating both the timings of such migrations in comparison with the climatic changes known to have occurred during this period, and the potential interactions between humans and the various species in the region.