Elements of Mathematical Ecology

by Mark Kot

• ISBN13: 9780521802130
• ISBN10: 052180213X
• Format: Hardcover
• Copyright: 2001-08-06
• Publisher: Cambridge University Press

Summary

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.

Author Biography

Mark Kot is Associate Professor in the Department of Applied Mathematics at the University of Washington, Seattle, USA.

Table of Contents

Preface	vii
Acknowledgments	ix
I. UNSTRUCTED POPULATION MODELS	1	(264)
Single-species models	3	(1)
Exponential, logistic, and Gompertz growth	3	(10)
Harvest models: bifurcations and breakpoints	13	(12)
Stochastic birth and death processes	25	(18)
Discrete-time models	43	(27)
Delay models	70	(23)
Branching processes	93	(14)
Interacting Populations	107	(1)
A classical predator-prey model	107	(9)
To cycle or not to cycle	116	(24)
Global bifurcations in predator-prey models	140	(21)
Chemostat models	161	(20)
Discrete-time predator-prey models	181	(17)
Competition models	198	(22)
Mutualism models	220	(17)
Dynamics of exploited populations	237	(1)
Harvest models and optimal control theory	237	(28)
II. STRUCTURED POPULATION MODELS	265	(160)
Spatially structured models	267	(1)
Formulating spatially structured models	267	(9)
Spatial steady states: linear problems	276	(18)
Spatial steady states: nonlinear problems	294	(17)
Models of spread	311	(34)
Age-structured models	345	(1)
An overview of linear age-structured models	345	(8)
The Lotka integral equation	353	(12)
The difference equation	365	(12)
The Leslie matrix	377	(14)
The McKendrick-von Foerster PDE	391	(10)
Some simple nonlinear models	401	(12)
Sex-structured models	413	(1)
Two-sex models	413	(12)
References	425	(18)
Author index	443	(4)
Subject index	447