Through his research on the Neolithic (Agricultural) Demographic Transition, carried out on a European and intercontinental scale with many French and foreign partners, Jean-Pierre Bocquet-Appel has reintroduced and renewed the demographic question in the analysis of the diffusion processes of the agro-pastoral economy, especially in the "old world". The demonstration of a strong demographic growth related to the establishment of this economy of production carried in germ the construction of models articulating this phenomenon with the other components, environmental, technical, sociological and cultural which conditioned the development of the societies of the medium / recent Holocene in Europe. The emblematic case chosen, the diffusion of the culture to Linear Ceramics, corresponds to the introduction of the agricultural system in Central and Central-Western Europe during the 6th and early 5th millennia. For having contributed very closely to these works I will present here the basic elements of this approach to underline just as much the simulated products directly interesting the neolithic archeology as the difficulties and limits reached within the framework of this first simulation.