title: Self-localized states in species competition.
abstract: 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 of 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 leads to the appearance of them.
authors.affiliation: IFISC (CSIC-UIB), Instituto de Física Interdisciplinar y Sistemas Complejos, Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain and Institute for Chemistry and Biology of the Marine Environment (ICBM), Carl-von-Ossietzky University of Oldenburg, Carl-von-Ossietzky-Strasse 9-11, 26111 Oldenburg, Germany.
authors.forename: Pavel V
authors.initials: PV
authors.lastname: Paulau
authors.affiliation: IFISC (CSIC-UIB), Instituto de Física Interdisciplinar y Sistemas Complejos, Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain.
authors.forename: Damià
authors.initials: D
authors.lastname: Gomila
authors.affiliation: IFISC (CSIC-UIB), Instituto de Física Interdisciplinar y Sistemas Complejos, Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain.
authors.forename: Cristóbal
authors.initials: C
authors.lastname: López
authors.affiliation: IFISC (CSIC-UIB), Instituto de Física Interdisciplinar y Sistemas Complejos, Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain.
authors.forename: Emilio
authors.initials: E
authors.lastname: Hernández-García
mesh_terms: D000818:Animals; D005075:Biological Evolution; D003163:Competitive Behavior / Q000502:physiology*; D003198:Computer Simulation; D017753:Ecosystem; D006801:Humans; D008954:Models, Biological; D011157:Population Dynamics; D011235:Predatory Behavior / Q000502:physiology*; D013045:Species Specificity