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In the same way that there are population models in epidemiology, for example the spread of diseases, is there anything equivalent in linguistics to model the dynamics of language formation? These models, despite being simplifications, allow us to understand the dynamics of the evolution of this system. And they can be constantly improved and simulated on computers.

I recently started to get interested in this topic, and I do more research in the area of ​​multi-agent systems. However, I had never done any research on this subject in linguistics and I don't even know where to look and how to ask. My question is this:

Are there population models on the dynamics of the evolution of a language?

For example, if we assume that there is a population that speaks a language, and that at one point, that population has been geographically separated in space, and like any natural language there will be rates of linguistic variation and a rate of fixation of these variations. It would be interesting if there were mathematical models that would allow us to simulate systems on the computer and set the parameters to see the impact that each type of parameter has on the model. Thus, the simulation could show how a language could branch out into two languages.

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I've seen one agent-based model recently: van Trijp, R. (2013), Linguistic Assessment Criteria for Explaining Language Change: A Case Study on Syncretism in German Definite Articles. This paper tries to explain the diachronic change of a small part of German grammar by having agents play "language games" (using Fluid Construction Grammar).

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The paper "Statistical physics of language maps in the USA" by Burridge, Vaux, Gnacik & Grudeva may be sort of what you're looking for. Languages aren't "formed", but they change. Since judgments as to whether two speech forms are "different languages" can be extremely subjective, there is no hope of computing the probability that two separated English speaking populations will have accumulated enough differences that we would deem them "different languages" rather that "dialects", but that paper at least has a mathematical framework for conducting an analysis.

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