Competitive Exclusion and Limiting Similarity: A Unified Theory

Meszena G, Gyllenberg M, Pasztor L, & Metz JAJ (2005). Competitive Exclusion and Limiting Similarity: A Unified Theory. IIASA Interim Report. IIASA, Laxenburg, Austria: IR-05-040

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Abstract

Robustness of coexistence against changes of parameters is investigated in a model-independent manner through analyzing the feed-back loop of population regulation. We define coexistence as fixed point of the community dynamics with no population having zero size. It is demonstrated that the parameter range allowing coexistence shrinks and disappears when the Jacobian of the dynamics decreases to zero. A general notion of regulating factors/variables is introduced. For each population, its 'impact' and 'sensitivity' niches a re defined as the differential impact on, and the differential sensitivity towards, the regulating variables, respectively. Either similarity of the impact niches, or similarity of the sensitivity niches, result in a small Jacobian and in a reduced likelihood of coexistence. For the case of a resource continuum, this result reduces to the usual "limited niches overlap" picture for both kinds of niche. As an extension of these ideas to the coexistence of infinitely many species, we demonstrate that Roughgarden's example for coexistence of a 'continuum' of populations is structurally unstable.

Item Type: Monograph (IIASA Interim Report)
Research Programs: Adaptive Dynamics Network (ADN)
Depositing User: IIASA Import
Date Deposited: 15 Jan 2016 02:18
Last Modified: 06 Nov 2016 19:45
URI: http://pure.iiasa.ac.at/7796

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