Language change - wave or tree?

Below my introduction is a copy-and-pasted section of an article that is on https://www.britannica.com/science/linguistics/The-comparative-method#ref411908.

It's a little academic but it talks about two contrasting theories/models of how language changes. First, belonging to the 'comparative' method of linguistic analysis (don't worry about that) is a 'family tree' model (August Schleicher's model), where change causes aspects of language to branch off from the standard and become separate e.g. dialects forming, or new languages splitting off from the parent language (for instance, pidgins and creoles). See if you can read closely to find out what the criticisms of this model are.

The contrasting model is the wave model (Johannes Schmidt), which visualises causes of change impacting like dropped stones in a pool where the waves spead out, becoming less powerful as they move from the impetus for change and can overlap and influence one another (see the diagram and explanation on the right of the Wikipedia article). This model explains why trends in language don't continue to create more and more diverse 'branches' but instead can re-converge, as we see in dialect levelling, or in standard language users using dialect or sociolect for covert prestige e.g. Martha's Vineyard.

Excerpt from the website link above:

Criticisms of the comparative method

One of the criticisms directed against the comparative method is that it is based upon a misleading genealogical metaphor. In the mid-19th century, the German linguist August Schleicher introduced into comparative linguistics the model of the “family tree.” There is obviously no point in time at which it can be said that new languages are “born” of a common parent language. Nor is it normally the case that the parent language “lives on” for a while, relatively unchanged, and then “dies.” It is easy enough to recognize the inappropriateness of these biological expressions. No less misleading, however, is the assumption that languages descended from the same parent language will necessarily diverge, never to converge again, through time. This assumption is built into the comparative method as it is traditionally applied. And yet there are many clear cases of convergence in the development of well-documented languages. The dialects of England are fast disappearing and are far more similar in grammar and vocabulary today than they were even a generation ago. They have been strongly influenced by the standard language. The same phenomenon, the replacement of nonstandard or less prestigious forms with forms borrowed from the standard language or dialect, has taken place in many different places at many different times. It would seem, therefore, that one must reckon with both divergence and convergence in the diachronic development of languages: divergence when contact between two speech communities is reduced or broken and convergence when the two speech communities remain in contact and when one is politically or culturally dominant.

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  August Schleicher, engraving

  Bildarchiv Preussischer Kulturbesitz, Berlin

The comparative method presupposes linguistically uniform speech communities and independent development after sudden, sharp cleavage. Critics of the comparative method have pointed out that this situation does not generally hold. In 1872 a German scholar, Johannes Schmidt, criticized the family-tree theory and proposed instead what is referred to as the wave theory, according to which different linguistic changes will spread, like waves, from a politically, commercially, or culturally important centre along the main lines of communication, but successive innovations will not necessarily cover exactly the same area. Consequently, there will be no sharp distinction between contiguous dialects, but, in general, the further apart two speech communities are, the more linguistic features there will be that distinguish them.