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\paragraph{Study area and presence data}  The geographical area of this study (20ºN to 70ºN, 10ºW to 70ºE) comprises Europe and the Irano-Turanian region. This area does not cover the entire known range of Neanderthals, which extended at least to Okladnikov in Southern Siberia \cite{Krause_2007}, but there is only one single Neanderthal record attributed to MIS 5e beyond the Caspian Sea citep[Ust-Izhul, Siberia,]{Rolland2010}  (Ust-Izhul, Siberia, \citep{Rolland2010}), and therefore the data available would be too scarce to build a reliable model for this region. We found up to 64 archaeological sites in the literature attributed to a Neanderthal presence during the last interglacial period (see SEI or Table 1?). 34 of these presences were attributed by their authors to MIS 5e, while the remaining ones were broadly attributed to MIS 5 and therefore excluded from our study. To reduce spatial clustering and pseudo-replication within the presence dataset we filtered the data applying a minimum distance of 100 km between nearby locations \cite{Guisan_2005}, which reduced the sample size to 25 presence records (see Fig. 1).