Community Ecology

, Volume 1, Issue 2, pp 215–225 | Cite as

Support of the hyperbolic connectance hypothesis by qualitative stability of model food webs

  • X. Chen
  • J. E. CohenEmail author


Local stability analysis of dynamical models of interacting populations predicted that food web connectance (C) is proportional to 1/S where S is species richness. This “hyperbolic connectance hypothesis” was initially supported by analyses of documented food webs. This study shows that the qualitative global asymptotic stability of the Lotka-Volterra cascade model with a finite number of species predicts a relationship between connectance and species richness that agrees closely with the hyperbolic connectance hypothesis predicted from the analysis of local asymptotic stability. Moreover, the threshold of the qualitative global asymptotic stability in the Lotka-Volterra cascade model separates food webs in constant environments from those in fluctuating environments. The obvious discrepancy between the C-S relationship based on some recent data and that predicted by the dynamical models could be due to the selection of data.


Local asymptotic stability Lotka-Volterra cascade model Qualitative global asymptotic stability 



Lotka-Volterra Cascade Model


Local Asymptotic Stability


Qualitative Global Asymptotic Stability


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Copyright information

© Akadémiai Kiadó, Budapest 2000

Authors and Affiliations

  1. 1.Laboratory of PopulationsRockefeller University and Columbia UniversityNew YorkUSA

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