Jim Michael Cushing is one of the pioneers in the field of mathematical ecology. His research is internationally recognized both for its high mathematical quality and for its relevance to real biological problems. Indeed, his work has addressed, and continues to address, questions of fundamental importance in ecology. His monographs, lecture notes, textbooks, and more than 140 research papers are established landmarks in the discipline, greatly influencing students and researchers alike.
Jim's major research contributions and current research interests lie in the following areas:
| • | Integro-differential equations in population biology. | ||||
| • | Analysis of structured population models. | ||||
| • | Nonlinear matrix models and their dynamics. | ||||
| • | Application of nonlinear dynamics to population biology, ecosystems, and animal behavior. | ||||
| • | Promotion of a bifurcation theoretic approach to the analysis of models and to the design of experiments. | ||||
| • | Evolutionary game theory and Darwinian dynamics. | ||||
Anticipating additional contributions in the future, we confine our remarks here to one of Jim's most notable research projects. In the early 1990’s, Jim joined statistician Brian Dennis and biologists R. F. Costantino and R. A. Desharnais to form the original “Beetle Team”. This interdisciplinary group set out to test the theory of nonlinear dynamics in the laboratory using flour beetles (genus Tribolium) as an animal model. Guided by the predictions of a stage-structured nonlinear matrix model, the team was able to induce chaotic dynamics in the insect populations by experimentally manipulating a parameter across a sequence of bifurcations. This work, announced in the journals Nature and Science in 1995 and 1997, has become a classic in the theory of population dynamics. The team, which eventually grew to six members, documented a wide variety of nonlinear phenomena that occurred in the experimental data. This project, which spanned nearly two decades, is described in the monograph “Chaos in Ecology: Experimental Nonlinear Dynamics”.
As of this writing, Jim has trained 7 postdoctoral and 14 graduate students, the majority of whom are women, minorities, or international students. He also involves undergraduate students in his research. He is well known as an ideal mentor who provides a collegial working atmosphere and promotes the careers of his students. Colleagues and students alike look to Jim as a natural leader, often seeking his wisdom and advice. His unassuming pursuit of excellence, as well as his openness, inclusiveness, integrity, mindfulness, compassion, and strong but gentle spirit, set a high standard for personal conduct, both inside and outside of academia.
During October 5–7, 2007, more than 90 of Jim's colleagues and former students gathered in Tucson at the University of Arizona for a research conference on mathematical biology held in his honor. Two consecutive issues of the Journal of Biological Dynamics and one issue of the Journal of Difference Equations and Applications are devoted to the research papers presented at that conference.
It is with the greatest warmth and respect that we dedicate this special issue of the Journal of Biological Dynamics to our colleague and friend, Jim Cushing.
The Guest Editors