Species clustering in competitive Lotka-Volterra models.
We study the properties of general Lotka-Volterra models with competitive interactions. The intensity of the competition depends on the position of species in an abstract niche space through an interaction kernel. We show analytically and numerically that the properties of these models change dramatically when the Fourier transform of this kernel is not positive definite, due to a pattern-forming instability. We estimate properties of the species distributions, such as the steady number of species and their spacings, for different types of interactions, including stretched exponential and constant kernels.
Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), Campus de la Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain.
Simone
S
Pigolotti
Cristóbal
C
López
Emilio
E
Hernández-García
D000818:Animals; D003163:Competitive Behavior; D008954:Models, Biological; D008962:Models, Theoretical; D011157:Population Dynamics; D013045:Species Specificity