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\textbf{Study area and presence data}  The geographical framework of this study (20ºN to 70ºN, 10ºW to 70ºE)  comprises Europe and the Irano-Turanian region (20ºN region. This geographical frame does not cover the entire known range of Neanderthals, that extended at least  to 70ºN, 10ºW Okladnikov, in Southern Siberia \cite{Krause_2007}, because we only found one single Neanderthal record attributed  to 70ºE). MIS 5e beyond the Caspian Sea (Ust-Izhul, Siberia, \citet{Rolland2010}), and therefore our data would be too scarce to build a reliable model for this region.  We found in the literature up to 65 archaeological sites attributed to Neanderthals presence during the last interglacial period (see Appendix). 35 of these presences were attributed by their authors to MIS 5e, while the remaining ones were broadly attributed to MIS 5, and therefore were excluded from our study. To reduce spatial clustering and pseudorreplication within the presence dataset we filtered the data applying a minimum distance of 100 km between nearby locations \cite{Guisan_2005}, what reduced the sample size down to 26 presence records (see Fig. 1).