Logistic Theory of Food Web Dynamics

• Published in: Ecology (Durham) Vol. 76; no. 2; pp. 336 - 343
• Main Authors: Berryman, A. A., Michalski, J., Gutierrez, A. P., Arditi, R.
• Format: Journal Article
• Language: English
• Published: Washington, DC Ecological Society of America 01.03.1995; The Ecological Society of America; Brooklyn Botanic Garden, etc
• Subjects: Animal populations; Animal, plant and microbial ecology; Biological and medical sciences; Concepts; Ecological competition; Ecological modeling; Ecology; Food webs; Fundamental and applied biological sciences. Psychology; General aspects. Techniques; Logistics; Methods and techniques (sampling, tagging, trapping, modelling...); Population ecology; Predators; Renewable resources; Species; Trophic levels; Trophic relationships; Trophic chain; Food web; Trophic level; Theory; Intraspecific competition; Trophic relation; Lotka Volterra model
• ISSN: 0012-9658; 1939-9170
• DOI: 10.2307/1941193

Classical food—web theory arises from Lotka—Volterra models. As an alternative, we develop a model from the logistic concept of demand and supply. We first extend the logistic to an arbitrary species in a trophic chain or stack by developing a simple equation for any population Xᵢ: 1/Xᵢ dXᵢ/dt = aᵢ — bᵢXᵢ — Xᵢ/cᵢXᵢ — ₁ — dᵢXᵢ ₊ ₁/Xᵢ, which includes the effects of intra—specific competition for fixed resources (the term bᵢXᵢ), intra—specific competition for renewable resources in the lower trophic level (the term Xᵢ/cᵢXᵢ — ₁), and consumers in the upper trophic level (the term dᵢXᵢ ₊ ₁/Xᵢ). This equation emerges from the basic logistic concept of demand and supply, as captured by the consumer/resource ratios, and fulfills all the requirements for a plausible food—chain equation. We then generalize the equation to any population in a food web of arbitrary complexity 1/Xᵢ dXᵢ/dt = aᵢ bᵢXᵢ — Xᵢ/sⱼ cᵢ ⱼXⱼFʳ ⱼ ⁽ ⁱ ⁾ — sₖ dᵢ ₖXₖFₖ ᶜ ⁽ ⁱ ⁾/Xᵢ, where Fʳ ⱼ ⁽ ⁱ ⁾ is the fraction of population Xⱼ that is a resource for i, and Fₖ ᶜ ⁽ ⁱ ⁾ is the fraction of population Xₖ that consumes i. This equation meets all the requirements for a general food web model. Some properties of the model are discussed.