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In this paper we present the first model of Neanderthals potential distribution across Europe during the Last Interglacial (Eemian, MIS 5e, ~130 ka BP). We have applied a robust state-of-the-art modeling approach to take advantage of a sparse set of archaeological records and a palaeoclimatic simulation to produce the model. We analyzed the model using regression-tree based statistical methods to assess how environmental variables shaped habitat suitability at continental and local scales, and assessed to what extent our preliminary hypothesis on the abiotic drivers of Neanderthals distribution matched the results of the model.  The papers by \citet{Richter2005}, \citet{Richter2006}, \citet{Wenzel_2007}, and \citet{Gaudzinski2011} are within the most relevant ones discussing the distribution and survival strategies of Neanderthals during the last years. These papers papers provide a valuable review on Eemian Neanderthal sites (many of them used to calibrate our model), offer a valuable discussion on whether the dense forests present in Central Europe during MIS 5e were suitable or not for Neanderthals due to the lack of large herds of mammals (specially \cite{Gaudzinski2011}). \citet{Gaudzinski2011}).  Since our model is focused on abiotic drivers, we cannot contribute to elucidate whether dense forests were a harsh environment for Neanderthals or not. But according to our results, the central and north European plains occupied by dense forests during the Eemian were already too cold and flat, resulting in low habitat suitability values. This does not mean that we consider abiotic factors to be more relevant in shaping Neanderthals distribution, and we are just simply adding new information that may help to formulate new questions about this topic. To disentangle the relative effect of climate, topography and the presence of dense forests over Neanderthals northern edge would require a reliable vegetation simulation (as in \citet{Allen20102604} or \citet{Gaillard2010483}), that is not available to date. Two of the papers enumerated above, (\citet{Wenzel_2007} and \citet{Richter2006}) discuss the use of beaches to obtain seafood. Many new Eemian sites are located by the sea, and our model shows that habitat suitability was very high across most parts of the Mediterranean Atlantic, Adriatic, Aegean and Black Sea coasts. Actually, the distribution of habitat suitability values interpreted along the newly  available sites challenges the idea of Neanderthals as a species mainly living in densely forested and moderately cold areas of Central Europe. central-european species.  Our model shows that these forested and relatively cold areas the presence records in northern Germany  could have been the tail of Neanderthals distribution, while abiotic conditions were potentially close to  optimum along the coastlines. Our findings support the idea of Eemian Neanderthals being a species mainly thriving in warm coastlines, able to exploit the resources provided by the sea  We hope our findings to promote a discussion about what were the habitats preferred by Neanderthals. \textbf{How do the model results fit the hypothesis presented in the introduction?}  According to our proposed hypothesis, the northern edge of Neanderthals distribution should be controlled by cold winters due to low availability of small and big game and cold stress. Our model confirms that minimum temperature of the coldest month influences habitat suitability at the continental scale, but the local scale analysis shows that the low habitat suitability of places within and beyond the northern edge (for example: Southern Baltic coast, Jutland peninsula, Southern Sweden, Southern Finland) can be explained by a combination of cold winters and plain slopes.