Supplementary material from "Quantifying the spatial pattern of dialect words spreading from a central population"

Some dialect words are shared among geographically distant groups of people without close interaction. Such a pattern may indicate the current or past presence of a cultural centre exerting a strong influence on peripheries. For example, concentric distributions of dialect variants in Japan may be explicable by repeated inventions of new variants at Kyoto, the ancient capital, with subsequent outward diffusion. Here we develop a model of linguistic diffusion within a population network to quantify the distribution of variants created at the central population. Equilibrium distributions of word ages are obtained for idealized networks and for a realistic network of Japanese prefectures. Our model successfully replicates the observed pattern, supporting the notion that a centre–periphery social structure underlies the emergence of concentric patterns. Unlike what has previously been claimed, our model indicates that a novelty bias in linguistic transmission is not always necessary to account for the concentric pattern, whereas some bias in the direction of transmission between populations is needed to be consistent with the observed absence of old words near the central population. Our analysis on the realistic network also suggests that the process of linguistic transmission was not much affected by between-prefecture differences in population size.