Geoscience Reference
In-Depth Information
6.3 Performance of
T
-Square Sampling
Zimmermann (1991) mentions two potential unwanted effects when plotless
methods are applied for the estimation of density. One is that searching for
nearest neighbors using circular regions may cause them to overlap, produc-
ing dependent measurements. The other problem is that edge effects may
cause problems as the distances to nearest neighbors tend to be larger near
the boundary than the distances in the interior of the searching region. To
cope with this second problem, several authors have suggested searching in
a smaller subregion within the study area. As an alternative, Zimmermann
(1991) explored censoring methods to avoid the reduction of the original
study area, relying on maximum likelihood methods for the estimation of
effects. He also studied the performance of some robust estimators, partic-
ularly under departures from the random location of items. Zimmermann
concluded that Byth's (1982) estimator
D
ˆ
T
appears to be efficient and robust
against edge and overlap effects and departures from complete spatial ran-
domness. However, Hall et al. (2001) argued that the need to locate a number
of random points in the field reduces the attractiveness of
T
T-square sampling
in areas like those of forestry, where the cost of locating random points is
large. These authors therefore recommended another family of plotless sam-
pling procedures, called wandering-quarter methods (Catana, 1963), that
may reduce the number of random starting points.
More tests of the performance of plotless sampling procedures were per-
formed by Engeman et al. (1994), who concluded that the usual
T
T-square esti-
mator based on Byth's equation is in the midrange of performance. Using a
simulation study, Steinke and Hennenberg (2006) compared the power of
plotless density estimators (PDEs), including the
T
T-square method, on plot
counts of two plant populations. Tests were developed to compare the densi-
ties of two independent populations, and the performance of the tests was
examined. All simulations were run for spatially random and aggregate data
patterns. Steinke and Hennenberg found that for completely random data,
all estimators and all tests are well behaved if the sampling intensity is the
same, but for the aggregate pattern, all PDEs were negatively biased and the
quadrat count estimator was unbiased.
6.4 Applications
Lamacraft et al. (1983) compared several plotless procedures seeking the
most convenient formula for density estimation of three plant species in
the arid rangelands of central Australia. They concluded that Byth's (1982)
