  Spontaneous symmetry breaking plays a fundamental role in many areas of
condensed matter and particle physics. A fundamental problem in ecology is the
elucidation of the mechanisms responsible for biodiversity and stability.
Neutral theory, which makes the simplifying assumption that all individuals
(such as trees in a tropical forest) --regardless of the species they belong
to-- have the same prospect of reproduction, death, etc., yields gross patterns
that are in accord with empirical data. We explore the possibility of birth and
death rates that depend on the population density of species while treating the
dynamics in a species-symmetric manner. We demonstrate that the dynamical
evolution can lead to a stationary state characterized simultaneously by both
biodiversity and spontaneously broken neutral symmetry.
