Environmental Engineering Reference
In-Depth Information
spatial structure at different spatial scales. These synthetic variables can then be used
in combination with constrained ordination methods (e.g., canonical correspondence
analysis and redundancy analysis; [
95
]) to identify the spatial scales at which data
are dominantly structured. Jombert et al. [
97
] also proposed a multi-scale pattern
analysis (MSPA) to determine which of these many scales are the most relevant to use
as spatial predictors in subsequent analyses such as partial ordination or multiple
regression [
85
].
Spatial Analyses Among Ecosystems
The ecotonal interfaces between ecosystems are important to delineate as they are
the locations where the exchange of nutrients and species turnover occurs [
7
]. It is
also important to determine not only the boundary location between ecosystems,
that is, where one system begins and another ends, but also its width (i.e., sharp/line
or gradual/zone) [
98
]. There are two different types of methods that can be used to
determine the interface between ecosystems: by creating spatial clusters or by
detecting boundaries [
99
]. In either case, the sampling design used to collect the
data is crucial: The determination of a boundary (i.e., area of high rate of changes in
the values of variables, hence a heterogeneous area) is relative to the two adjacent
spatially homogeneous ecosystems. Therefore, the sampled data should cover
enough of both ecosystems such that their interface can be detected.
Spatial Clustering
To delimit boundaries between ecosystems, spatially homogeneous clusters can be
determined based on the degree of similarity of sample attributes and their spatial
adjacencies [
66
,
99
,
100
]. The degree of similarity can be based on commonly used
clustering algorithms (agglomerative,
k
-means, fuzzy logic, etc.) and adjacency can be
based on network connectivity algorithms (e.g., nearest neighbors, minimum spanning
tree, Gabriel network, Delaunay network; [
7
]). Spatial clustering provides the mem-
bership of each location to a spatial cluster and therefore, as a by-product, identifies
boundaries among clusters. However, clustering procedures do not provide any
information about the location and width of the identified boundaries between
clusters. When information about location and width are needed, other methods
should be used such as boundary detection methods ([
99
]; but see [
101
]).
Spatial Boundary Analyses
Ecological boundaries can be defined as areas of high rates of change or large
absolute differences between adjacent locations [
102
]. Boundary detection methods
[
98
] include edge detection algorithms (Laplacian, Canny, Sobel, Monomier, etc.),
