Two families of quantitative methods have been used to infer geographical homelands of language families: Bayesian phylogeography and the 'diversity method'. Bayesian methods model how populations may have moved using a phylogenetic tree as a backbone, while the diversity method assumes that the geographical area where linguistic diversity is highest likely corresponds to the homeland. No systematic tests of the performances of the different methods in a linguistic context have so far been published. Here, we carry out performance testing by simulating language families, including branching structures and word lists, along with speaker populations moving in space. We test six different methods: two versions of BayesTraits; the relaxed random walk model of BEAST 2; our own RevBayes implementations of a fixed rate and a variable rates random walk model; and the diversity method. As a result of the tests, we propose a hierarchy of performance of the different methods. Factors such as geographical idiosyncrasies, incomplete sampling, tree imbalance and small family sizes all have a negative impact on performance, but mostly across the board, the performance hierarchy generally being impervious to such factors. This article is part of the theme issue 'Reconstructing prehistoric languages'.
Keywords: Bayesian phylogeography; historical linguistics; homelands; migration; phylogenetics.