Winnerless competition principle and prediction of the transient dynamics in a Lotka–Volterra model

Predicting the evolution of multispecies ecological systems is an intriguing problem. A sufficiently complex model with the necessary predicting power requires solutions that are structurally stable. Small variations of the system parameters should not qualitatively perturb its solutions. When one i...

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Bibliographic Details
Published in:Chaos (Woodbury, N.Y.) N.Y.), 2008-12, Vol.18 (4), p.043103-043103-9
Main Authors: Afraimovich, Valentin, Tristan, Irma, Huerta, Ramon, Rabinovich, Mikhail I.
Format: Article
Language:English
Subjects:
Animals
Biological Evolution
Computer Simulation
Ecosystem
Game Theory
Humans
Models, Biological
Nonlinear Dynamics
Population Dynamics
Predatory Behavior - physiology
Selection, Genetic
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Summary:Predicting the evolution of multispecies ecological systems is an intriguing problem. A sufficiently complex model with the necessary predicting power requires solutions that are structurally stable. Small variations of the system parameters should not qualitatively perturb its solutions. When one is interested in just asymptotic results of evolution (as time goes to infinity), then the problem has a straightforward mathematical image involving simple attractors (fixed points or limit cycles) of a dynamical system. However, for an accurate prediction of evolution, the analysis of transient solutions is critical. In this paper, in the framework of the traditional Lotka–Volterra model (generalized in some sense), we show that the transient solution representing multispecies sequential competition can be reproducible and predictable with high probability.
ISSN:1054-1500
1089-7682
DOI:10.1063/1.2991108