Elements of Mathematical Ecology
Cambridge University Press, 8/21/2008
EAN 9780521001502, ISBN10: 0521001501
Paperback, 464 pages, 24.4 x 17 x 2.3 cm
Language: English
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.