Elements of Mathematical Ecology

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Cambridge University Press, Jul 19, 2001 - Mathematics - 453 pages
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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.
  

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Contents

SINGLESPECIES MODELS
3
Harvest models bifurcations and breakpoints
13
Stochastic birth and death processes
25
Discretetime models
43
Delay models
70
Branching processes
93
INTERACTING POPULATIONS
107
To cycle or not to cycle
116
SPATIALLY STRUCTURED MODELS
267
Spatial steady states linear problems
276
Spatial steady states nonlinear problems
294
Models of spread
311
AGESTRUCTURED MODELS
345
The Lotka integral equation
353
The difference equation
365
The Leslie matrix
377

Global bifurcations in predatorprey models
140
Chemostat models
161
Discretetime predatorprey models
181
Competition models
198
Mutualism models
220
DYNAMICS OF EXPLOITED POPULATIONS
237
STRUCTURED POPULATION MODELS
265
The McKendrickvon Foerster PDE
391
Some simple nonlinear models
401
SEXSTRUCTURED MODELS
413
References
425
Author index
443
Subject index
447
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