The intuitive appeal of this model should be obvious; indeed, at first it may be hard to imagine how else languages could evolve. Moreover, its clear resemblance to models that are used in other historical disciplines (notably evolutionary biology) makes it possible to apply powerful computational techniques from these fields to comparative language data (see Ringe et al. 2002; Gray & Atkinson 2003, inter multa alia).
Unfortunately, there is one assumption of the tree model that often fails to hold: that the proto-language develops independently in each subcommunity. In fact, it is rare for communities to be completely isolated from each other (when they are geographically adjacent), and it is common for an innovation arising in one community to spread to adjacent communities, especially at a stage when the emerging dialects are still mutually intelligible (i.e., still varieties of the “same language”). As dialectologists know well (Saussure 1916; Bloomfield 1933), the diffusion of innovations across a dialect continuum typically results in a patchwork of intersecting innovations, rather than the neat, nested pattern that would be expected under the tree model. Given that many (if not most) language families are descended from dialect networks (i.e., are linkages), this is what we should expect in language families as well—a fact that was recognised by proponents of the wave model (e.g. Schmidt 1872).
There have been many proposals in the literature for representations of language genealogy that capture the facts of the wave model (e.g. Hock’s “‘truncated octopus-like’ tree”, Southworth’s “tree envelopes”, or most recently NeighborNet). However, unlike the tree model, none of them has succeeded in combining formalism and precision with ready historical interpretability—and indeed, this is probably why none of them has been as widely adopted.
We have created our own non-tree representation of language genealogy, which we call Historical Glottometry. (The name is modeled on “dialectometry”, which was one of our initial inspirations.) The tutorial explains how this approach works.