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\textbf{Importance of environmental factors}  At the local scale, the variable with a higher R squared across the presence records Neanderthal sites used to calibrate the model  was slope (Fig. 5). The rest of the factors showed lowerbut similar  importance scores, while topographic diversity showed the minimum local importance. The plot showing the local importance of slope at the Eemian neanderthal sites (Fig. 6) showed that low habitat suitability sites (mainly belonging to Germany) were in 50 km cells with a positive (and robust) relationship between habitat suitability and slope. This result indicates that low slopes could be limiting habitat suitability values in sites located in Germany. Spanish locations showed was  the opposite trend, with high slope values, and a negative relationship between habitat suitability and slope. This means that an increment in slope in these places would lead to a reduction in habitat suitability, and therefore they were located at optimum slopes. least important variable.  The continental analysis of variable importance performed with random forest (Fig. 7) showed that annual rainfall (bio12) and minimum winter temperature (bio6) were the factors controlling habitat suitability values at the continental scale. The response curves showed a clear increment of habitat suitability beyond 500 mm of annual rainfall (bio12) and minimum winter temperatures higher than -10 Cº (see response curves at Appendix). Topographical slope and maximum summer temperature (bio5) were the factors with a higher contribution to model uncertainty (standard deviation of the ensemble) at the continental scale. Topographic slopes beyond 10 degrees combined with rainfall values beyond 1500 milimeters leaded to the higher uncertainty values (see Appendix).