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.

Fisheries Management--An Essay for Ecologists

Author: P. A. Larkin, 1978

This essay is a limpid overview of fisheries science as it stood in the late seventies. My suspicion is that many of the issues Larkin flags continue to be relevant today. For example, he discusses the importance of optimal control as a modeling tool, as well as conceptually rich multi-species models. He also theorizes that there may come a day when specifically targeting mid-sized fish is viable, a dream that may long since have become reality (it would be interesting to find out.) Larkin discusses the utility of numerical modeling. He says that a "computer simulation can be a marvelous crutch to the imagination", though he cautions against modeling that is so system-specific that it lacks scientific generality. He debunks the common modeling ruse of assuming catch is proportional to abundance. He concludes by arguing for "experimental" management practices, i.e. adaptive types of control, and hopes that aquaculture and farming will provide solutions in the future. This is a good paper to return to for quotes to spike technical papers. A few examples: "The central problem of fisheries science remains: how to manipulate the circumstances of a fishery to social and economic advantage within some constraints of ecological prudence." "For better or for worse, most contemporary theory on the regulation of commercial fish populations is based on a huge mass of circumstantial evidence in the form of catch statistics." "... there is wide margin for wonder about whether density-dependent or density-independent processes more commonly regulate abundance, the usual implicit assumption being that the former prevail on a state set by the latter." "The machineries of density-dependent regulation commonly observed in fisheries nevertheless include: suppression of growth rate with an associated delay in age of maturity, and to a lesser extent a decline in fecundity; cannibalism, particularly on young of the year; predation, commonly by a wide range of species; and parasitisms and diseases (concerning which there are few quantitative epidemiological data)." "It is most commonly assumed that environmental factors influence survival multiplicatively, and hence generate log normal-type distributions in which there is equal probability that animals will be half as abundant or twice as abundant as would be the case deterministically."