Archaeologists argue that the replacement of Neanderthals by modern humans was driven by interspecific competition due to a difference in culture level. To assess the cogency of this argument, we construct and analyze an interspecific cultural competition model based on the Lotka−Volterra model, which is widely used in ecology, but which incorporates the culture level of a species as a variable interacting with population size. We investigate the conditions under which a difference in culture level between cognitively equivalent species, or alternatively a difference in underlying learning ability, may produce competitive exclusion of a comparatively (although not absolutely) large local Neanderthal population by an initially smaller modern human population. We find, in particular, that this competitive exclusion is more likely to occur when population growth occurs on a shorter timescale than cultural change, or when the competition coefficients of the Lotka−Volterra model depend on the difference in the culture levels of the interacting species.Lotka−Volterra | cultural evolution | Paleolithic | feedback | replacement N eanderthals are a human species (or subspecies) that went extinct, after making a small contribution to the modern human genome (1, 2). Hypotheses for the Neanderthal extinction and their replacement by modern humans, in particular as recorded in Europe, can be classified into those emphasizing competition with modern humans and those arguing that interspecific competition was of minor relevance. Among the latter are the climate change (3) and epidemic/endemic (4) hypotheses. However, an ecocultural niche modeling study has shown that Neanderthals and modern humans exploited similar niches in Europe (5), which, together with a recent reassessment of European Paleolithic chronology showing significant spatiotemporal overlap of the two species (6), suggests a major role for interspecific competition in the demise of the Neanderthals.Replacement of one species (or population) by another is ultimately a matter of numbers. One competing species survives while the other is reduced to, or approaches, zero in size. In the classical Lotka−Volterra model of interspecific competition, this process is called competitive exclusion (7). If Neanderthals were indeed outcompeted by modern humans, the question arises: Wherein lay the advantage to the latter species? Many suggestions have been made, including better tools (8), better clothing (9, 10), and better economic organization (11). These hypotheses share the premise that modern humans were culturally more advanced than the coeval Neanderthals.The purpose of our paper is threefold. First, we extend the Lotka−Volterra-type model of interspecific competition by incorporating the "culture level" of a species as a variable that interacts with population size (12, 13). Here, culture level may be interpreted as the number of cultural traits, toolkit size, toolkit sophistication, etc. Although, as noted above, many anthropological and archaeological discussions i...