Geoscience Reference
In-Depth Information
Following the work of Diggle (2003), the randomness of the objects
arranged in space can be tested using the statistic
=π
ˆ
2
I
D d
/2
,
wq
wq
i
i
2
which is distributed as χ
N
when the spatial pattern of items is completely
random (
N
being the total number of wandering distances).
2
EXAMPLE 6.2 Japanese Pine Point Pattern
The data in this case consist of 65 Japanese black pine (
Pinus thunbergii
)
saplings
in a square sampling region in a natural forest. Numata (1961)
originally collected the tree locations in a square 5.7 × 5.7 m, but the
region has been rescaled to unit squares and the point data rounded to
two decimal places. Like the example given in
T
T-square sampling using
the Lansing Woods data, saplings are completely mapped, but the appli-
cation of the wandering-quarter method and the density estimation
allow a comparison between the estimate produced by Catana's formula
in Equation (6.6) to the actual sapling density in the rescaled plot. The
placement of transects in the unit square was simulated, where these
four transects indicate the search direction of saplings and determine
the quadrat (quarter) from where wandering distances are measured
(see Figure 6.5). The use of Equation (6.6) in this case is completely justi-
fied because the spatial pattern of the 65 Numata's black pine saplings
appears to be random (Diggle, 2003). The estimated density based on the
resulting 27 wandering distances is
D
ˆ
=
63.55
saplings per unit area.
wq
6.6 Further Extensions and Recent Developments
in Plotless Sampling Methods
Bostoen et al
.
(2007) provided an extension of the
T
T-square method appli-
cable to designs seeking to establish planning resource requirements or
assessing health needs where sampling frames are unavailable. The proce-
dure, basically a combination of
T
T-square sampling and optimization tech-
niques, is executed in two stages. The first one optimizes the sample size,
and the second one optimizes the pathway connecting the sampling points,
which entails the solution of the well-known traveling salesperson problem
(Applegate et al., 2006). Coincidently, in the same article, Bostoen et al
.
(2007)
suggest the wandering-quarter method as an alternative sampling proce-
dure applicable to human populations.
Angles between objects can also be used for revealing spatial patterns in
plotless sampling. As an example, Assunção (1994) has proposed a sampling
