Foreword |
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xiii | |
Preface |
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xv | |
Acknowledgements |
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xix | |
Introduction |
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xxi | |
About the Companion Website |
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xxv | |
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1 Spatial Simulation Models: What? Why? How? |
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1 | (28) |
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1.1 What are simulation models? |
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2 | (10) |
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4 | (3) |
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7 | (1) |
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1.1.3 Mathematical models |
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7 | (1) |
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8 | (1) |
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9 | (3) |
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1.2 How do we use simulation models? |
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12 | (3) |
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1.2.1 Using models for prediction |
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13 | (1) |
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1.2.2 Models as guides to data collection |
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13 | (1) |
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1.2.3 Models as `tools to think with' |
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14 | (1) |
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1.3 Why do we use simulation models? |
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15 | (8) |
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1.3.1 When experimental science is difficult (or impossible) |
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16 | (2) |
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1.3.2 Complexity and nonlinear dynamics |
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18 | (5) |
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1.4 Why dynamic and spatial models? |
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23 | (6) |
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1.4.1 The strengths and weaknesses of highly general models |
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23 | (4) |
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1.4.2 From abstract to more realistic models: controlling the cost |
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27 | (2) |
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2 Pattern, Process and Scale |
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29 | (28) |
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2.1 Thinking about spatiotemporal patterns and processes |
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30 | (8) |
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30 | (1) |
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31 | (1) |
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32 | (6) |
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2.2 Using models to explore spatial patterns and processes |
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38 | (18) |
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2.2.1 Reciprocal links between pattern and process: a spatial model of forest structure |
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39 | (1) |
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2.2.2 Characterising patterns: first- and second-order structure |
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40 | (3) |
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2.2.3 Using null models to evaluate patterns |
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43 | (3) |
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2.2.4 Density-based (first-order) null models |
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46 | (2) |
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2.2.5 Interaction-based (second-order) null models |
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48 | (1) |
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2.2.6 Inferring process from (spatio-temporal) pattern |
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49 | (4) |
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2.2.7 Making the virtual forest more realistic |
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53 | (3) |
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56 | (1) |
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3 Aggregation and Segregation |
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57 | (40) |
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3.1 Background and motivating examples |
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58 | (2) |
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3.1.1 Basics of (discrete spatial) model structure |
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59 | (1) |
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60 | (4) |
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3.2.1 Local averaging with noise |
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63 | (1) |
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64 | (6) |
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65 | (3) |
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3.3.2 Twisted majority annealing |
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68 | (1) |
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69 | (1) |
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3.4 A more general framework: interacting particle systems |
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70 | (13) |
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3.4.1 The contact process |
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71 | (2) |
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3.4.2 Multiple contact processes |
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73 | (3) |
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3.4.3 Cyclic relationships between states: rock-scissors-paper |
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76 | (2) |
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78 | (2) |
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3.4.5 Voter models with noise mutation |
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80 | (3) |
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83 | (3) |
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86 | (2) |
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3.6.1 Iterative subdivision |
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86 | (1) |
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3.6.2 Voronoi tessellations |
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87 | (1) |
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3.7 Applying these ideas: more complicated models |
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88 | (9) |
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3.7.1 Pattern formation on animals' coats: reaction-diffusion models |
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89 | (2) |
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3.7.2 More complicated processes: spatial evolutionary game theory |
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91 | (2) |
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3.7.3 More realistic models: cellular urban models |
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93 | (4) |
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4 Random Walks and Mobile Entities |
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97 | (36) |
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4.1 Background and motivating examples |
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97 | (2) |
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99 | (12) |
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4.2.1 Simple random walks |
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99 | (3) |
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4.2.2 Random walks with variable step lengths |
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102 | (1) |
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103 | (5) |
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4.2.4 Bias and drift in random walks |
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108 | (1) |
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4.2.5 Levy flights: walks with non-finite step length variance |
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109 | (2) |
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4.3 Walking for a reason: foraging and search |
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111 | (8) |
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4.3.1 Using clues: localised search |
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115 | (1) |
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4.3.2 The effect of the distribution of resources |
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116 | (3) |
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4.3.3 Foraging and random walks revisited |
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119 | (1) |
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4.4 Moving entities and landscape interaction |
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119 | (2) |
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4.5 Flocking: entity-entity interaction |
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121 | (4) |
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4.6 Applying the framework |
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125 | (8) |
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126 | (2) |
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4.6.2 Human `hunter-gatherers' |
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128 | (1) |
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4.6.3 The development of home ranges and path networks |
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129 | (1) |
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4.6.4 Constrained environments: pedestrians and evacuations |
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129 | (2) |
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131 | (2) |
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5 Percolation and Growth: Spread in Heterogeneous Spaces |
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133 | (36) |
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133 | (4) |
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137 | (11) |
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5.2.1 What is percolation? |
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137 | (1) |
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5.2.2 Ordinary percolation |
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138 | (4) |
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142 | (3) |
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5.2.4 Invasion percolation |
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145 | (3) |
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5.3 Growth (or aggregation) models |
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148 | (10) |
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5.3.1 Eden growth processes: theme and variations |
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149 | (6) |
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5.3.2 Diffusion-limited aggregation |
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155 | (3) |
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5.4 Applying the framework |
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158 | (10) |
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5.4.1 Landscape pattern: neutral models and percolation approaches |
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158 | (4) |
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5.4.2 Fire spread: Per Bak's `forest fire model' and derivatives |
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162 | (4) |
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5.4.3 Gullying and erosion dynamics: IP + Eden growth + DLA |
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166 | (2) |
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168 | (1) |
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6 Representing Time and Space |
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169 | (24) |
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170 | (5) |
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6.1.1 Synchronous and asynchronous update |
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170 | (2) |
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6.1.2 Different process rates |
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172 | (1) |
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6.1.3 Discrete time steps or event-driven time |
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173 | (1) |
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174 | (1) |
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6.2 Basics of spatial representation |
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175 | (4) |
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6.2.1 Grid or lattice representations |
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175 | (2) |
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6.2.2 Vector-based representation: points, lines, polygons and tessellations |
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177 | (2) |
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6.3 Spatial relationships: distance, neighbourhoods and networks |
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179 | (6) |
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6.3.1 Distance in grids and tessellations |
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179 | (2) |
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6.3.2 Neighbourhoods: local spatial relationships |
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181 | (2) |
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6.3.3 Networks of relationships |
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183 | (2) |
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6.4 Coordinate space: finite, infinite and wrapped |
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185 | (3) |
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185 | (1) |
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6.4.2 Infinitely extensible model space |
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186 | (1) |
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6.4.3 Toroidal model space |
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187 | (1) |
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6.5 Complicated spatial structure without spatial data structures |
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188 | (2) |
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6.6 Temporal and spatial representations can make a difference |
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190 | (3) |
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7 Model Uncertainty and Evaluation |
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193 | (36) |
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7.1 Introducing uncertainty |
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193 | (1) |
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7.2 Coping with uncertainty |
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194 | (4) |
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7.2.1 Representing uncertainty in data and processes |
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195 | (3) |
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7.3 Assessing and quantifying model-related uncertainty |
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198 | (13) |
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200 | (1) |
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7.3.2 Sensitivity analysis |
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200 | (2) |
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7.3.3 Uncertainty analysis |
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202 | (2) |
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7.3.4 Analysis of model structural uncertainty |
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204 | (2) |
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7.3.5 Difficulties for spatial data and models |
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206 | (1) |
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7.3.6 Sensitivity and uncertainty analysis for a simple spatial model |
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207 | (4) |
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7.4 Confronting model predictions with observed data |
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211 | (5) |
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7.4.1 Visualisation and difference measures |
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212 | (2) |
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7.4.2 Formal statistical tests |
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214 | (2) |
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7.5 Frameworks for selecting between competing models |
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216 | (6) |
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216 | (1) |
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217 | (3) |
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7.5.3 Multi-model inference |
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220 | (2) |
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7.6 Pattern-oriented modelling |
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222 | (4) |
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7.6.1 POM case-study: understanding the drivers of treeline physiognomy |
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224 | (2) |
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7.7 More to models than prediction |
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226 | (3) |
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8 Weaving It All Together |
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229 | (36) |
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8.1 Motivating example: island resource exploitation by hunter-gatherers |
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230 | (1) |
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231 | (13) |
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232 | (4) |
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236 | (2) |
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238 | (6) |
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8.3 Model development and refinement |
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244 | (3) |
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8.3.1 The model development process |
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244 | (2) |
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246 | (1) |
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247 | (15) |
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247 | (7) |
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8.4.2 Sensitivity analysis |
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254 | (4) |
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8.4.3 Uncertainty analysis |
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258 | (4) |
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262 | (3) |
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265 | (6) |
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9.1 On the usefulness of building-block models |
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265 | (1) |
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9.2 On pattern and process |
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266 | (2) |
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9.3 On the need for careful analysis |
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268 | (3) |
References |
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271 | (28) |
Index |
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299 | |