WaST: a formalisation of the Wave model with associated statistical inference and applications

2026-04-09

AI Summary

Traditional tree-based models struggle to capture the non-tree-like co-evolution of closely interacting groups—such as dialects—under sustained contact. This work presents the first rigorous mathematical formalization of the Wave model from historical linguistics, introducing a fully Bayesian generative model grounded in a fixed graph structure. In this framework, linguistic innovations propagate across the graph and stochastically disappear according to a death process, with posterior inference performed via Metropolis–Hastings within Gibbs sampling. The proposed approach offers a unified modeling paradigm for diverse diffusion phenomena in the human sciences and demonstrates superior accuracy in reconstructing the evolutionary dynamics of populations under continuous interaction, as validated on both simulated and real-world data.

Abstract

We propose a mathematical formalisation of the ``wave model'' originally developed in historical linguistics but with further applications in human sciences. This model assumes new traits appear in a population and spread to nearby populations depending on their closeness. It is mostly used to describe joint evolution of closely related populations, for example of several dialects. These situations of permanent contact are not accurately represented by its competitors based on tree structures. We built a fully Bayesian generative model where innovation spread along a fixed graph and disappear according to a death process. We then develop a Metropolis-Hastings within Gibbs sampler to sample from the posterior distribution on the graph. We test our method on simulated datasets as well as on several real dataset.

Problem

• Wave model
• historical linguistics
• population evolution
• dialects
• contact-induced change

Innovation

• Wave model
• Bayesian generative model
• Metropolis-Hastings within Gibbs
• graph-based diffusion
• statistical inference