Appendix with the article "Likelihood calculation in a multistate model of vocabulary evolution for linguistic dating" by Philipp Rönchen, Tilo Wiklund and Harald Hammarström, published in LDC 14 (2024).

<p dir="ltr">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. </p><p dir="ltr">This appendix provides proof of a technical nature, generalized results for nonbinary trees, and our method for estimating meaningwise change rates in the case study.</p>