Summed probability distributions of radiocarbon dates are an increasingly popular means by which to reconstruct prehistoric population dynamics, enabling more thorough cross-regional comparison and more robust hypothesis testing, for example with regard to the impact of climate change on past human demography. Here we review another use of such summed distributions – to make spatially explicit inferences about geographic variation in prehistoric populations. We argue that most of the methods proposed so far have been strongly biased by spatially varying sampling intensity, and we therefore propose a spatial permutation test that is robust to such forms of bias and able to detect both positive and negative local deviations from pan-regional rates of change in radiocarbon date density. We test our method both on some simple, simulated population trajectories and also on a large real-world dataset, and show that we can draw useful conclusions about spatio-temporal variation in population across Neolithic Europe.