Darwin saw similarities between the evolution of species and the evolution of languages, and it is now widely accepted that similarities between related languages can often be interpreted in terms of a bifurcating descent history ('phylogenesis'). Such interpretations are supported when the distributions of shared and unshared traits (for example, in terms of etymological roots for elements of basic vocabulary) are analysed using tree-building techniques and found to be well-explained by a phylogenetic model. In this article, we question the demographic assumption which is sometimes made when a tree-building approach has been taken to a set of cultures or languages, namely that the resulting tree is also representative of a bifurcating population history. Using historical census data relating to Gaelic- and English-speaking inhabitants of Sutherland (Highland Scotland), we have explored the dynamics of language death due to language shift, representing the extreme case of lack of congruence between the genetic and the culture-historical processes. Such cases highlight the important role of selective cultural migration (or shifting between branches) in determining the extinction rates of different languages on such trees.