Elements of Mathematical Ecology provides an introduction to classical and modern mathematical models, methods, and issues in population ecology. The first part of the book is devoted to simple, unstructured population models that ignore much of the variability found in natural populations for the sake of tractability. Topics covered include density dependence, bifurcations, demographic stochasticity, time delays, population interactions (predation, competition, and mutualism), and the application of optimal control theory to the management of renewable resources. The second part of this book is devoted to structured population models, covering spatially-structured population models (with a focus on reaction-diffusion models), age-structured models, and two-sex models. Suitable for upper level students and beginning researchers in ecology, mathematical biology and applied mathematics, the volume includes numerous clear line diagrams that clarify the mathematics, relevant problems thoughout the text that aid understanding, and supplementary mathematical and historical material that enrich the main text.
Preface; Part I. Unstructured Population Models; Section A. Single Species Models: 1. Exponential, logistic and Gompertz growth; 2. Harvest models - bifurcations and breakpoints; 3. Stochastic birth and death processes; 4. Discrete-time models; 5. Delay models; 6. Branching processes; Section B. Interacting Populations: 7. A classical predator-prey model; 8. To cycle or not to cycle; 9. Global bifurcations in predator-prey models; 10. Chemosts models; 11. Discrete-time predator-prey models; 12. Competition models; 13. Mutualism models; Section C. Dynamics of Exploited Populations: 14. Harvest models and optimal control theory; Part II. Structured Population Models; Section D. Spatially-Structured Models: 15. Spatially-structured models; 16. Spatial steady states: linear problems; 17. Spatial steady states: nonlinear problems; 18. Models of spread; Section E. Age-Structured Models: 19. An overview of linear age-structured models; 20. The Lokta integral equation; 21. The difference equation; 22. The Leslie matrix; 23. The McKendrick-von Foerster PDE; 24. Some simple nonlinear models; Section F. Gender-Structured Models: 25. Two-sex models; References; Index.
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