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Our hypothesis and objectives.  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, while high topographic diversity combined with moderate slopes influenced their distribution favored occupation  at the local scale. Winter temperatures at the northern edge would exert a negative impact over Neanderthals populations in two related ways: 1) reducing primary productivity and therefore dwindling the availability of both small and big game, and 2) increasing cold stress, worsened by a low-caloric diet. High temperatures and summer drought linked to continentality would have prevented the occupation of southern plains in the Mediterranean peninsulas due to a low primary productivity and increased heat stress, but Mediterranean coastal areas could have been suitable because of the buffering effect of the sea over temperatures and the constant availability of resources like shellfish (CITATION). At the local scale, high topographic diversity linked with an increased availability of ecological niches (CITATION) could have provided the required abundance and diversity of preys, but moderate to low slopes may have been important to reduce the energetic cost of local mobility. Our hypothesis does not