Food Web Theory and Stability

Author: A. Hastings, 1988.

This very brief article argues that food web theory is not an adequate approach for understanding questions about stability. He makes several salient points: 1. "Stability" is not the same thing as "persistence"--the latter implies species never go extinct, the former is a mathematical construct that may or may not be applicable to biological systems. 2. Systems may not be persistent, but may still have stable equilibria or limit cycles (e.g. a one-species system with an Allee effect.) 3. Persistence does not imply stability. Indeed, nonequilibrium solutions are important in allowing multiple species to coexist on limited resources. 4. There are a few key "structural" elements to ecological models, including age, spatial distribution, genetic and phenotypic patterns. Hastings argues that non-linear density dependence is critical, as it allows complex dynamics (food web models are often based on Lotka-Volterra dynamics, and are thus globally stable; introducing non-linearities in systems with even three species can lead to chaos.) He also argues that including age or stage structure is very important. Food web theorists tend to include such things by introducing the idea of "trophic" species, but Hastings argues that this notion is incompatible with dynamic models. The article is summed up in the conclusion: "The understanding of stability and dynamics must be based on detailed models, which include structure within species. Food web theory and general models may be appropriate for questions at the static level, but they are not detailed enough to understand stability questions." In other words, stability is not a matter for food webs, but for detailed, concrete systems.