  In spoken languages, speakers divide up the space of phonetic possibilities
into different regions, corresponding to different phonemes. We consider a
simple exemplar model of how this division of phonetic space varies over time
among a population of language users. In the particular model we consider, we
show that, once the system is initialized with a given set of phonemes, that
phonemes do not become extinct: all phonemes will be maintained in the system
for all time. This is in contrast to what is observed in more complex models.
Furthermore, we show that the boundaries between phonemes fluctuate and we
quantitatively study the fluctuations in a simple instance of our model. These
results prepare the ground for more sophisticated models in which some phonemes
go extinct or new phonemes emerge through other processes.
