Environmental Engineering Reference
In-Depth Information
examination of the cumulative frequency distributions (cfd) of patch sizes where
statistical differences can be examined by the familiar distributional tests (e.g. the
KS test, Zar 1996). Even more powerful methods exist if the expected change in the
cfd can be defined
a priori
, allowing parametric comparison of the observed with
the appropriate theoretical distributions (Johnson and Kotz 1969, 1970). Because
the cfd of patch sizes varies with map dimension, resolution and methods used to
classify land-cover types, it is usually impossible to pre-define an expected shift in
the cfd and compare this shift with an appropriate probability distribution. In these
cases one must rely on neutral models to generate the “expected” cfd to compare to
an observed landscape using the appropriate statistical test(s). It is these principles
of analysis that are illustrated in the following example.
15.3 Methods
The neutral models available in previous versions of Qrule have all assumed that
landscapes could be represented as a rectangular lattice (grid). Large, irregular
landscapes were simply truncated to form a rectangular map. Although remote
imagery is composed of square pixels, the boundaries of most landscapes are rarely
rectangular. A new neutral model was created for the analysis presented here;
one primarily designed to eliminate this truncation effect. This method, labeled
“Random-with-Constraints” (RwC) first examines the actual landscape, extracts the
boundaries and other embedded constraints (i.e. user-defined areas such as rivers
and lakes where habitat cannot be located), constructs a mask from this information,
and then randomly generates habitat within the area permitted by the mask. The
number of land-cover types generated is also user controlled but must be equal to or
less than the number of cover types in the original mask. During programme
execution and before the original land cover map is evaluated, the user can
aggregate cover types. In the current analysis, non-habitat (class “0”) was combined
with open water (class “1”) to create the mask; classes 5, 6, and 7, which had no
representation within the original map were re-classed to 0; and the remaining
cover types of urban, barren lands, forest, agriculture and wetlands were sequen-
tially renumbered to cover classes 1-5, respectively. The fraction of sites in each of
these five classes,
p
i
, within the actual land-cover map was recorded and sub-
sequently used to generate random cover types in the ten Monte Carlo iterations
of the RwC model. The result was ten random maps with the distributional area
equal to the original map (each map having five land cover types in proportion to
the observed frequencies of the original map).
A second revision to Qrule was the reconfiguration of the data files used for
statistical testing. The four files (Table
15.1
) produced for each execution of Qrule
are:
rulerun.log
which records all programme input and provides a statistical
summary of results, including the land cover association matrix and indices char-
acterizing patch attributes;
assmat.dat
, the association matrices of land cover types
(one matrix for each map iteration);
stats.csv,
the output record for each iteration
