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Given the rapidly evolving landscape of linguistic prevalence, whereby amajority of the world's existing languages are dying out in favor of theadoption of a comparatively fewer set of languages, the factors behind thisphenomenon has been the subject of vigorous research. The majority ofapproaches investigate the temporal evolution of two competing languages in theform of differential equations describing their behavior at large scale. Incontrast, relatively few consider the spatial dimension of the problem.Furthermore while much attention has focused on the phenomena of languageshift---the adoption of majority languages in lieu of minorityones---relatively less light has been shed on linguistic coexistence, where twoor more languages persist in a geographically contiguous region. Here, we studythe geographical component of language spread on a discrete medium to monitorthe dispersal of language species at a microscopic level. Language dynamics ismodeled through a reaction-diffusion system that occurs on a heterogeneousnetwork of contacts based on population flows between urban centers. We showthat our framework accurately reproduces empirical linguistic trends driven bya combination of the Turing instability, a mechanism for spontaneouspattern-formation applicable to many natural systems, the heterogeneity of thecontact network, and the asymmetries in how people perceive the status of alanguage. We demonstrate the robustness of our formulation on two datasetscorresponding to linguistic coexistence in northern Spain and southern Austria.

Linguistic evolution driven by network heterogeneity and the Turing mechanism