  We study the conditions under which species interaction, as described by
continuous versions of the competitive Lotka-Volterra model (namely the
nonlocal Kolmogorov-Fisher model, and its differential approximation), can
support the existence of localized states, i.e. patches of species with
enhanced population surrounded in niche space by species at smaller densities.
These states would arise from species interaction, and not by any preferred
niche location or better fitness. In contrast to previous works we include only
quadratic nonlinearities, so that the localized patches appear on a background
of homogeneously distributed species coexistence, instead than on top of the
no-species empty state. For the differential model we find and describe in
detail the stable localized states. For the full nonlocal model, however
competitive interactions alone do not allow the conditions for the observation
of self-localized states, and we show how the inclusion of additional
facilitative interactions lead to the appearance of them.
