Skip to main content

Mathematical Bioeconomics: The Mathematics of Conservation, 3rd Edition



Mathematical Bioeconomics: The Mathematics of Conservation, 3rd Edition

Colin W. Clark

ISBN: 978-0-470-37299-9 May 2010 368 Pages


Overall, this is an appealing work for students and professionals, and is certain to remain as one of the key works in natural resource analysis.
—Mathematical Reviews

Biological renewable resources, essential to the survival of mankind, are increasingly overexploited by individuals and corporations that often sacrifice long-term economic health and sustainability for short-term gains. Mathematical Bioeconomics: The Mathematics of Conservation, Third Edition analyzes the economic forces underlying these misuses of renewable resources and discusses more effective methods of resource management. Promoting a complete understanding of general principles, the book allows readers to discover how rigorous mathematical models that incorporate both economic and biological factors should replace intuitive arguments for conservation and sustainability.

This Third Edition continues to combine methodologies from the fields of economics, biology, and mathematics to explain how analytic models are essential for developing a complete understanding of complex resource systems. The book has been updated to address the need for incorporating individual economic incentives, the value of diversity, and the overriding importance of uncertainty in mathematical models. Coverage of game theory, overcapacity, uncertainty, and risk analysis has been added as well a expanded treatment of topics such as:

  • Models of individual harvest behavior and economic incentives
  • Response of individual harvester to various types of harvesting regulations
  • Reasons underlying excess harvesting capacity
  • Externalities in resource harvesting industries
  • Decision analysis in biological resource management

Fundamental concepts of population dynamics and economics are utilized throughout the book while mathematical techniques are incorporated in an accessible manner. Relevant data from current research sheds light on the presented material, and exercises provide readers with an opportunity to test comprehension of discussed mathematical methods and techniques.

Continuing to provide a complete and modernized presentation of the fundamental principles of the topic, Mathematical Bioeconomics, Third Edition is an excellent book for courses on applied mathematics, resource management, and environmental studies at the upper-undergraduate and graduate levels. It also serves as an insightful reference for resource managers, ecologists, biologists, and other professionals who work to improve the management of renewable resources and develop sustainable practices in the environmental sciences.



1 A Generic Bioeconomic Model.

1.1 What is Conservation?

1.2 What is a Model?

1.3 A Dynamic Resource-Harvesting Model.

1.4 A Bioeconomic Model.

1.5 A Dynamic Optimization Model.

1.6 A Model of Individual Behavior.

1.7 Individual Vessel Quotas.

1.8 The Veil of Uncertainty.

1.9 Other Resources.

2 Dynamic Optimization.

2.1 Constrained Optimization.

2.2 Optimal Control Theory in One Dimension.

2.3 Nonlinear Control Problems.

2.4 Discrete-time Optimal Control.

2.5 Appendix.

3 Basic Economic Concepts.

3.1 Interest and Discounting.

3.2 Supply and Demand.

3.3 Demand-limited Bionomic Equilibrium.

3.4 Optimal Harvesting Strategies.

3.5 External Costs.

3.6 Competition, Cooperation, and the Theory of Games.

3.7 The Economics of Uncertainty.

4 Investing in Harvesting Capacity.

4.1 Optimal Harvesting Capacity.

4.2 Investment Decisions under Competition.

4.3 Eliminating Excess Capacity.

4.4 Appendix: Optimal Investment.

5 Regulation of Renewable Resource Harvesting.

5.1 The Consequences of Unregulated Resource Harvesting.

5.2 Methods of Regulating Resource Harvesting.

5.3 Shadow Prices, Taxes and Tradeable Quotas.

5.4 Regulation without Taxes or Tradeable Quotas.

6 Growth and Aging.

6.1 Forestry Models.

6.2 Fisheries: The Cohort Model.

6.3 Multicohort Fisheries.

7 Resource Management under Uncertainty.

7.1 Process and Observational Uncertainty.

7.2 Understanding Uncertainty.

7.3 Process Uncertainty.

7.4 An Introduction to Decision Analysis.

7.5 Economic Uncertainties.

7.6 Appendix.

8 Disaggregated Resource Models.

8.1 Source-sink Models.

8.2 Predator-prey Models.

8.3 Mixed-species Harvesting.

9 Synopsis.

Problem Solutions.