Skepticism regarding the tree model has a long tradition in historical linguistics. Although scholars have
emphasized that the tree model and its long-standing counterpart, the wave theory, are not necessarily incompatible, the opinion
that family trees are unrealistic and should be completely abandoned in the field of historical linguistics has always enjoyed a
certain popularity. This skepticism has further increased with the advent of recently proposed techniques for data visualization
which seem to confirm that we can study language history without trees. In this article, we show that the concrete arguments that
have been brought up in favor of achronistic wave models do not hold. By comparing the phenomenon of incomplete lineage sorting
in biology with processes in linguistics, we show that data which do not seem as though they can be explained using trees can
indeed be explained without turning to diffusion as an explanation. At the same time, methodological limits in historical
reconstruction might easily lead to an overestimation of regularity, which may in turn appear as conflicting patterns when the
researcher is trying to reconstruct a coherent phylogeny. We illustrate how, in several instances, trees can benefit language
comparison, although we also discuss their shortcomings in modeling mixed languages. While acknowledging that not all aspects of
language history are tree-like, and that integrated models which capture both vertical and lateral language relations may depict
language history more realistically than trees do, we conclude that all models claiming that vertical language relations can be
completely ignored are essentially wrong: either they still tacitly draw upon family trees or they only provide a static display
of data and thus fail to model temporal aspects of language history.
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