Mind the gaps: testing for hiatuses in regional radiocarbon date sequences

Long gaps in regional radiocarbon sequences are often considered evidence for occupation hiatuses, but they might also be a product of stochastic processes of occupation and limited numbers of dates. Here we show that, if radiocarbon dates over a span of time are distributed as a Poisson random variable (such that any point in that span has an equal probability of being dated), the gaps between dates will approximate a negative exponential distribution, with many short gaps and a few long ones. Long gaps between dates are to be expected under these conditions, even in the absence of true occupation hiatuses. This exponential distribution of gap lengths is robust even when the uniform probability assumption is relaxed, though true hiatuses have a distinctive, if subtle, signature. We use this model to assess the regional radiocarbon sequence from Qinghai Lake basin, western China, which shows two long possible occupation hiatuses during the period 12,500-4200 14C BP.