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In this paper we present a hypothesis about the abiotic drivers of Neanderthals distribution deeply rooted on the Grinnellian niche concept \cite{Grinnell_1917}, the hierarchical framework to explain the importance of species-distribution drivers at different scales proposed by \cite{Pearson_2003}, and our current knowledge on the ecology of Neanderthals (see references above). According to \citet{Pearson_2003}, climate influences species distribution at global to regional scales, while the effect of topography is restricted to scales ranging from regional to local. We hypothesize that the northern and southern edges of Neanderthals range were respectively limited by cold winter temperatures and a combination of high temperatures and low water availability during the summer, whereas a high topographic diversity combined with moderate slopes could have favored occupation at the local scale. Winter temperatures at the northern edge could have exert a negative impact over Neanderthals populations in two related ways: 1) lower availability of small and big game than in temperate areas \cite{Badgley_2000} would have compromised the high caloric intake required by this species \cite{Steegmann_2002, S_rensen_2009}; 2) increased cold stress worsened by a low-caloric diet would have lead to an even more reduced fertility \cite{Bocquet_Appel_2013} and a higher mortality rate \cite{Steegmann_2002}, compromising population survival. Summer temperatures linked to continentality and the higher solar radiation of lower latitudes could have prevented the occupation of southern plains in the Mediterranean peninsulas due to increased heat stress, specially considering the low surface area/volume ratio of this species \cite{Churchill2006}, that hampers heat dissipation. Also, summer drought could have probably reduced access to plant resources, making these areas unsuitable during the warm season. Mediterranean coastal areas could have been suitable because of the buffering effect of the sea over temperature, and the permanent availability of resources like shellfish \cite{Hardy_2011}. At the local scale, high topographic diversity, that fosters biodiversity by an increased availability of ecological niches \cite{Tews_2003}, provided the required abundance and diversity of preys and shelter \cite{Daujeard_2012}, but moderate to low slopes may have been important to reduce the high energetic expenditure of mobility in steep terrain. This limitation, combined with the lower abundance of animals at higher elevations \cite{Brown_2001} could have prevented Neanderthals presence in the higher elevations of the European mountain ranges.  To test our hypothesis, we have modeled and analyzed the distribution of Neanderthals during the full Eemian (MIS 5e, ~130 ka BP) using a paleo species distribution modeling approach (PSDMs hereafter) \cite{Franklin20151} \cite{Svenning20112930} \cite{Varela2011451}. \cite{Franklin20151, Svenning20112930, Varela2011451}.  PSDMs rely on the same principles of species distribution modeling (SDMs, \cite{Guisan2000147}, \cite{Guisan_2005}). \citet{Guisan2000147, Guisan_2005}).  PSDMs require presence coordinates representing the location of fossil remains, a set of predictors (usually palaeo-climatic simulations), and an algorithm to define the relationship between presence and predictors. The result of a PSDM can be defined as an \textit{habitat suitability map}, a raster map in which each cell is ranked according how well they resemble the ecological conditions of those locations at which the focal species occur (\cite{Soberon_2005}). PSDMs rely on the assumption that the modeled species is in equilibrium with its environment, and therefore occurs in all the localities with suitable habitat \cite{Guisan_2005}. Aside from providing a graphical description of the potential distribution of the species, PSDMs can be used to analyze the influence of particular drivers over the species distribution and gain ecological knowledge (e.g. \cite{Varela_2009} \cite{Rodr_guez_S_nchez_2008}). \citet{Varela_2009, Rodr_guez_S_nchez_2008}).  PSDMs have been used before to study the distribution of Neanderthals and Anatomically Modern Humans \cite{Burke201435} \cite{Banks_2008} \cite{Banks2008481} \cite{Beeton_2013}. \cite{Burke201435, Banks_2008, Banks2008481, Beeton_2013}.  We selected the Eemian (MIS 5e, ~130 ka BP) as modeling period for three different reasons: 1) the distribution of Neanderthals during this period has been previously assessed by \citet{Richter2005}, \citet{Richter2006}, \citet{Wenzel_2007}, and \citet{Gaudzinski2011}, being these studies mainly focused on the core and northern edge of the distribution area across central Europe, but lacking a quantitative description of Neanderthals distribution and its limiting factors; 2) Since the publication of \cite{Wenzel_2007}, Neanderthal remains attributed to the Eemian have been found in Spain \cite{ÁlvarezAlonso2014288} \cite{Arsuaga2012629}, Italy (CITATION), (CITATION!),  France \cite{Moncel200765}, and those new sites considered together have the potential to change our view about the Eemian distribution of Neanderthals; 3) During the Eemian, the warmer climatic conditions freed Europe from the Saalian ice sheet, offering the Neanderthals a unique opportunity to thrive and spread throughout Europe for 10000 years, and probably allowing them to reach their maximum range size. The Eemian can be therefore considered the most suitable period to assume a pseudo-equilibrium with climate for Neanderthals distribution, a key assumption for PSDMs \cite{Guisan_2005} \cite{Guisan2000147}. \cite{Guisan_2005, Guisan2000147}.  In summary, in this paper we propose a hypothesis about how abiotic drivers (climate and topography) could have shaped Neanderthals distribution throughout Europe, and we test ithypothesis  by fitting and analyzing a PSDM describing their distribution during the Last Interglacial.