There is a long-standing controversy between two models of the Neolithic transition. The demic model assumes that the Neolithic range expansion was mainly due to the spread of populations, and the cultural model considers that it was essentially due to the spread of ideas. Here we integrate the demic and cultural models in a unified framework. We show that cultural diffusion explains ∼40% of the spread rate of the Neolithic transition in Europe, as implied by archaeological data. Thus, cultural diffusion cannot be neglected, but demic diffusion was the most important mechanism in this major historical process at the continental scale. This quantitative approach can be useful also in regional analysis, the description of Neolithic transitions in other continents, and models of many human spread phenomena.he Neolithic transition, a major episode in human history, is defined as the shift from a hunter-gatherer economy (Paleolithic) into another one based on agricultural activities (Neolithic) (1). In the Near East, this transition took place ∼12,000 y ago, and from there it spread across Europe until ∼5,000 y ago (2-4). Archaeologists have provided many data that make it possible to measure the speed of the spread of the Neolithic transition, but they disagree on which of the following possibilities is correct: (i) it was mainly a demic process (range spread of farmers) (5); (ii) it was mainly a cultural one (transmission of the plants, animals and knowledge of farmers to hunter-gatherers (6)); or (iii) it was mainly demic in some regions and mainly cultural in others (7). It is important to note that many authors have clearly argued for the importance of both demic and cultural diffusion. For example, Ammerman and Cavalli-Sforza (8), when introducing their demic diffusion model in 1973, wrote that demic and cultural diffusion are not mutually exclusive, and discussed the interactions between the Neolithic and Paleolithic populations that would have led to cultural diffusion and genetic clines. These authors also made some crucial statements: "The real question may well be to evaluate the relative importance of demic and cultural diffusion in different regions of Europe" because "in some areas both are likely to have contributed to the spread of farming," but "what is necessary before such an attempt can be made is the introduction of much more specific models" (ref. 4, pp. 6, 135, and 62, respectively). This is precisely the problem to which the present paper aims to contribute: we will here present a model, and apply it to determine the importance of demic and cultural diffusion on the spread rate at the continental scale. We will also outline how our model could be applied to solve the same problem at regional scales in future work.Several aspects of transitions in human prehistory have been analyzed during the past decade using increasingly refined mathematical models (9-16). On the other hand, genetic studies have led to an increasing consensus that demic dispersal was important in the Neolithic transition in ...