If every productive form of linguistic expression can be described by some idealized human grammar, an individuals's variable linguistic behavior (Weinreich, Labov, & Herzog, 1968) can be modeled as a statistical distribution of multiple idealized grammars. The distribution of grammars is determined by the interaction between the biological constraints on human grammar and the properties of linguistic data in the environment during the course of language acquisition. Such interaction can be formalized precisely and quantitatively in a mathematical model of language learning. Consequently, we model language change as the change in grammar distribution over time, which can be related to the statistical properties of historical linguistic data. As an empirical test, we apply the proposed model to explain the loss of the verb-second phenomenon in Old French and Old English based on corpus studies of historical texts.