  We review the task of aligning simple models for language dynamics with
relevant empirical data, motivated by the fact that this is rarely attempted in
practice despite an abundance of abstract models. We propose that one way to
meet this challenge is through the careful construction of null models. We
argue in particular that rejection of a null model must have important
consequences for theories about language dynamics if modelling is truly to be
worthwhile. Our main claim is that the stochastic process of neutral evolution
(also known as genetic drift or random copying) is a viable null model for
language dynamics. We survey empirical evidence in favour and against neutral
evolution as a mechanism behind historical language changes, highlighting the
theoretical implications in each case.
