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.
Ferret ReleasesNet Population Growth RateFerret DispersalSpatial DefinitionFerret Reintroduction in South DakotaThe Spatial Optimization ModelThe Black-Footed Ferret: A Case StudyDiscussionThe Modeling ApproachSustainability of Species RichnessThe Logistic DistributionTransformationsDeclining Monotonicity of Natural LogarithmResultsAllocation Over Time and SpaceResultsContinuous Choice VariablesResultsThe ProblemAn ExampleThe ModelA Cellular Model of Wildlife Population Growth and DispersalMethodsDynamic MovementRow-Total Variance ReductionAn ExamplePost-Optimization CalculationsSimulation Versus OptimizationAn Adaptive Management ContextSynthesisA New Definition for a Regulated ForestSingle-Species EmphasisAccounting for MortalitySensitivity to Planning Horizon LengthSensitivity to Minimum Harvest AgeModel ReductionLinear Approximation of Objective FunctionsA Coastal Douglas-fir Case StudyObjective FunctionsWildlife Habitat Fragmentation EffectsEdge Effects A Cellular Model of Wildlife Habitat Spatial RelationshipsStatic Spatial RelationshipsA Final Introductory NoteSolvability of Nonlinear ProgramsSolvability of (0-1) Integer ProgramsMethodsOrganizationViewpointIntroductionThe ProblemPragmatic Approaches to Handling Risk and UncertaintyDiscussionResultsThe ProblemAn ExampleRectanglesCirclesOptimizationChance MaximizationSpatial AutocorrelationConnectivityTheoryA Geometric Wildlife Model with Spatial Autocorrelation and Habitat ConnectivityDiscussionResultsThe ProblemAn ExampleA Cellular Timber Model with Spatial AutocorrelationApproximation of the CDFTotal Probability Chance-Maximizing ProgrammingJoint Probability Chance-Maximizing ProgrammingMAXMIN Chance-Maximizing ProgrammingChance-Maximizing ProgramsTotal Probability Chance ConstraintJoint Probability Chance ConstraintIndividual Chance ConstraintsChance-Constrained ProgrammingSpatial AutocorrelationDiscussionResultsThe ProblemAn ExampleA Spatial Recreation Allocation ModelThe Case of More Than One Proposed SiteThe Travel Cost ModelSpatial Supply-Demand Equilibrium: A Recreation ExampleDiscussionResultsAn ExampleSpatial Effects A Geometric Model of Wildlife Habitat Spatial RelationshipsDiscussionResultsThe ProblemAn ExampleWildlife Habitat Size ThresholdsResultsA Steady-State ExampleDetermining the Optimal Steady StateSpecies Richness Objective FunctionsDiversity and SustainabilityDiscussionResultsTwo ExamplesThe Spatial Optimization ApproachA Nested-Schedule Model of StormflowDiscussionResultsThe ProblemAn ExampleThe ModelA Cellular Model of Pest ManagementModel ResultsFerret Carrying Capacity