The clumping transition in niche competition: A robust critical phenomenon

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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 on whether the niche width of the species s is above or below a threshold sc, which for large n coincides with 2/n, there are two different regimes. For s > sc the lumpy pattern emerges directly from the dominant eigenvector of the competition matrix because its corresponding eigenvalue becomes negative. For s = sc the lumpy pattern disappears. Furthermore, this clumping transition exhibits critical slowing down as s is approached from above. We also find that the number of lumps of the species distribution versus s 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 this value is consistent with field measurements for a wide range of the model parameters
Original languageEnglish
Article numberP05005
JournalJournal of Statistical Mechanics: Theory and Experiment
Issue number5
Publication statusPublished - 2010


  • limiting similarity
  • body-size
  • entropy
  • space


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