Likelihood calculation in a multistate model of vocabulary evolution for linguistic dating

Computational methods of language dating make inferences about the divergence times of protolanguages by evaluating the patterns of inheritance in the vocabulary of modern languages, given the specification of a model of vocabulary evolution. We consider a model that describes vocabulary evolution as the replacement of traits by new traits from an infinite state space along a tree. This model has been introduced in previous literature but so far it has not been used in many applications. We give a general recursive algorithm for calculating likelihoods and argue that the model gives a more realistic representation of vocabulary evolution over time, compared to existing models like the Stochastic Dollo model. We also provide a case study demonstrating the model’s potential applications.