Stochastic structure and nonlinear dynamics of food webs

Qualitative stability in a Lotka-Volterra cascade model

J. E. Cohen, T. Luczak, Charles Newman, Z. M. Zhou

Research output: Contribution to journalArticle

Abstract

Two competing models currently offer to explain empirical regularities observed in food webs. The Lotka-Volterra model describes population dynamics; the cascade model describes trophic structure. In a real ecological community, both population dynamics and trophic structure are important. This paper proposes and analyses a new hybrid model that combines population dynamics and trophic structure: the Lotka-Volterra cascade model (LVCM). The LVCM assumes the population dynamics of the Lotka-Volterra model when the interactions between species are shaped by a refinement of the cascade model. A critical surface divides the three-dimensional parameter space of the LVCM into two regions. In one region, as the number of species becomes large, the limiting probability that the LVCM is qualitatively globally asymptotically stable is positive. In the region on the other side of the critical surface, and on the critical surface itself, this limiting probability is zero. Thus the LVCM displays an ecological phase transition: gradual changes in the probabilities of various kinds of population dynamical interactions related to feeding can have sharp effects on a community's qualitative stability. The LVCM shows that an inverse proportionality between connectance and the number of species, and a direct proportionality between the number of links and the number of species, as observed in data on food webs, need not be directly connected with the qualitative global asymptotic stability or instability of population dynamics. Empirical testing of the LVCM will require field data on the population dynamical effects of feeding relations.

Original languageEnglish (US)
Pages (from-to)607-627
Number of pages21
JournalProceedings. Biological sciences / The Royal Society
Volume240
Issue number1299
DOIs
StatePublished - 1990

Fingerprint

Nonlinear Dynamics
Food Chain
Population Dynamics
food webs
food web
Population dynamics
population dynamics
trophic structure
Lotka-Volterra model
Biota
Phase Transition
Population
phase transition
Asymptotic stability

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Earth and Planetary Sciences(all)
  • Environmental Science(all)

Cite this

Stochastic structure and nonlinear dynamics of food webs : Qualitative stability in a Lotka-Volterra cascade model. / Cohen, J. E.; Luczak, T.; Newman, Charles; Zhou, Z. M.

In: Proceedings. Biological sciences / The Royal Society, Vol. 240, No. 1299, 1990, p. 607-627.

Research output: Contribution to journalArticle

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