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.

• Part 1: Introduction 1. Sources of Patterns in Population Dynamics 2. Connecting Models with Data 3. Exploring State Space Part 2: Population Data and Models 4. The Tribolium Laboratory Model 5. The LPA Model Part 3: Models as Scientific Hypotheses 6. Transitions between Attractors 7. A Route to Chaos 8. Lattice Effects 9. How Is Chaos Manifest in Noisy Populations? 10. Demographic Stochasticity 11. Controlling Chaos Part 4: Recognizing Nonlinear Phenomena in Ecology 12. Saddles and Manifolds 13. Cycles and Phase Switching 14. Resonance, Attenuance, and Multiple Attractors in Fluctuating Habitats Part 5: Further Exploration 15. Competition: Park Revisited 16. Spectral Analyses of Population Dynamics 17. Time Scales of Ecological Synchrony 18. Dynamics of Natural Selection 19. Continuous-time LPA Model 20. Life Stages: Interactions and Spatial Patterns 21. In Summary

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.

• Part 1: Introduction 1. Sources of Patterns in Population Dynamics 2. Connecting Models with Data 3. Exploring State Space Part 2: Population Data and Models 4. The Tribolium Laboratory Model 5. The LPA Model Part 3: Models as Scientific Hypotheses 6. Transitions between Attractors 7. A Route to Chaos 8. Lattice Effects 9. How Is Chaos Manifest in Noisy Populations? 10. Demographic Stochasticity 11. Controlling Chaos Part 4: Recognizing Nonlinear Phenomena in Ecology 12. Saddles and Manifolds 13. Cycles and Phase Switching 14. Resonance, Attenuance, and Multiple Attractors in Fluctuating Habitats Part 5: Further Exploration 15. Competition: Park Revisited 16. Spectral Analyses of Population Dynamics 17. Time Scales of Ecological Synchrony 18. Dynamics of Natural Selection 19. Continuous-time LPA Model 20. Life Stages: Interactions and Spatial Patterns 21. In Summary