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Index
Half title page
Frontispiece
Frontispiece
Title page
Copyright page
Dedication
Contents
Preface
1 Spatial concepts and notions
Introduction
1.1 The spatial context
1.2 Ecological data
1.3 Spatial structure: spatial dependence and spatial autocorrelation
1.4 Spatial scales
1.5 Sampling design
1.5.1 The sample size (the number of observations ‘n’)
1.5.2 Spatial resolution
1.5.3 The size of the study area: extent
1.5.4 The location in the landscape
1.5.5 The size of the sampling or observational units: grain
1.5.6 The shape of the sampling or observational units
1.5.7 The spatial sampling design
1.5.8 Spatial lag
1.5.9 Edge effect
1.6 Stationarity
1.7 Spatial statistics
1.7.1 First-order statistics
1.7.2 Second-order statistics
1.8 Ecological hypotheses and spatial analysis
1.9 Randomization tests for spatially structured ecological data
1.9.1 Restricted randomizations
1.10 In conclusion: what is space?
2 Ecological and spatial processes
Introduction
2.1 Ecological processes and spatial structure
2.2 Spatial processes by species level of organization
2.3 Spatial process
3 Points, lines and graphs
Introduction
3.1 Points: spatial patterns of point events
3.1.1 Topological neighbours
3.1.2 Distance-based spatial neighbours
3.1.3 Directional angle-based spatial neighbours
3.2 Lines: fibre pattern analysis
3.2.1 Aggregation and overdispersion of fibres
3.2.2 Fibres with properties
3.2.3 Curving fibres
3.2.4 Branching curved fibres
3.2.5 Congruence and parallelism of curved fibres
3.3 Points and lines together
3.4 Points and lines: spatial graphs
3.4.1 Signed and directed graphs and networks
3.4.2 How to create subgraphs
3.4.3 Graph models
3.5 Network analysis of areal units
3.6 Spatial analysis of movement
3.6.1 Transport and gravity models
3.6.2 Least-cost paths
3.6.3 Circuit theory
3.6.4 Spatial graphs and movement
3.6.5 Corridors
3.7 Testing hypotheses with graphs
3.7.1 Comment on spatial graph randomization
3.8 Concluding remarks
Glossary: graph definitions and properties
4 Spatial analysis of complete point location data
Introduction
4.1 Mapped point data in two dimensions
4.1.0 Introduction: three pattern types
4.1.1 Distance to neighbours methods
4.1.2 Refined nearest neighbour analysis
4.1.3 Second-order point pattern analysis
4.1.4 Bivariate data
4.1.5 Multivariate point pattern analysis data
4.2 Mark correlation function
4.3 Ripley’s K-function for inhomogeneous point pattern analysis
4.3.1 Bivariate and multivariate non-stationary point patterns
4.3.2 Quantitative marks: markcorrelation
4.4 Point patterns in other dimensions
4.4.1 One dimension
4.4.2 Lacunarity
4.4.3 Three dimensions
4.5 Circumcircle methods
4.5.1 Univariate analysis
4.5.2 Bivariate analysis
4.5.3 Multivariate analysis
4.6 Concluding remarks
5 Contiguous units analysis
Introduction
5.1 Quadrat variance methods
5.2 Significance tests for quadrat variance methods
5.3 Adaptations for two or more species
5.4 Two or more dimensions
5.5 Spectral analysis and related techniques
5.6 Wavelets
5.7 Concluding remarks
6 Spatial analysis of sample data
Introduction
6.1 Join count statistics
6.1.1 Join count statistics for k-categories
6.2 Global spatial statistics
6.2.1 Spatial covariance
6.2.2 Spatial autocorrelation coefficients for one variable
6.2.3 Variography
6.2.4 Fractal dimension
6.3 Sampling design effects on the estimation of spatial pattern
6.4 Spatial relationship between two variables
6.5 Local spatial statistics
6.6 Spatial scan statistics
6.7 Interpolation and spatial models
6.7.1 Proximity polygons
6.7.2 Trend surface analysis
6.7.3 Inverse distance weighting
6.7.4 Kriging
6.8 Concluding remarks
7 Spatial relationship and multiscale analysis
Introduction
7.1 Correlation between spatially autocorrelated variables
7.2 Correlation of distance matrices
7.2.1 Mantel test
7.2.2 Partial Mantel tests and multiple-matrix regression
7.3 Canonical (constrained) ordination
7.4 Multiscale analysis
7.4.1 Generalized Moran’s eigenvector maps
7.4.2 Multiresolution spectral decomposition analysis based on wavelets
7.5 Concluding remarks
8 Spatial autocorrelation and inferential tests
Introduction
8.1 Models dealing with one-dimensional autocorrelated data
8.2 Dealing with spatial autocorrelation in inferential models
8.2.1 Simple adjustments
8.2.2 Adjusting the effective sample size
8.2.3 More on induced autocorrelation and the relationships between variables
8.2.4 Correlation and related methods
8.3 Randomization procedures
8.3.1 Restricted randomization and bootstrap
8.3.2 Markov Chain Monte Carlo
8.4 Spatial regressions
8.4.1 Spatial filtering using autoregressive models
8.4.2 Spatial filtering using moving average models
8.4.3 Spatial filtering using Moran’s eigenvector maps
8.4.4 Spatial error regression
8.4.5 Geographically weighted regression
8.4.6 Remove spatial autocorrelation from the residuals
8.4.7 Example of the use of non-spatial and spatial regressions
8.5 Considerations for sampling and experimental design
8.5.1 Sampling
8.5.2 Experimental design
8.6 Concluding remarks
9 Spatial partitioning: spatial clusters and boundary detection
Introduction
9.1 Patch identification
9.1.1 Patch properties
9.1.2 Spatial clustering
9.1.3 Fuzzy classification
9.2 Boundary delineation
9.2.1 Ecological boundaries
9.2.2 Boundary properties
9.2.3 Boundary detection and analysis for one-dimensional transect data
9.2.4 Boundary detection based on two-dimensional data
9.3 Boundary statistics
9.4 Boundary overlap statistics
9.5 Hierarchical spatial partitioning
9.5.1 Edge enhancement with kernel filters
9.6 Concluding remarks
10 Spatial diversity analysis
Introduction
10.1 Space in diversity analysis
10.1.1 Spatial heterogeneity
10.1.2 Spatial location and environmental gradients
10.1.3 Spatial scale
10.1.4 Propinquity and spatial dependence
10.2 First-order diversity
10.2.1 α-diversity
10.2.2 β-diversity
10.2.3 γ-diversity
10.2.4 Why space in first-order diversity analysis?
10.3 Species combinations and composition: agreement and complementarity
10.3.1 Species combinations
10.3.2 Comments on species compositional diversity
10.3.3 Nested subsets, constraining compositional diversity
10.4 Multiple classifications
10.5 Spatial diversity: putting it all together with spatial graphs
10.6 Temporal aspects of spatial diversity
10.7 Concluding remarks
11 Spatio-temporal analysis
Introduction
11.1 Change in spatial statistics
11.2 Spatio-temporal join count
11.3 Spatio-temporal analysis of clusters and contagion
11.4 Spatio-temporal scan statistics
11.5 Polygon change analysis
11.6 Analysis of movement
11.7 Process and pattern
11.7.1 Tree regeneration, growth and mortality
11.7.2 Plant mobility
11.7.3 Population synchrony
11.7.4 Spatio-temporal chaos
11.8 Spatio-temporal graphs
11.8.1 Characteristics and classification
11.8.2 Animal movement with spatio-temporal graphs
11.8.3 Other applications
11.8.4 Final comment on spatio-temporal graphs
11.9 Concluding remarks
11.9.1 Recommendations
12 Closing comments and future directions
Introduction: myths, misunderstandings and challenges
12.1 Back to basics
12.2 Numerical solutions: software programs and programming
12.3 Statistical and ecological tests
12.4 Complementarity of current methods
12.5 Analyses in both space and time
12.5.1 Analysis of permanent sample plot data
12.5.2 Spatially linked time series
12.5.3 Spatial analysis of animal–vegetation according to data types
12.6 Future work
12.6.1 Ongoing development
12.6.2 The hierarchical Bayesian approach
12.6.3 Hypothesis testing with spatio-temporal graphs
12.7 Other future directions
References
Index
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