Introduction

We discuss the problem of characterizing the evolutionary dynamics of linguistic populations over successive generations. Here we introduce the framework of Cavalli-Sforza and Feldman (1981) for the treatment of cultural evolution and show how to apply it to the particular case of language change. We relate the approach to that of Niyogi and Berwick (1995) and show how to map trajectories in one to those in the other. In both models, language acquisition serves as the mechanism of transmission of language from one generation to the next. For memoryless learning algorithms and the case of two languages in contact, we derive particular dynamical systems under the assumptions of both kinds of models. As an application of such computational modeling to historical change, we consider the evolution of English from the 9th century to the 14th century A.D. and discuss the role of such modeling to judge the adequacy of competing linguistic accounts for historical phenomena.

The problem of language change

A central concern for historical linguists is to characterize the dimensions along which human languages change over time and explain why they do so. Under the assumptions of contemporary linguistic theory, change in linguistic behavior of human populations must be a result of a change in the internal grammars that successive generations of humans employ. The question then becomes: why do the grammars of successive generations differ from each other? In order to answer this question, we need to know how these grammars are acquired in the first place and how the grammars of succeeding generations are related to each other.