  One proposed mechanism of language change concerns the role played by
second-language (L2) learners in situations of language contact. If
sufficiently many L2 speakers are present in a speech community in relation to
the number of first-language (L1) speakers, then those features which present a
difficulty in L2 acquisition may be prone to disappearing from the language.
This paper presents a mathematical account of such contact situations based on
a stochastic model of learning and nonlinear population dynamics. The
equilibria of a deterministic reduction of the model, describing a mixed
population of L1 and L2 speakers, are fully characterized. Whether or not the
language changes in response to the introduction of L2 learners turns out to
depend on three factors: the overall proportion of L2 learners in the
population, the strength of the difficulty speakers face in acquiring the
language as an L2, and the language-internal utilities of the competing
linguistic variants. These factors are related by a mathematical formula
describing a phase transition from retention of the L2-difficult feature to its
loss from both speaker populations. This supplies predictions that can be
tested against empirical data. Here, the model is evaluated with the help of
two case studies, morphological levelling in Afrikaans and the erosion of null
subjects in Afro-Peruvian Spanish; the model is found to be broadly in
agreement with the historical development in both cases.
