Environmental Engineering Reference
In-Depth Information
Urban 2007) and the latest version of the programme is available on the web (
http://
www.al.umces.edu/Qrule.htm
). Consequently, we will not explain the details
required to perform Monte Carlo simulations with Qrule, assuming that the reader
is either aware of the above resources or can refer to them directly.
RULE (now called Qrule) was originally designed for a very specific purpose:
the generation and analysis of random maps and comparison of these neutral
models with actual landscapes. Because other software for landscape analysis
was available when RULE was written; first a programme by Monica Turner
(SPAN, described in Turner and Ruscher 1988) and later FRAGSTATS (McGarigal
et al. 2002), a parsimonious subset of metrics were implemented in Qrule. The
choice of metrics was based on the need for a minimum summary of pattern
characteristics for each land cover type (the metrics
p
, the total fraction of the
map occupied; the total number of patches; and the total amount of edge were
selected for this purpose) and the introduction of new metrics and principles of
analysis to landscape ecology, based on percolation theory. Stauffer's topic (1985)
emphasized two significant problems in the analysis of random structures generated
on gridded landscapes: the first problem was that the shape of the grid, whether
triangular, rectangular or hexagonal, dominated the shape of smaller clusters. Thus,
for many metrics there was a need to use large maps and to restrict the analysis to
the largest clusters. The fractal index was sensitive to grid effects approaching the
value of 2.0 on a rectangular lattice when cluster sizes where small (the rectangular
lattice is typically used in landscape studies, though hexagonal lattices have been
employed, e.g. Roberts 1987). The second problem was that random maps and
actual landscapes often have a large number of small, isolated clusters. These small
patches, which usually compose only a minor fraction of the total area occupied by
that land cover type, will bias the estimates of metrics that are based on arithmetic
mean values. These two problems are avoided in percolation theory and subse-
quently in Qrule, which adopted this approach by estimating the fractal dimension
for only the largest cluster on the map and by using geometric averages for
summary statistics. The discussion of the effect of map extent on the reliability of
landscape metrics was extensively evaluated in Gardner et al. (1987). With the
exception of the addition of lacunarity analysis to Qrule circa 1991 (Plotnick et al.
1993, 1996), changes to the programme through time have focused on fixing bugs
and increasing the convenience and efficiency of programme execution.
The philosophy of a limited scope for Qrule resulted in an emphasis on the
import and export of data. It is not uncommon for landscape analysis projects that
use Qrule to export spatial data from ArcInfo, to rescale these maps using PDW
(Gardner et al. 2008), to analyze the resulting patterns with Qrule, and display
summary statistics using R (R project). To enable this flexibility, an extensive suite
of data files are used in Qrule (Table
15.1
): there are four different options for
output of generated maps, with a 5th map type always created to visualize and
analyze results in ArcInfo; and there are four data sets used to statistically summa-
rize results (Table
15.1
).
The comparison of neutral models with the observed pattern of actual landscape
has always been based on traditional principles of statistical inference. If the
