Pseudo Dollo models for the evolution of binary characters along a tree

The stochastic Dollo model is a model for capturing evolution of features, for example cognate data in language evolution. However, it is rather sensitive to borrowing events, coding errors, semantic shift and other anomalies, so other models, in particular the covarion model, tends to have a better fit to the data. Here, we introduce the pseudo Dollo model, a model of character evolution along a tree that can be formulated as a three-state continuous time Markov chain (CTMC) model. The initial state represent absence of a feature, then a birth event allows the feature to be present. A death event can follow so that the feature becomes absent again. However, no new birth events are allowed after a death event has taken place. We examine the model in a fully Bayesian setting, and demonstrate it can have a better fit than some of the popular alternative models on some real world datasets. Some variations on the pseudo Dollo model are introduced as well, including the multi-state pseudo Dollo model and pseudo Dollo covarion model. The model is implemented in open source software Babel, a package to BEAST [2] licensed under LGPL. A user friendly way to set up an analysis is available through BEAUti, the graphical user interface of BEAST.