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\paragraph{Study area and presence data}  Thegeographical area of this  study area  (20ºN to 70ºN, 10ºW to 70ºE) comprises Europe and the Irano-Turanian region. This area It  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 singleNeanderthal  record (Ust-Izhul, Siberia) attributed to MIS 5e beyond the Caspian Sea \cite{Rolland2010}, and therefore the data available would be too scarce to build a reliable model for this region. We reviewed the literature searching for archaeological sites with Neanderthal fossil or lithic remains attributed to MIS 5e either by absolute or relative dating methods. Sites broadly attributed to MIS 5 were therefore excluded from our study. excluded.  We found 50 records located in fourteen countries, 25 of them with absolute dates obtained with a variety of methods (Electronic Spin Resonance, Uranium/Thorium, Optically Stimulated Luminiscence, and Thermo Luminiscence), dates,  and 25 of them with relative datesbased on biostratigraphy, correlated stratigraphy and pollen data  (see Table 1). To reduce spatial clusteringand 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 29 presence records (see Fig. 1). \paragraph{Environmental variables}  To represent variables influencing Neanderthals distribution at the continental scale we We  selected a palaeoclimatic simulation of the start of the Eemian ($\sim$130 ka BP) performed with the NCAR Community Climate System Model \cite{Otto2006}. The results of this palaeoclimatic model fit very well with the available climatic proxies for the given period \cite{Otto2006}. This simulation is available at www.worldclim.com \ref{Hijmans20051965} as a set of maps downscaled to 1km resolution representing 19 bioclimatic variables. We processed the digital elevation model (SRTM model aggregated to 1km resolution) provided by www.worldclim.com \cite{Farr_2007,Hijmans2005196} and derived maps of slope, topographic wetness index, and topographic diversity (see appendix for further details). All the variables were aggregated to 5 km resolution using GRASS GIS (GRASS development team 2012). To represent the Eemian shoreline the sea level was set at 7 m.a.s.l \cite{Dutton_2012}.