Qualitative Modeling of Complex Systems: An Introduction to Loop Analysis and Time Averaging

by Charles J Puccia, Richard Levins

Overview

In this modern era of mathematical modeling, applications have become increasingly complicated. As the complexity grows, it becomes more and more difficult to draw meaningful conclusions about the behavior of theoretical models and their relations to reality. Alongside methods that emphasize quantitative properties and the testing of scientific details, there is a need for approaches that are more qualitative. These techniques attempt to cover whole families of models in one bold stroke, in a manner that allows robust conclusions to be drawn about them.

Loop analysis and time averaging provide a means of interpreting the properties of systems from the network of interactions within the system. The authors' methodology concentrates on graphical representation to guide experimental design, to identify sources of external variability from the statistical pattern of variables, and to make management decisions.

Although most of the examples are drawn from ecology, the methods are relevant to all of the pure and applied sciences. This relevance is enhanced by case studies from such diverse areas as physiology, resource management, the behavioral sciences, and social epidemiology. The book will be useful to a broad readership from the biological and social sciences as well as the physical sciences and technology. It will interest undergraduate and graduate students along with researchers active in these disciplines. Here the reader will find a strong rationale for maintaining a holistic approach, revealing what insights and advantages are retained by the broader perspective and, more explicitly, by the synergistic effects that cannot be discerned by reducing systems to their smallest parts.

Product Details

ISBN-13:	9780674435063
Publisher:	Harvard
Publication date:	10/01/2013
Edition description:	Reprint 2014 ed.
Pages:	267
Product dimensions:	6.14(w) x 9.21(h) x 0.63(d)

About the Author

Charles J. Puccia is in the Department of Population Sciences, Harvard School of Public Health.Levins Richard :

Richard Levins is John Rock Professor of Population Sciences, Harvard School of Public Health.

Table of Contents

1. Qualitative Models

Uses of Models

Qualitative versus Quantitative Models

Preview of Models

Limitations of Models

Strategy for Qualitative Model Applications

2. Loop Models: Definition of Terms and Calculation of Model Properties

Symbols of Signed Digraphs

Notation

Paths, Links, and Loops

Conjunct and Disjunct Loops

Feedback

Stability

3. Loop Models: Predicting Change

Parameter Change

Open Paths and Complementary Subsystems

Changes in Equilibrium Abundance

Tables of Predictions

Links from Equations

4. Qualitative Predictions

Equilibrium Levels and Turnover Rates

Correlations from Predictions

From Model to Predictions

Some General Observations

Lumping Variables

Model Ambiguity

Experimental Design and Loop Models

Correlation Patterns

5. From Concept to Model

Ecological Examples

Changes in the Graph Structure

From Data to Graph

6. Dynamical Systems and Loop Analysis

Equilibrium

Stability

Self-Effect Terms (Self-Damping)

Signed Digraphs, the Characteristic Equation, and Feedback

Eigenvectors

Discrete Systems

7. Time Averaging

Definitions

Operations with Time Averaging

Finite Intervals

Discrete-Time Processes

Time Averaging and Loop Analysis

Linear Equations

Nonlinear Equations

Appendix: Some Mathematical Operations and Concepts

References

Index