Linguistic evolution in time and space: addressing the methodological challenges

One of the most specific features of the human language faculty is its intrinsic spatio-temporal dynamic, as reflected in languages' characteristic mode of extra-genomic evolution. Understanding what has emerged in the hominin lineage therefore requires capturing this dynamic and the diversity of languages and structures that it generates. In this chapter, we review the state of the art in probabilistic models designed for this task. Current approaches tend to excel either in capturing temporal or spatial processes. We summarize these and describe avenues for integrating them, illustrated by a case study on the evolution of sound inventories over time and space.