  Lateral transfer, a process whereby species exchange evolutionary traits
through non-ancestral relationships, is a frequent source of model
misspecification in phylogenetic inference. Lateral transfer obscures the
phylogenetic signal in the data as the histories of affected traits are mosaics
of the overall phylogeny. We control for the effect of lateral transfer in a
Stochastic Dollo model and a Bayesian setting. Our likelihood is highly
intractable as the parameters are the solution of a sequence of large systems
of differential equations representing the expected evolution of traits along a
tree. We illustrate our method on a data set of lexical traits in Eastern
Polynesian languages and obtain an improved fit over the corresponding model
without lateral transfer.
