The Clumping Transition in Niche Competition: a Robust Critical Phenomenon

Details The Clumping Transition in Niche Competition: a Robust Critical Phenomenon The Clumping Transition in Niche Competition: a Robust Critical Phenomenon

2010-05-11

arxiv.org/abs/1005.1961v1

Journal of Statistical Mechanics JSTAT P05005 (2010)

Nonlinear Sciences

Adaptation and Self-Organizing Systems

16 pages, 7 figures; http://iopscience.iop.org/1742-5468/2010/05/P05005

Scientific paper

10.1088/1742-5468/2010/05/P05005

We show analytically and numerically that the appearance of lumps and gaps in the distribution of n competing species along a niche axis is a robust phenomenon whenever the finiteness of the niche space is taken into account. In this case depending if the niche width of the species $\sigma$ is above or below a threshold $\sigma_c$, which for large n coincides with 2/n, there are two different regimes. For $\sigma > sigma_c$ the lumpy pattern emerges directly from the dominant eigenvector of the competition matrix because its corresponding eigenvalue becomes negative. For $\sigma

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