Spatial Optimization for Managed Ecosystems

Paperback | 1 April 1998 | Edition Number 1

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Spatial optimization is a methodology used to maximize or minimize a management objective, given the limited area, finite resources, and spatial relationships in an ecosystem. Optimization approaches can be used to evaluate a great variety of options and allow tradeoff analyses that might be impossible with other methods.

This book presents ideas and methods for directly optimizing the spatial layout of the landscape features in which an ecosystem functions. The problems Hof and Bevers address are complex, and the book relies heavily on mathematical presentations; the ideas are explained in a tutorial fashion that allows readers to grasp the general principals even if they skip the math. The first of four parts treats static spatial relationships that reflect the importance of shape, size, and proximity within an ecosystem. Part 2 considers spatial autocorrelation in a chance-constrained modeling framework. Part 3 discusses dynamic spatial changes within modeled ecosystems, and the final section focuses on diversity and sustainability. Although most discussion concerns wildlife habitat issues, the authors also include chapters on recreation, timber management, water runoff, and pest management.

Industry Reviews

The authors do an excellent job of explaining in words, diagrams, and mathematical symbolism the nature of spatial modeling and optimization across several ecosystem examples. . . . Recommend[ed] . . . as a must read for any operations researcher in the environmental area. Also recommend[ed] to any OR professional who has an interest in how our natural resources are allocated and used.

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Series Editors' Foreword	p. xi
Preface	p. xix
Introduction	p. 1
Viewpoint	p. 1
Organization	p. 2
Methods	p. 5
Solvability of (0-1) Integer Programs	p. 6
Solvability of Nonlinear Programs	p. 7
A Final Introductory Note	p. 8
Static Spatial Relationships	p. 11
A Cellular Model of Wildlife Habitat Spatial Relationships	p. 14
Edge Effects	p. 16
Wildlife Habitat Fragmentation Effects	p. 18
Wildlife Habitat Size Thresholds	p. 22
An Example	p. 22
The Problem	p. 22
Results	p. 24
Discussion	p. 28
Appendix	p. 31
A Geometric Model of Wildlife Habitat Spatial Relationships	p. 35
Spatial Effects	p. 36
An Example	p. 36
Results	p. 40
Discussion	p. 44
Spatial Supply-Demand Equilibrium: A Recreation Example	p. 46
The Travel Cost Model	p. 46
The Case of More Than One Proposed Site	p. 47
A Spatial Recreation Allocation Model	p. 48
An Example	p. 52
The Problem	p. 52
Results	p. 55
Discussion	p. 58
Spatial Autocorrelation	p. 59
Chance-Constrained Programming	p. 60
Individual Chance Constraints	p. 60
Joint Probability Chance Constraint	p. 61
Total Probability Chance Constraint	p. 62
Chance-Maximizing Programs	p. 63
Maxmin Chance-Maximizing Programming	p. 63
Joint Probability Chance-Maximizing Programming	p. 65
Total Probability Chance-Maximizing Programming	p. 65
Approximation of the CDF	p. 66
A Cellular Timber Model with Spatial Autocorrelation	p. 68
An Example	p. 69
The Problem	p. 69
Results	p. 73
Discussion	p. 80
A Geometric Wildlife Model with Spatial Autocorrelation and Habitat Connectivity	p. 81
Theory	p. 82
Connectivity	p. 82
Spatial Autocorrelation	p. 83
Chance Maximization	p. 84
Optimization	p. 84
Circles	p. 85
Rectangles	p. 87
An Example	p. 90
The Problem	p. 90
Results	p. 91
Discussion	p. 97
Pragmatic Approaches to Handling Risk and Uncertainty	p. 99
The Problem	p. 99
Post-Optimization Calculations	p. 100
An Example	p. 101
Row-Total Variance Reduction	p. 107
Dynamic Movement	p. 113
Methods	p. 114
A Cellular Model of Wildlife Population Growth and Dispersal	p. 118
The Model	p. 119
An Example	p. 122
The Problem	p. 122
Results	p. 124
Continuous Choice Variables	p. 129
Results	p. 130
Discussion	p. 134
The Black-Footed Ferret: A Case Study	p. 135
Spatial Optimization Model	p. 136
Ferret Reintroduction in South Dakota	p. 141
Spatial Definition	p. 142
Ferret Dispersal	p. 142
Net Population Growth Rate	p. 143
Ferret Releases	p. 143
Ferret Carrying Capacity	p. 144
Model Results	p. 145
A Cellular Model of Pest Management	p. 153
The Model	p. 154
An Example	p. 159
The Problem	p. 159
Results	p. 160
Discussion	p. 169
A Nested-Schedule Model of Stormflow	p. 170
The Spatial Optimization Approach	p. 171
Two Examples	p. 176
Results	p. 181
Discussion	p. 184
Diversity and Sustainability	p. 187
Species Richness Objective Functions	p. 191
Determining the Optimal Steady State	p. 192
A Steady-State Example	p. 195
Results	p. 196
Allocation over Time and Space	p. 201
Results	p. 203
Appendix	p. 205
Declining Monotonicity of Natural Logarithm Transformations	p. 206
The Logistic Distribution	p. 207
Sustainability of Species Richness	p. 208
The Modeling Approach	p. 208
Objective Functions	p. 209
A Coastal Douglas-fir Case Study	p. 212
Linear Approximation of Objective Functions	p. 213
Model Reduction	p. 215
Sensitivity to Minimum Harvest Age	p. 215
Sensitivity to Planning Horizon Length	p. 221
Accounting for Mortality	p. 222
Single-Species Emphasis	p. 223
A New Definition for a Regulated Forest	p. 224
Appendix	p. 227
Synthesis	p. 230
An Adaptive Management Context	p. 231
Simulation Versus Optimization	p. 234
References	p. 237
Index	p. 249
Table of Contents provided by Syndetics. All Rights Reserved.

Spatial Optimization for Managed Ecosystems

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