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The expansion of the human species out of Africa in the Pleistocene, and the subsequent development of agriculture in the Holocene, resulted in waves of linguistic diversification and replacement across the planet. Analogous to the growth of populations or the speciation of biological organisms, languages diversify over time to form phylogenies of language families. However, the dynamics of this diversification process are unclear. Bayesian methods applied to lexical and phonetic data have created dated linguistic phylogenies for 18 language families encompassing ~3,000 of the world’s ~7,000 extant languages. In this paper we use these phylogenies to quantify how fast languages expand and diversify through time both within and across language families. The overall diversification rate of languages in our sample is ~0.001 yr-1 (or a doubling time of ~700 yr) over the last 6,000 years with evidence for nonlinear dynamics in language diversification rates over time, where both within and across language families, diversity initially increases rapidly and then slows. The expansion, evolution, and diversification of languages as they spread around the planet was a non-constant process. [ABSTRACT FROM AUTHOR]