I will describe properties of niche models of biological species competing for a partially shared resource, of the general form of Lotka-Volterra competition equations [1,2,3]. The intensity of competition depends on the position of species in an abstract niche space. Depending on the shape of the interaction kernel, a pattern-forming instability may occur which leads either to extinction of species too close to a successful one, or to the formation of clusters of similar species periodically spaced from other groups. We estimate properties of the species distributions, such as the steady number of species and their spacing, for different types of interactions. The effects of adding ecological, evolutionary or numerical effects to the basic niche model, as well as the influence of the choice of carrying capacity function is also discussed.
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[1] Simone Pigolotti, Cristóbal López and Emilio Hernández-García, Species clustering in competitive Lotka-Volterra models, Physical Review Letters 98, 258101 (2007).
[2] Simone Pigolotti, Cristóbal López, Emilio Hernández-García and Ken H. Andersen,
How competition leads to lumpy or uniform species distributions, arXiv preprint 0802.3274 (2008).
[3] Emilio Hernández-García, Cristóbal López, Simone Pigolotti, Ken H. Andersen. Species competition: coexistence, exclusion and clustering,
arXiv preprint 0812.1279 (2008).