Abstract Vertical and horizontal models of language relatedness, such as tree models and wave models, approach language change from two fundamentally different perspectives. Vertical models capture the diachronic nature of language differentiation but do not offer a satisfactory way to show diffusion across linguistic boundaries. Horizontal models excel at modeling diffusion but are essentially distributional models and have no temporal element. In this paper, a mixed model that incorporates both vertical and horizontal innovation spread is used to analyze the development of rhotacism in the Upper Kapuas-Mahakam languages of central Borneo. It is shown that subtle differences in the outcomes of rhotacism suggest a historical diffusion of rhotacism between dialects in a Proto-Upper Kapuas-Mahakam community. The subgroup-wide application of rhotacism interacted with other, localized changes that were restricted to specific dialects. Subgroup-wide changes therefore interact with already established dialectical divisions, leaving a mark on the historical evolution of languages in a dialectically heterogeneous community.
Alexander D. Smith (2026) studied this question.