On a new method to study drastic change in ecosystems

We describe a novel method to study drastic change in ecosystems, based on generic functions used in the study of phase transitions and related physical phenomena. We illustrate its use by applying it to the problem of shallow lake eutrophication, and express our results in terms of an interplay between phosphorus content in the water column and fluxes of this substance between the lake and both its biological community and its surroundings. We contrast our solution to this problem with a previous one based on the concept of resilience, and on bifurcation analysis of a dynamical equation that also involves phosphorus concentration and fluxes. We then suggest a generalized dynamical scheme incorporating the generic functions above, that reduces to our original method in the stationary condition, and allows in addition dealing with cyclic and chaotic regimes, as illustrated through a particular example.