Management and Analysis of Biological Populations demonstrates the usefulness of optimal control theory in the management of biological populations and the Liapunov function in simulating an ecosystem model under large perturbations of its initial state and continual disturbances on its dynamics. The first chapter of the book introduces the topic by presenting the different models in ecology and discussing the stability concepts, the ecological engineering, and various relevant functions in ecosystem modeling. The next chapter contains a brief survey of static optimization techniques and optimal control theory for systems, which are modeled by differential and difference equations. Another chapter covers methods that use Liapunov and Liapunov-like functions to establish that a given population model is stable relative to finite perturbations of its initial state and that it is non-vulnerable relative to large continual disturbances. The book also covers fisheries and logistic modeling, including a discussion of a few management problems. Moreover, this reference considers stability in an ecosystem model with complexities due to species richness, nonlinearities, time delays, and spatial heterogeneity. Finally, it explains how to manage pests and greenhouse crops. The book is an excellent reference source for students and professionals in ecology and environmental engineering. Research professionals and extended workers in agriculture and agronomy will also find this book invaluable.

Table of Contents

Preface Chapter 1. Introduction 1.1. Models in ecology 1.2. Stability concepts in ecology 1.3. Ecological engineering 1.4. Liapunov functions 1.5. Differential equations and difference equations in ecosystem modeling Selected references Chapter 2. Optimization techniques 2.1. Introduction 2.2. Static optimization problems 2.3. Relaxed optimization problem method 2.4. Multiple objectives decision problems 2.5. Continuous time optimal control 2.6. Discrete time optimal control Selected references Chapter 3. Stability and nonvulnerability 3.1. Introduction 3.2. Local stability 3.3. Finite and global stability 3.4. Single-species models 3.5. Exploited single-species models 3.6. Models with unspecified parameters 3.7. Two-species Lotka—Volterra models 3.8. Gilpin and Ayala's competition model 3.9. Prey—predator system with Type 2 functional response 3.10. Nonlinear two-species models 3.11. Region of ultimate confinement 3.12. Nonvulnerability 3.13. Discrete time models: local stability 3.14. Finite and global stability in discrete time models 3.15. Region of ultimate confinement and nonvulnerability 3.16. A discrete time model of two competing species Selected references Chapter 4. Fisheries 4.1. Introduction 4.2. The logistic model 4.3. Optimal control of the logistic model 4.4. Stability of bionomic equilibrium 4.5. Stock recruitment model 4.6. Stability of a stock recruitment model 4.7. Global stability of the Ricker model 4.8. The Beverton—Holt model: Optimal size limit 4.9. Optimal control of the Beverton—Holt model 4.10. Fishery with a limited fishing season 4.11. Fishery with delayed recruitment 4.12. The Antarctic fin whale population 4.13. Harvesting a multispecies community Selected references Cha


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@qu:The book should be compulsory reading for everyone devoted to theoretical ecology and ecological modelling. A more clear presentation of these difficult topics will be difficult to find. @source: Biological Populations @qu:The book's examples are easily understood and the diligent student should be able to recreate many of the solutions. @source: Biometrics @qu:There is much to be gained from the text even without the mathematical detail...I recommend this book to those who dare tread on the frontiers of ecological research. It will also be thought-provoking for those policy-makers striving to place resource management on a truly renewable basis. @source: Transactions of the American Fisheries Society