Abstract
Reconstructing the spatial evolution of languages can deepen our understanding of the demic diffusion and cultural spread. However, the phylogeographic approach that is frequently used to infer language dispersal patterns has limitations, primarily because the phylogenetic tree cannot fully explain the language evolution induced by the horizontal contact among languages, such as borrowing and areal diffusion. Here, we introduce the language velocity field estimation, which does not rely on the phylogenetic tree, to infer language dispersal trajectories and centre. Its effectiveness and robustness are verified through both simulated and empirical validations. Using language velocity field estimation, we infer the dispersal patterns of four agricultural language families and groups, encompassing approximately 700 language samples. Our results show that the dispersal trajectories of these languages are primarily compatible with population movement routes inferred from ancient DNA and archaeological materials, and their dispersal centres are geographically proximate to ancient homelands of agricultural or Neolithic cultures. Our findings highlight that the agricultural languages dispersed alongside the demic diffusions and cultural spreads during the past 10,000 years. We expect that language velocity field estimation could aid the spatial analysis of language evolution and further branch out into the studies of demographic and cultural dynamics.