A minimal model of sound change


Social networks are an important structural property of evolutionary processes in culture and language. While great strides have been made in modeling the dynamics of discrete linguistic features in reproducing populations, such as individual signs (Nowak et. al. 1999) and grammatical rules (Niyogi 2006), these models haven’t been completely explored on graph structures, and continuous parameters such as those defining vowel formant frequencies or other cultural quantities of interest, such as garment length, are also ill-understood. We discuss a simple model for a reproducing population in which an individual occupies a node on a graph and decides on the value of a single continuous parameter based on the examples received from neighboring nodes. In the context of sound change, this model recapitulates many core results: dispersion of neighboring phonemes in chain shifts (Martinet 1955), the irreversibility of phoneme mergers (Garde 1961) and the uniform expansion of mergers (Herzog 1965). We also compare results of the model to existing studies of sound change in social networks (Labov 2001). These types of events in language evolution are largely “from below”, meaning they are little affected by other meaningful social variables. Time permitting, we will discuss how to expand the model to explore change “from above”, where nodes are decorated with other features to denote membership in different groups, and Sturtevant’s (Sturtevant 1947) conjecture that language change ends when social change ends.

arXiv, PDF