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Several recent lines of evidence indicate more intensive contact between LBK farmers and indigenous foragers in Central Europe (5600–5400 calBC). Strong continuity has been identified between Mesolithic and Neolithic material cultures; faunal assemblages, and isotopic analyses of diet have revealed a greater role of hunting in LBK communities; genetic analyses have suggested that the modern Central European gene pool is mainly of Palaeolithic origin. Surprisingly little attention has been paid to demographic aspects of the Neolithic transition. In our study, demographic simulations were performed to assess the demographic conditions that would allow LBK farmers to spread across central Europe without any admixture with Mesolithic foragers. We constructed a stochastic demographic model of changes in farming population size. Model parameters were constrained by data from human demography, archaeology, and human ecology. Our results indicate that the establishment of farming communities in Central Europe without an admixture with foragers was highly improbable. The demographic conditions necessary for colonization were beyond the potential of the Neolithic population. Our study supports the integrationists’ view of the Neolithic transition in Central Europe.