Following its initial arrival in SE Europe 8,500 years ago agriculture spread throughout the continent, changing food production and consumption patterns and increasing population densities. Here we show that, in contrast to the steady population growth usually assumed, the introduction of agriculture into Europe was followed by a boom-and-bust pattern in the density of regional populations. We demonstrate that summed calibrated radiocarbon date distributions and simulation can be used to test the significance of these demographic booms and busts in the context of uncertainty in the radiocarbon date calibration curve and archaeological sampling. We report these results for Central and Northwest Europe between 8,000 and 4,000 cal. BP and investigate the relationship between these patterns and climate. However, we find no evidence to support a relationship. Our results thus suggest that the demographic patterns may have arisen from endogenous causes, although this remains speculative.