Related Experiment Video
Updated: Aug 19, 2026

Layers of Symbiosis - Visualizing the Termite Hindgut Microbial Community
Published on: May 28, 2007
Trichotomous-noise-induced catastrophic shifts in symbiotic ecosystems
Romi Mankin1, Ain Ainsaar, Astrid Haljas
1Department of Natural Sciences, Tallinn Pedagogical University, Narva maantee 25, 10120 Tallinn, Estonia.
Abstract:
An N-species Lotka-Volterra stochastic model of a symbiotic ecological system with the Verhulst self-regulation mechanism is considered. The effect of fluctuating environment on the carrying capacity of a population is modeled as the colored three-level Markovian (trichotomous) noise. In the framework of the mean-field theory an explicit self-consistency equation for stationary states is presented. Stability and instability conditions and colored-noise-induced discontinuous transitions (catastrophic shifts) in the model are investigated. In some cases the mean field exhibits hysteresis as a function of the noise parameters. It is shown that the occurrence of catastrophic shifts can be controlled by noise parameters, such as correlation time, amplitude, and flatness. The dependence of the critical coupling strengths on the noise parameters is found and illustrated by phase diagrams. Implications of the results on some modifications of the model are discussed.
Related Concept Videos
Symbiosis
Threats to Biodiversity
Ecological Disturbance
Evolution of New Traits in Microbes
Microbial Interactions: Mutualism
Microbe-Plant Interactions

