Food Web Assembly Rules for Generalized Lotka-Volterra Equations.

ABSTRACT: In food webs, many interacting species coexist despite the restrictions imposed by the competitive exclusion principle and apparent competition. For the generalized Lotka-Volterra equations, sustainable coexistence necessitates nonzero determinant of the interaction matrix. Here we show that this requirement is equivalent to demanding that each species be part of a non-overlapping pairing, which substantially constrains the food web structure. We demonstrate that a stable food web can always be obtained if a non-overlapping pairing exists. If it does not, the matrix rank can be used to quantify the lack of niches, corresponding to unpaired species. For the species richness at each trophic level, we derive the food web assembly rules, which specify sustainable combinations. In neighboring l

SUBMITTER: Haerter JO 

PROVIDER: S-EPMC4734619 | biostudies-literature | 2016 Feb

REPOSITORIES: biostudies-literature