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\textbf{Habitat connectivity.} \textbf{Implications for Neanderthal dispersal}  The habitat suitability model presented in this study provides guidelines to interpret the potential effect of climatic and topographic barriers over Neanderthals dispersal and gene flow. Mountain ranges like Alps and Pyrenees were probably strong barriers during the Eemian (and during the early Weischselian, according to \cite{Andel}) that could have offer an opportunity to be crossed during the summer, but a rough topography could have been still an issue for the mobility requirements of Neanderthals. Extense plains dominated by a continental climate (Pannonian plain, North European plains) could have also prevented Neanderthals migration, specially during summers in the south and winters in the north. Finally, migration and gene flow through suitable coastal areas could have been prevented by the complex shape of the coast line, water bodies (Aegean sea).   Our model shows at least six suitable geographical regions more or less isolated from each other: the Iberian Peninsula, limited by the Pyrenees; France and Western Germany, limited by the Alps, the north European plains and the sea; British Islands, but Neanderthals presence during the Eemian has not been confirmedhere \cite{Penkman_2011}; Italian peninsula, limited by the Po Valley and the Alps; Peloponese and Aegean Islands, limited by the sea (but see \cite{Ferentinos_2012} and \cite{Broodbank_2006} for a discussion about the possibility of seafaring by Neanderthals), but without any reliable Neanderthal material attributed to MIS 5e; and the coasts of Anatolia, Lebanon and Israel.  In the long term, the compartimentation of Neanderthal populations could have lead to genetic differentiation, as shown in \cite{Fabre_2009}. In this paper the authors studied genetic variation within twelve samples of mitochondrial DNA obtained from Neanderthal samples dated between 100 and 29 ka BP (but according to \cite{Higham_2014} the latter date may be more probably around 40 ka BP). They defined two genetic demes within our study area (see Fig. 2 in \cite{Fabre_2009}): a northern region that comprises the North of the Iberian Peninsula, Eastern France, Germany and the rest of central Europe; a southern region comprising the East of the Iberian Peninsula, South of France, Italian Peninsula, and the Balcans. These demes do not completely fit with our habitat suitability model: there seem to be connectivity between Eastern and Western Iberian Peninsula due to a corridor of suitable habitat at the south of Pyrenees, and between Western and Eastern France, that show a large extension of well connected suitable habitat. But both models agree in the important effect of the Alps as the main geographic accident shaping the separation between ecologically suitable areas and genetic demes.  According to \cite{Andel}, the Alps and the Carpathian mountains were rarely crossed even during the warmest phases of the Weischselian.  \cite{Harvati} and \cite{Jiménez-Espejo2007836} interpret that Neanderthals presence in Central Europe was probably sporadic, and very likely concentrated in a few small areas.