  We study communities emerging from generalised random Lotka--Volterra
dynamics with a large number of species with interactions determined by the
degree of niche overlap. Each species is endowed with a number of traits, and
competition between pairs of species increases with their similarity in trait
space. This leads to a model with random Hopfield-like interactions. We use
tools from the theory of disordered systems, notably dynamic mean field theory,
to characterise the statistics of the resulting communities at stable fixed
points and determine analytically when stability breaks down. Two distinct
types of transition are identified in this way, both marked by diverging
abundances, but differing in the behaviour of the integrated response function.
At fixed points only a fraction of the initial pool of species survives. We
numerically study the eigenvalue spectra of the interaction matrix between
extant species. We find evidence that the two types of dynamical transition
are, respectively, associated with the bulk spectrum or an outlier eigenvalue
crossing into the right half of the complex plane.
