Environmental Engineering Reference
In-Depth Information
Spatial Analyses within an Ecosystem
Ecological variables that are geographically distributed in space and time tend to be
more similar when compared close together [
66
]. Autocorrelation is a feature of
most data and can be quantified by the degree of self-similarity or dissimilarity in
a variable between pairs of locations at a given distance apart (i.e., spatial lag
determined in terms of equidistant classes). Note that spatial statistics on their own
cannot differentiate between spatial dependence to environmental factors and
spatial autocorrelation due to ecological processes; only prior knowledge and
multiple testing can differentiate between these two sources of spatial structure.
Spatial Description of the Pattern
The objective of many spatial statistics is often to characterize to what degree
spatial data are autocorrelated, if they are oriented in a particular direction (anisot-
ropy), and at what scale. As these spatial statistics have been thoroughly reviewed
elsewhere [
7
,
58
], we focus on three topics (1) methods of spatial pattern analysis
devoted to identifying structure in point data, (2) methods of spatial analysis that
are devoted to identifying structure and pattern in two-dimensional raster (pixel) or
polygon data, and (3) methods of spatial analysis explicitly concerned with
identifying the scale, or scales of structure that are present in either point or two-
dimensional data. Both the data types discussed can be examined in uni-, bi-, and
multivariate contexts and can include either categorically or continuously measured
variables.
Point Pattern Analysis
Spatial point processes describe phenomena that produce events represented as
points in space [
67
,
68
]. The objective of point pattern analysis is to determine
whether the distribution of events (points in space) is more or less spatially
aggregated than is expected by chance and tests the null hypothesis of complete
spatial randomness. The use of complete spatial randomness assumes that the
underlying process is the same over the study area (i.e., stationarity). When it is
not the case, the study area is said to “inhomogeneous” such that significance
cannot be achieved using a single process such as complete spatial randomness.
Modified statistics and corrections have been developed to account for inhomoge-
neity within the study area [
69
,
70
]. Point pattern analysis also assumes complete
census of all point occurrences in the study area [
7
]. Fortin et al. [
71
] showed that
the significance of spatial aggregation estimations is biased only when a subset of
sample points is used rather than the entire set of points in the study area.
