Nutrients, Algae and Herbivores — the Paradox of Enrichment Revisited

Abstract

Lotka (1925) and Volterra (1926) independently developed simple mathematical descriptions of the interaction between predators and their prey. These theories later became the ancestors of a whole family of what is collectively known as Lotka-Volterra models. Elementary ecology text books usually concentrate on the simplest kind of Lotka-Volterra model, where the prey have an unbounded capacity for exponential growth in the absence of predators, and where the predators have an unbounded capacity for killing prey. As noted by May (1975), such a system has certain pathological dynamic properties which are equivalent to the neutral stability of a frictionless pendulum: the system oscillates forever with an amplitude that is determined solely by the initial conditions.

Rosenzweig’s results might more reasonably have been used to prompt questions such as the following What are the critical values of enrichment? How does the time to extinction of a system vary with the degree of enrichment? How do critical levels of enrichment and time to extinction vary with other parameters? Why does nature not collapse?

McAllister, LeBrasseur and Parsons (1972).