  We develop a model of phonological contrast in natural language.
Specifically, the model describes the maintenance of contrast between different
words in a language, and the elimination of such contrast when sounds in the
words merge. An example of such a contrast is that provided by the two vowel
sounds 'i' and 'e', which distinguish pairs of words such as 'pin' and 'pen' in
most dialects of English. We model language users' knowledge of the
pronunciation of a word as consisting of collections of labeled exemplars
stored in memory. Each exemplar is a detailed memory of a particular utterance
of the word in question. In our model an exemplar is represented by one or two
phonetic variables along with a weight indicating how strong the memory of the
utterance is. Starting from an exemplar-level model we derive
integro-differential equations for the evolution of exemplar density fields in
phonetic space. Using these latter equations we investigate under what
conditions two sounds merge, thus eliminating the contrast. Our main conclusion
is that for the preservation of phonological contrast, it is necessary that
anomalous utterances of a given word are discarded, and not merely stored in
memory as an exemplar of another word.
