Quantitative ecological theory : an introduction to basic models

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Bibliographic Information

Quantitative ecological theory : an introduction to basic models

Michael R. Rose

Croom Helm, c1987

  • : pbk

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Note

Includes bibliography and index

Description and Table of Contents

Volume

ISBN 9780709922889

Description

This book is concerned with theoretical ecology and the mathematical basis of ecological theory. It examines the construction and analysis of models prevalent in current theory. These include a priori models, simulation, phenomenological models and inductive models. The book is not intended as a general text but more as a manual, with relevant background information, on how to construct and develop models in a mathematical way. Of the major theoretical 'issues' in ecology, the problem of ecosystem stability, co-existence of competitors, chaos, predator-prey cycles, and multiple stable-states are all considered as they arise naturally from discussion of particular models. Some basic grounding in ecology, population biology and mathematics is assumed on the part of readers, who will be mainly students taking advanced courses in ecology. This book should be of interest to students taking advanced courses in ecology.

Table of Contents

Introduction. Part II: Population growth. Continuous-time models. Discrete-time models. Population growth models with age structure. Time-lag models. Part III: Competition. Lotka-Volterra models. Other competition models. Symbiosis and mutualism. Part IV: Predation. Continuous-time models. Discrete-time models. Host-parasitoid models. Spatial structure. Part V: Simple ecosystems. Two predators and one prey. One predator and two prey. Three-species food chains
Volume

: pbk ISBN 9780709922896

Description

This is an inadvertent book, though it did arise naturally enough from a course I give in theoretical ecology. But I wouldn't have given the course at all if one colleague in my department hadn't left for a leave of absence, while another abruptly resigned. This propelled me to the fore where this teaching responsibility was concerned, one I had never had any intention of discharging. Then it turned out that one of my students was regularly unable to make half the classes. As a result, I began giving him my lecture notes each week. As I knew that someone else would be reading them, I began to write my notes more carefully. Naturally enough, the other students soon began to demand the notes too. Eventually they were indulged. Thus I found myself writing a textbook manuscript. By the next year, the students were handed all their notes in one package at the outset. But these were still just hand-written. Inevitably, the demand that they be typed arose. This I didn't want to do until I found a publisher. As it turned out, Tim Hardwick of Croom Helm was willing to have his firm fill this role, to my great satisfaction. * and his considerable frustration. I have been a desultory author about producing this final text, and can only express my gratitude for his enduring patience over more than 18 months of delays.

Table of Contents

Theoretical Models in Ecology.- Models Covered Here.- 1. Population Growth.- 1.1 Linear Continuous-Time Models.- The "Malthusian" or Density-Independent Model.- The Logistic Model.- 1.2 Nonlinear Continuous-Time Models.- General Autonomous Models.- Density-Independent Nonautonomous Models.- 1.3 Discrete-Time Models.- Density-Independent Model.- Discrete-Time Logistic Model.- General Autonomous Models.- Density-Independent Nonautonomous Models.- Time-Lag Models.- 1.4 Models with Age-Structure.- Discrete-Time: The Leslie Matrix.- Continuous-Time Models.- 1.5 Exercises.- 2. Competition.- 2.1 Lotka-Volterra Models: Special Cases.- No Carrying Capacities.- One Carrying Capacity.- 2.2 Classical Lotka-Volterra Model.- 2.3 General Continuous-Time Models.- 2.4 Discrete-Time Models.- General Two-Species Models.- The Hassell-Comins Model.- 2.5 Symbiosis.- Lotka-Volterra Models.- General Continuous-Time Models.- 2.6 Exercises.- 3. Predation.- 3.1 Lotka-Volterra Models.- Original Lotka-Volterra Model.- An Alternative Lotka-Volterra Model.- 3.2 Generalized Predator-Prey Models.- 3.3 Discrete-Time Models.- Lotka-Volterra Model without Density-Dependence.- Lotka-Volterra Model with Density-Dependence.- Other Discrete-Time Predation Models.- 3.4 Parasitoid Models.- A General Model.- Classical Nicholson-Bailey Model.- Nicholson-Bailey Model with Density-Dependence.- Generalized Nicholson-Bailey Model.- 3.5 Exercises.- 4. Simple Ecosystems.- 4.1 Two Predators and One Prey.- Continuous-Time Models.- Discrete-Time Models: Two Parasitoids.- 4.2 One Predator and Two Prey.- Continuous-Time Models.- Discrete-Time Models: Polyphagous Parasitoids.- 4.3 Three-Species Food Chains.- Continuous-Time Models.- Discrete-Time Models: Parasitoid-Hyperparasitoid Systems.- 4.4 Exercises.- 5. Complex Ecosystems.- 5.1 Local Equilibrium Stability.- Time-Structure and Local Asymptotic Stability.- Arbitrary Complexity and Local Stability.- Ecosystem Model Structure and Local Stability.- 5.2 Global Complex Ecosystem Dynamics.- 6. Migration.- 6.1 Population Growth with Migration.- Recipient Peripheral Populations.- Migrant Pool Model.- Two Habitats.- 6.2 Competition with Migration.- Recipient Peripheral Populations.- Migrant Pool Model.- Two Habitats.- 6.3 Predation with Migration.- Recipient Peripheral Populations.- Migrant Pool Model.- Two Habitats.- 6.4 Ecosystems with Migration.- 6.5 Exercises.

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