When two communities live apart and communicate littlelittle with each other, over time some innovations tend to differentiate the respective linguistic varieties until two systematically distinguishable dialects are formed. It is also known that speech varies from generation to generation, and certain isoglosses have a different frequency in different age cohorts. This is the informal description usually given for new dialect emergence.
But, are there any studies or models that attempt to quantify the weight of factors? For example, could the presence in antiquity of mountain ranges or rivers be quantified with respect to linguistic diversity? How tocan we measure the degree of interaction in different linguistic communities and how tocan we study the numerical correlation between that degree of interaction and the degree of linguistic divergence?