Time‐Delay Versus Stability in Population Models with Two and Three Trophic Levels

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Abstract
If a biological or other system has a potentially stabilizing negative feedback mechanism, which, however, is applied with a time lag long compared to the natural time scale of the system, the result is instability, not stability. This theme is developed in detail for vegetation—herbivore and vegetation—herbivore—carnivore systems in which the stabilizing resource—limitation effect operates on the herbivore population with a time lag. Under certain conditions, which are commonly met in nature, the vegetation—herbivore—carnivore system is stable (with population fluctuations being damped out), while the vegetation—herbivore system with no predators is unstable. This model, which can be supported with some observational data, suggests inter alia that herbivore population numbers may often be set neither by predators alone nor by vegetation alone, but by an explicit interplay between both effects.

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