Species competition: coexistence, exclusion and clustering
  We present properties of Lotka-Volterra equations describing ecological competition among a large number of competing species. First we extend to the case of a non-homogeneous niche space stability conditions for solutions representing species coexistence. Second, we discuss mechanisms leading to species clustering and obtain an analytical solution for a lumped state in a specific instance of the system. We also discuss how realistic ecological interactions may result in different types of competition coefficients. 
Emilio Hernandez-Garcia, Cristobal Lopez (IFISC), Simone Pigolotti   (NBI), Ken H. Andersen (AQUA)