Workshop Homepage	Preliminary Program	Contributor Perspectives
Twenty-five Years of Ecological Chaos: Do Mathematical Models Really Work After All?
	Workshop Homepage Ecological Society of America 2002 Annual Meeting. Tucson, Arizona
Annotated Bibliography	Registered Participants	Biological Dynamics

Date and Time:

August 4, 2002. 1230-1630 h.
Graham Meeting Room.
Tucson Convention Center
Tucson, Arizona.

Participant Limits:

Minimum: 15.    Maxmium: None.

Organizers:

R. F. Costantino Dept. Ecol. Evol. Biology University of Arizona Tucson, AZ 85721 Tel: (520) 621-7295 Fax: (520) 626-5370 Email: rfc@u.arizona.edu

W. M. Schaffer Dept. Ecol. Evol. Biology University of Arizona Tucson, AZ 85721 Tel: (520) 621-7295 Fax: (520) 626-5370 Email: wms@u.arizona.edu

Abstract:

The current flowering of interest, now 25 years old, in nonlinear dynamics owes much to theoretical ecology which provided both the models and the analysis that captured the imagination of scientists in a broad range of disciplines. Still, the effect of these discoveries on ecology itself remains minimal. For a science concerned with understanding and preserving natural systems, this is somewhat surprising. No one seriously questions the proposition that ecological interactions are nonlinear, or the fact that nonlinear systems can evidence abrupt and often dramatic changes in behavior in response to small variations in ambient conditions. Indeed, the growing realization that ecological systems are embedded in an ever changing physical environment, as evidenced, for example, by changing climate, underscores the importance of viewing ecological processes from a nonlinear perspective.

We view nonlinear dynamics in ecology as a working hypothesis whereby fluctuations in diversity and abundance result from the interaction of random and deterministic forces. What distinguishes this mix from traditional accounts is the nature of the determinism that nonlinear dynamics brings to the intellectual table. Essentially, nonlinearity introduces two properties which are conceptually novel. The first, to which we have already alluded, entails the propensity of nonlinear systems to evidence qualitative changes in behavior (bifurcations) in response to small changes in parameters. The second concerns the geometry of the phase space which is the theater in which dynamical dramas are enacted. When the play is nonlinear, the phase space can be populated by multiple invariant sets, which may be attracting, repelling or have the stability character of saddles. Some of these sets, equilibria and cycles, are familiar; others, on which the motion is quasiperiodic or chaotic, less so. In the absence of stochasticity, only those sets which are attracting matter: given sufficient time, all trajectories tend to such a set to an arbitrary degree of closeness. But with the addition of random perturbations, a ubiquitous and unavoidable feature of real-world ecology, the picture changes. In this case, the system’s time evolution resembles an elaborate choreography, whereby evolving trajectories successively visit the different invariant sets, spending varying amounts of time in the vicinity of each, before moving on to the next. Both the magnitude and the nature of the perturbations turn out to be important with the consequence that stochasticity and nonlinear determinism become co-equal components of the theory which results. Additionally, the resulting dynamics may exhibit both the "messiness" and predictability of ecological systems in nature.

The present workshop highlights population dynamic and ecological studies with a strong focus on nonlinearity and dynamical complexity. A principal objective of these investigations is to demonstrate how the concepts, techniques and procedures of nonlinear dynamics can be used to make ecological hypotheses more accessible to experimental scrutiny. In addition, the workshop will emphasize the application of nonlinear theory to problems of practical import. Among the topics to be considered are the following:

Complex Dynamics. The intellectual underpinnings and vocabulary of nonlinear dynamics being unfamiliar to many biologists, the unstated question is often "What benefit will accrue to those willing to devote the time and effort necessary to master new ways of thinking and what amounts to a new language?" Kevin Higgins addresses this question directly, contrasting chaos and density dependence in the presence of noise as alternative ecological paradigms. Complementing this discussion are presentations by Shandelle Henson and John Vandermeer. The former author explores some of the surprising consequences which follow from the fact that organisms often come in integer numbers (whole organism effect); the latter considers coupled oscillators as prototypical ecological models.   The Model-Data Interface. Chaos and other forms of complex dynamics are mathematical phenomena, so it is not surprising that their investigation is often tied to the study of mathematical models. In our view, such models are no better than their ability to predict the behavior of the systems they seek to caricature. This brings us to the "model-data interface" and to Brian Dennis, who considers the general issue of connecting mathematical models with experimental data, and Aaron King, who discusses some specific examples.   Long Term Changes in Species Abundance and Climate. Ecological systems typically operate on time scales which vastly exceed those accessible to direct observation and experiment. Reconstructing the histories of such systems, and the climatic variations to which they are subject, thus becomes an essential part of any attempt to understand their mechanistic essentials. For nonlinear systems, this is especially important, the point being that the short-term behavior of such systems is often unrepresentative of long-term patterns of fluctuation and abundance. These matters will be discussed by Tom Swetnam.

To encourage discussion, formal presentations will be complemented by a panel discussion, the members of the panel having been chosen to represent laboratory/field experimental (Bob Costantino, Jim Hayward), statistical (Bob Desharnais, Bruce Kendall), and mathematical (Jim Cushing) points of view. It is hoped that this format will encourage audience participation, The proceedings will be introduced by W. M. Schaffer. Bob Costantino will serve as moderator. Overall, the workshop’s principal aim is to promote awareness of, and interest in, nonlinear dynamics in ecology.

Speakers / Titles:

Brian Dennis. The University of Idaho. Connecting models with data.

Shandelle M. Henson. Andrews University. Lattice effects observed in chaotic dynamics of experimental populations.

Kevin Higgins. University of South Carolina. Wild fluctuations from small perturbations, but where is the chaos?

Aaron A. King. University of Tennessee. Order in real data: Model-predicted temporal patterns in chaotic population data.

W. M. Schaffer. University of Arizona. Introduction: Twenty-five years of ecological chaos.

Tom Swetnam. University of Arizona. Using tree rings to reconstruct multi-century insect dynamics and climatic linkages.

John Vandermeer. University of Michigan. Coupled oscillators as models of ecosystem dynamics.

Panelists / Perspectives:

Jim Cushing.	University of Arizona.	(Mathematician's Perspective).
R. F. Costantino.	University of Arizona.	(Experimentalist's Perspective).
James L. Hayward.	Andrews University.	(Experimentalist's Perspective).
R. A. Desharnais.	Cal. State Los Angeles.	(Statistician’s Perspective).
Bruce Kendall.	UC Santa Barbara.	(Statistician’s Perspective).