Complex Population Dynamics

Complex Population Dynamics: Theory and Data brings together over two decades of research and reflection on experimental nonlinear population dynamics. The broad theme of the book is the interface of population data and mathematical models. The authors establish a cornerstone example of a low-dimensional mathematical population model for which quantitative predictions, often unexpected, were borne out in controlled and replicated experiments. Central messages include the importance of low-dimensional, mechanistic models that serve as testable hypotheses; the importance of model validation on independent data; the prediction of novel outcomes in response to parameter manipulation; the interaction of nonlinearity and stochasticity—and how stochasticity illuminates, rather than obscures, deterministic forces; abrupt transitions in dynamic regimes in response to interventions; and how chaotic dynamics are expressed in discrete-state, noisy population systems. The book explores nonlinear phenomena in experimental data, including equilibria, cycles, bifurcations, invariant loops, multiple attractors, resonance and attenuance, saddles, stable and unstable manifolds, basins of attraction, basin boundaries, and chaos, and shows how these dynamics manifest in real data in both time series and state space plots.

The book offers an invaluable resource to professional ecologists and applied mathematicians. Although primarily a reference text, it is written to be accessible and engaging to a student audience and could be used as supplementary reading in an advanced ecological modeling class.

Features

• Written in an engaging style with minimal mathematical prerequisites, making it accessible to an audience of general ecologists as well as a more specialized mathematical audience
• A complete accompanying data set from all experiments is freely available on Dryad
• Readers can conveniently explore the model dynamics under discussion with an online LPA simulator.

Shandelle M. Henson is an emeritus Professor of Mathematics and Professor of Ecology at Andrews University. She uses dynamical systems theory and bifurcation theory to study nonlinear population dynamics. She also studies the effects of climate change on the behavior of marine organisms. 

Robert A. Desharnais is an emeritus Professor of Biological Sciences at the California State University, Los Angeles. He conducts both theoretical and experiment research focused on nonlinear models in ecology and population genetics. He has also collaborated with colleagues at Cal State LA to develop and test spatially-explicit models of marine mussel beds. In addition, he develops innovative web-based applications for science education that are widely used in high schools, colleges, and universities.

J. M. Cushing is an emeritus Professor at the University of Arizona, affiliated with the Department of Mathematics and the Interdisciplinary Program in Applied Mathematics. He uses dynamical systems theory and bifurcation theory to study nonlinear population, ecological, and evolutionary dynamics. He has authored and co-authored over 180 journal articles and 7 books. He is a Fellow of the American Mathematical Society and winner of the 2021 Bernd Aubach Prize for contributions to discrete dynamical systems and their applications. 

Brian Dennis is an emeritus Professor of Wildlife and Statistics at the University of Idaho, Moscow, ID.  He received his master’s degree in statistics and PhD in ecology at Pennsylvania State University (G Evelyn Hutchinson is his professional grandfather).  His research and teaching career has been devoted to improving ways in which ecological models could be connected to ecological data, and to studying how stochastic modelling could enhance ecological theory. His scientific papers have been cited over 10,000 times; recently two of his papers were selected by a panel of ecological editors for inclusion in volume 2 of the Foundations of Ecology series. 

R. F. Costantino is an emeritus Professor of Zoology from the University of Rhode Island. His research interests are experimental and theoretical ecology. He designs and conducts laboratory tests of nonlinear dynamics theory. He also teaches honors courses in nonlinear dynamics at the University of Arizona.