by Marten Scheffer, Marten.Scheffer@Aqec.WKAO.WAU.NL and Bob Kooi firstname.lastname@example.org
Prof. S. Rinaldi had informal discussions with Marten Scheffer, he was a speaker at the symposium held Tuesday 27 June 2000 VU Amsterdam and he asked questions on the defence by Martin Boer of the thesis entitled ``Tritrophic food chain dynamics''. The program of this symposium was given in the previous issue of the Newsletter, dated May 18, 2000.
Martin Boer was the first speaker and for an abstract of his talk the reader is referred to the summary of his PhD thesis given in the May 18 issue. At the website http://www.bio.vu.nl//thb/deb/deblab/art.html you will find a number of figures presented by Martin during his contribution One figure shows a 3-D plot of the domain of attraction for a chaotic attractor of a tri-trophic food chain consisting of a nutrient, prey, predator and a top-predator in the chemostat. Other figures show a homoclinic orbit of a saddle cycle and a heteroclinic orbit between a saddle equilibrium and a saddle cycle
Abstracts of the talks by Sergio Rinaldi (Milaan) and Marten Scheffer
(Wageningen UR) are:
Sergio Rinaldi, Politecnico di Milano, Italy, email@example.com.
Peak-to-Peak Dynamics in food chains
Dynamical systems with chaotic behavior sometimes enjoy a remarkable
property, called peak-to-peak dynamics (PPD). Such PPD can be either
simple or complex. When a simple PPD exists in a chaotic system, the
next maximum (peak) of any relevant variable can be predicted from the
last maximum through a 1-dimensional map. The same is true for the
time of occurrence of the peak. The existence of PPD is critically
related with the fractal dimension of the strange attractor. Simple
PPD have been discovered in various fields of science, in particular
in electrochemistry, both through laboratory experiments and
modelling exercises. By contrast, in population dynamics only a few
convincing examples have been discovered until now. Examples of PPD
in ecology are presented by discussing some models, among which a
forest-pest model, a forest-fire model and a plankton-fish model.
This means that it is virtually possible to forecast pest-outbreaks in
forest ecosystems, fires in Mediterranean forests, and plankton blooms
in lakes: a quite remarkable result. The sensitivity of PPD to
measurement and environmental noise is also discussed, together with
the possibility of using PPD for solving management problems.
Marten Scheffer, Wageningen UR, Marten.Scheffer@Aqec.WKAO.WAU.NL
Between models and reality
Although the merits of combining modeling and empirical research are broadly recognized the approaches remain quite segregated in practice. Also, within the modeling world there is a distinct separation between theoreticians working with abstract minimal models and groups working on more applied quantitative simulation models. Meanwhile, in empirical aquatic ecology many experimentalists disguise whole lake manipulations as uninterpretable, whereas lake manipulators argue that the approach of controlled 'bottle experiments' has revealed little about how the real world works. Obviously, the different approaches may produce different fragments of the complex image of how aquatic ecosystems work. Whole lake experiments help to identify the main regulatory mechanisms, but the conditions are difficult to control and there are usually no replicates. As a result it is often difficult to understand what happened for what reason in the hindsight. Small scale replicated and controlled experiments, on the other hand, are necessarily conducted under rather unnatural conditions and do not reveal how the mechanism addressed interacts with other mechanisms in the field. Elaborate simulation models can help putting different processes into quantitative perspective but are difficult to study due to their mere complexity. Very simple ``minimal'' models are easier to understand but do not help to reveal the relative importance of the addressed mechanism in the field. Obviously, linking these approaches could boost our insight. This leads one to wonder what are the main causes of the separatism between approaches and how it could be overcome. It seems likely that the high cost-benefit ratio of integration of approaches is a major limitation. Focusing on the problem of relating models to reality, it takes a major investment from a modeller to publish outside the relatively protected environment of purely theoretically oriented journals. Not only are reviewers likely to eliminate descriptions of many technical aspects, they also tend to question the value of the model for enhancing insight and point out numerous omissions in discussing empirical literature. Indeed, the effort of linking a model to reality is generally much larger than the effort required to formulate and analyze the model. I argue that, nonetheless, at this stage true advancement of insight in the functioning of aquatic ecosystems may well benefit more from such laborious linking than from digging deeper along separate tracks.