{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:BMJR7HW3GCAXEBWA67VVMN27OK","short_pith_number":"pith:BMJR7HW3","schema_version":"1.0","canonical_sha256":"0b131f9edb30817206c0f7eb56375f7292661cd10036d416eca6d7ecd3850615","source":{"kind":"arxiv","id":"1005.1961","version":1},"attestation_state":"computed","paper":{"title":"The Clumping Transition in Niche Competition: a Robust Critical Phenomenon","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","physics.bio-ph"],"primary_cat":"nlin.AO","authors_text":"E. van Nes, H. Fort, M. Scheffer","submitted_at":"2010-05-11T22:11:15Z","abstract_excerpt":"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 emerges directly from the dominant eigenvector of the competition matrix because its corresponding eigenvalue becomes negative. For $\\sigma