Optimal linear estimation models predict 1400-2900 years of overlap between Homo sapiens and Neandertals prior to their disappearance from France and northern Spain.

Recent fossil discoveries suggest that Neandertals and Homo sapiens may have co-existed in Europe for as long as 5 to 6000 years. Yet, evidence for their contemporaneity at any regional scale remains highly elusive. In France and northern Spain, a region which features some of the latest directly-dated Neandertals in Europe, Protoaurignacian assemblages attributed to Homo sapiens appear to 'replace' Neandertal-associated Châtelperronian assemblages. Using the earliest and latest known occurrences as starting points, Bayesian modelling has provided indication that these occupations may in fact have been partly contemporaneous. The reality, however, is that we are unlikely to ever identify the 'first' or 'last' appearance of a species or cultural tradition in the archaeological and fossil record. Here, we use optimal linear estimation modelling to estimate the first appearance date of Homo sapiens and the extinction date of Neandertals in France and northern Spain by statistically inferring these 'missing' portions of the Protoaurignacian and Châtelperronian archaeological records. Additionally, we estimate the extinction date of Neandertals in this region using a dataset of directly-dated Neandertal fossil remains. Our total dataset consists of sixty-six modernly produced radiocarbon determinations which we recalibrated using the newest calibration curve (IntCal20) to produce updated age ranges. The results suggest that the onset of the Homo sapiens occupation of this region likely preceded the extinction of Neandertals and the Châtelperronian by up to 1400-2900 years. This reaffirms the Bayesian-derived duration of co-existence between these groups during the initial Upper Palaeolithic of this region using a novel independent method, and indicates that our understanding of the timing of these occupations may not be suffering from substantial gaps in the record. Whether or not this co-existence featured some form of direct interaction, however, remains to be resolved.