Elements of Mathematical Ecology

An introduction to classical and modern mathematical models, methods, and issues in population ecology.

Mark Kot (Author)

9780521001502, Cambridge University Press

Paperback, published 19 July 2001

464 pages, 239 b/w illus. 11 tables
24.4 x 17 x 2.4 cm, 0.73 kg

'… suitable for a year's course of study for upper level students and beginning researchers in ecology, mathematical biology and applied mathematics. … an excellent introduction to mathematical ecology for the reader with an appropriate mathematical background (calculus, differential equations and probability theory).' Zentralblatt MATH

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.

Subject Areas: Maths for engineers [TBJ], Ecological science, the Biosphere [PSAF], Maths for scientists [PDE], Mathematical modelling [PBWH]