Species competition: coexistence, exclusion and clustering

We present properties of Lotka-Volterra equations describing ecological competition
among a large number of interacting species. First we extend previous stability
conditions to the case of a non-homogeneous niche space, i.e. that of a carrying
capacity depending on the species trait. Second, we discuss mechanisms leading to
species clustering and obtain an analytical solution for a state with a lumped species
distribution for a specific instance of the system. We also discuss how realistic
ecological interactions may result in different types of competition coeffcients.