A theory of vowel dispersion based on probabilistic modeling of optimized speakers and listeners

Abstract

Dispersion Theory (Liljencrants and Lindblom, 1972; Lindblom, 1986) holds that optimal vowel systems maximize perceptual contrast by maximizing psycho-acoustic distance between vowels, successfully predicting much of the acoustic typology of natural languages. Here we explore probabilistic models of optimized speakers and listeners to see if they might yield more accurate and principled predictions about vowel dispersion. Given a set of vowel distributions and a set of categorical perceptual boundaries optimized for those distributions, the optimal set of vowel distributions maximizing the percentage of correctly perceived tokens is not in general the same as the original set of distributions. This motivates an iterated confusion minimization algorithm that can model dispersion as an incremental diachronic process that achieves globally optimized vowel systems by locally optimizing each vowel category against its own perceptual boundaries at each generation. We show this model provides a principled explanation for several nuanced patterns observed in cross-linguistic corpora, including greater distances in F2 than F1 and even spacing of F1 in log(Hz) rather than auditory-based scales (Becker-Kristal, 2010). A new prediction of this model is that lower-probability vowel pairs should be less dispersed; survey work now in progress so far confirms this prediction.