Management and Analysis of Biological Populations

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.

Inhalt

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
Chapter 5. Complex ecosystems
5.1. Introduction
5.2. Mathematical relationships between stability and complexity
5.3. Stability of nonlinear multispecies models
5.4. Stability of multispecies Lotka-Volterra models
5.5. Stability of a class of nonlinear models
5.6. Connective stability
5.7. Nonvulnerability of nonlinear multispecies models
5.8. Sector stability
5.9. Population models with time delays
5.10. Spatial heterogeneity in population dynamics
Selected references
Chapter 6. Management of pests and greenhouse crops
6.1. Introduction
6.2. Some applications of stability concepts in pest control
6.3. Graphical analysis of a control two-species system
6.4. Optimal control of a prey-predator system
6.5. Optimal control of epidemics for pest control
6.6. Optimal management o f greenhouse crops
Selected references
References
Author Index
Subject Index