Elements of Mathematical Ecology

by Mark Kot

Overview

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 throughout the text that aid understanding, and supplementary mathematical and historical material that enrich the main text.

Product Details

ISBN-13:	9780521802130
Publisher:	Cambridge University Press
Publication date:	07/19/2001
Pages:	464
Product dimensions:	6.69(w) x 9.61(h) x 0.98(d)

Table of Contents

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.

Editorial Reviews

Kot (applied mathematics, U. of Washington) presents an introductory text on the methods of classical and mathematical models and methods in population ecology. Covering density dependence, bifurcations, demographic stochasticity, time delays, population interactions, and application of optimal control theory to the management of renewable resources; the first section of the work presents simplified unstructured population models. Structured models are then discussed, with chapters covering spatially structured, age-structured, and two- sex models. The material is focused on mechanistic models that generate hypotheses, rather than complex models for detailed forecasts. Formal theorems and proofs are at a minimum. Annotation c. Book News, Inc., Portland, OR (booknews.com)

"[T]his book is fun...useful and interesting..." Northeastern Naturalist

"Mark Kot has written a superb introduction to many aspects of population ecology, covering spatially structured, age-structured, and sex-structured models... The treatment is interesting, and represents a genuine stimulus to keep going, even for an ecologist! Yet, the real excitement is invariably in the mathematics... Kot's new book represents an exemplary introduction to the mathematics behind population biology." Robert van Hulst, Ecoscience

"I cannot emphasize this enough, Kot's explanations are outstandingly clear. He presents, step by step, the calculations that are required to analyze the models that underlie population ecology. This is a valuable book. Ecology is becoming more quantitative and more dynamic, not less, and Kot's book fills the need for a rigorous, graduate-level textbook in mathematical population ecology, and does it very well." The Quarterly Review of Biology

"Elements of Mathematical Ecology is a thorough and imminently readable technical introduction to the discipline, and is highly recommended." Acta Biotheoretica

"Kot offers a solid introduction to applied mathematical ecology, especially as it relates to population ecology.... Unusual for such a work, this one is written clearly and much of the writing is accessible even to those without a strong math background.... [S]tudents and researchers in population, applied population, and mathematical ecology will find this book highly useful." Choice

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