Ecosystems and Spatial Patterns - Ecological Systems - page 108

from a diverse set of disciplines such as geography, geostatistics, and ecology, only
the key concepts related to the most commonly used methods that quantify spatial
structure within and among ecosystems are presented. Before describing the differ-
ent types of analysis, some fundamental issues related to the spatial analysis of data
are presented.
Assumption of Stationarity
To infer spatial pattern from samples spatial statistics require that the area under
study is governed by the same underlying process (i.e., the assumption of
stationarity; [ 7 ]). As it is often impossible to be sure that the underlying process
is stationary, one needs either to assume it or to determine whether or not the
observed data are stationary (i.e., their statistical properties such as mean, variance,
isotropy do not vary with spatial distance). Nonstationary processes may arise when
more than one process is present and that these multiple processes may be acting at
different spatial or temporal scales. Yet, in most forest ecosystems, processes
interact with one another, resulting in unique types and scales of spatial pattern
which violate the assumption of stationarity. In such circumstances, it is required to
first identify stationary subregions within such a larger spatial context. A few
spatial analysis methods do not require the stationarity such as lacunarity analysis,
local quadrat variance methods, and wavelets [ 7 ]. It is worth noting that these types
of analyses although different and originating from different developmental
histories are quite similar to one another mathematically [ 56 ].
Data Type
Spatial pattern within ecosystems can be represented using categorical or continu-
ous data depending on the nature of the variable under investigation. Each type of
data requires different methods of analysis ( Fig. 7.3 ;[ 7 ]). Categorical data can be
described by the amount and configuration of the different discrete types on the
landscape. Examples of categorical spatial data include forest type and age, or
classified habitat patches. Both amount and configuration can be described in
numerous ways using landscape pattern metrics [ 9 , 57 , 58 ]. Continuous data
requires more subtlety in describing patterns and can include variables such as
soil moisture, forest basal area, or remotely sensed reflectance indices (e.g., NDVI).
Composition of continuous variables can be described using the density distribution
of the variable and configuration is usually described by a spatial covariance
function that captures the strength, directionality, and scale of autocorrelation of
the variable [ 5 , 7 , 59 ].
In addition to the categorical/quantitative dichotomy of data types, patterns can
be described using different geometric topologies of spatial features or units: the