Trudgill (2004) proposed that the emergence of New Zealand English, and of isolated new dialects generally, is purely deterministic. It can be explained solely in terms of the frequency of occurrence of particular variants and the frequency of interactions between different speakers in the society. Trudgill's theory is closely related to usage-based models of language, in which frequency plays a role in the representation of linguistic knowledge and in language change. Trudgill's theory also corresponds to a neutral evolution model of language change. We use a mathematical model based on Croft's usage-based evolutionary framework for language change (Baxter, Blythe, Croft, & McKane, 2006), and investigate whether Trudgill's theory is a plausible model of the emergence of new dialects. The results of our modeling indicate that determinism cannot be a sufficient mechanism for the emergence of a new dialect. Our approach illustrates the utility of mathematical modeling of theories and of empirical data for the study of language change.