7.2.4
Spatial Heterogeneity . . . . . . . . . . . . . . . . . . . . . . . . . . 303
7.2.5
Spatial Correlation or Autocorrelation Functions
and Spatial Correlograms . . . . . . . . . . . . . . . . . . . . . . . 303
7.2.6
Testing for the Presence of Spatial Correlation:
Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308
7.2.7
Modelling Spatial Structures . . . . . . . . . . . . . . . . . . . . . 309
7.3
Multivariate Trend-Surface Analysis . . . . . . . . . . . . . . . . . . . . . 309
7.3.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309
7.3.2
Trend-Surface Analysis in Practice . . . . . . . . . . . . . . . . 310
7.4
Eigenvector-Based Spatial Variables and Spatial Modelling . . . . . 314
7.4.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314
7.4.2
Distance-Based Moran’s Eigenvector Maps
(dbMEM) and Principal Coordinates of Neighbour
Matrices (PCNM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315
7.4.3
MEM in a Wider Context: Weights Other than
Geographic Distances . . . . . . . . . . . . . . . . . . . . . . . . . . 333
7.4.4
MEM with Positive or Negative Spatial Correlation:
Which Ones should Be Used? . . . . . . . . . . . . . . . . . . . . 348
7.4.5
Asymmetric Eigenvector Maps (AEM):
When Directionality Matters . . . . . . . . . . . . . . . . . . . . . 348
7.5
Another Way to Look at Spatial Structures: Multiscale
Ordination (MSO) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355
7.5.1
Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355
7.5.2
Application to the Mite Data – Exploratory
Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356
7.5.3
Application to the Detrended Mite
and Environmental Data . . . . . . . . . . . . . . . . . . . . . . . . 359
7.6
Space-Time Interaction Test in Multivariate ANOVA,
Without Replicates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361
7.6.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361
7.6.2
Testing the Space-Time Interaction with the
sti Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364
7.7
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367
8 Community Diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369
8.1
Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 369
8.2
The Multiple Facets of Diversity . . . . . . . . . . . . . . . . . . . . . . . . 370
8.2.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370
8.2.2
Species Diversity Measured by a Single Number . . . . . . 370
8.2.3
Taxonomic Diversity Indices in Practice . . . . . . . . . . . . 374
8.3
When Space Matters: Alpha, Beta and Gamma Diversities . . . . . . 379
8.4
Beta Diversity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379
8.4.1
Beta Diversity Measured by a Single Number . . . . . . . . 379
8.4.2
Beta Diversity as the Variance of the Community
Composition Table: SCBD and LCBD Indices . . . . . . . . 382
Contents
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