BackgroundRecent advances in sequencing technologies have allowed for the retrieval of ancient DNA data (aDNA) from skeletal remains, providing direct genetic snapshots from diverse periods of human prehistory. Comparing samples taken in the same region but at different times, hereafter called “serial samples”, may indicate whether there is continuity in the peopling history of that area or whether an immigration of a genetically different population has occurred between the two sampling times. However, the exploration of genetic relationships between serial samples generally ignores their geographical locations and the spatiotemporal dynamics of populations. Here, we present a new coalescent-based, spatially explicit modelling approach to investigate population continuity using aDNA, which includes two fundamental elements neglected in previous methods: population structure and migration. The approach also considers the extensive temporal and geographical variance that is commonly found in aDNA population samples.ResultsWe first showed that our spatially explicit approach is more conservative than the previous (panmictic) approach and should be preferred to test for population continuity, especially when small and isolated populations are considered. We then applied our method to two mitochondrial datasets from Germany and France, both including modern and ancient lineages dating from the early Neolithic. The results clearly reject population continuity for the maternal line over the last 7500 years for the German dataset but not for the French dataset, suggesting regional heterogeneity in post-Neolithic migratory processes.ConclusionsHere, we demonstrate the benefits of using a spatially explicit method when investigating population continuity with aDNA. It constitutes an improvement over panmictic methods by considering the spatiotemporal dynamics of genetic lineages and the precise location of ancient samples. The method can be used to investigate population continuity between any pair of serial samples (ancient-ancient or ancient-modern) and to investigate more complex evolutionary scenarios. Although we based our study on mitochondrial DNA sequences, diploid molecular markers of different types (DNA, SNP, STR) can also be simulated with our approach. It thus constitutes a promising tool for the analysis of the numerous aDNA datasets being produced, including genome wide data, in humans but also in many other species.Electronic supplementary materialThe online version of this article (10.1186/s12863-017-0575-6) contains supplementary material, which is available to authorized users.