학술논문
The Clumping Transition in Niche Competition: a Robust Critical Phenomenon
Document Type
Working Paper
Author
Source
Journal of Statistical Mechanics JSTAT P05005 (2010)
Subject
Language
Abstract
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 $\sigma - sigma_c$ the lumpy pattern disappears. Furthermore, this clumping transition exhibits critical slowing down as $\sigma$ is approached from above. We also find that the number of lumps of species vs. $\sigma$ displays a stair-step structure. The positions of these steps are distributed according to a power-law. It is thus straightforward to predict the number of groups that can be packed along a niche axis and it coincides with field measurements for a wide range of the model parameters.
Comment: 16 pages, 7 figures; http://iopscience.iop.org/1742-5468/2010/05/P05005
Comment: 16 pages, 7 figures; http://iopscience.iop.org/1742-5468/2010/05/P05005