Exploratory time-series analysis of radiocarbon data from archaeological contexts is used to reconstruct the population history of arid Australia, allowing this to be read in concert with records of climatic variability over the last 20 000 years. Probability distribution plots of 971 radiocarbon ages from 286 sites in five dryland regions (the arid west coast, Pilbara and Murchison, Nullarbor, arid interior and the southeastern arid zone) provide a proxy record of prehistoric population fluctuations in these areas. There is regional variation, but the radiocarbon density plots suggest a step-wise pattern of population growth and expansion, with significant thresholds at 19, 8 and 1.5 cal. kyr BP. Within this, the plots suggest a saw-tooth pattern of rapid population growth and decline on a 1—3 kyr frequency, with a marked collapse of dryland hunter-gatherer populations around 3—2.5 cal. kyr BP affecting most regions. Comparison with climate data shows broad correlations with past temperature and rainfall variability, sea-level change and ENSO activity, but the interaction of prehistoric populations and these environmental changes is not well resolved. High amplitude environmental changes appear to have triggered stadial changes in population, rather than smooth transitions. Dryland populations may also have become more sensitive to small environmental changes in the late Holocene, as population density increased. A large increase in population around 1.5 cal. kyr BP is associated with small changes in regional palaeoecology, which are not otherwise represented in palaeoclimatic data sets. Spectral analysis identifies two cyclical periodicities of 1340 and 175 years within the population histories, also suggesting responses to millennial and submillennial climatic variability, a pattern most marked in the late Holocene.