Geoscience Reference
In-Depth Information
EXAMPLE 6.1 Trees in Lansing Woods
As an example of the
T
T-square sampling and the corresponding density
estimation using Byth's formula from Equation (6.3), consider data on
the locations of 2251 trees in a 19.6-acre plot in Lansing Woods, Clinton
County, Michigan, USA (Gerrard, 1969). The original plot size (924 × 924 ft)
has been rescaled to unit squares. Trees are identified according to their
botanical classification as hickories, maples, red oaks, white oaks, black
oaks, or miscellaneous trees. For the purpose of the present example,
density estimation was made only for hickories and oaks (red, white, and
black oaks combined). It is worth noticing that the trees in this data set are
completely mapped; thus, there are better sampling methods for density
estimation than
T
T-square sampling. Nevertheless, the
T
T-square sampling
for these data is used here for illustrative purposes, with the advantage
that it is possible to compare the estimates produced by Byth's formula to
the actual tree density in the rescaled plot. A systematic sample of
n
= 25
random points in a 5 × 5 grid was taken, with each random point selected
from the interior of each subplot determined by the grid. Figure 6.2 shows
T−square sampling. Oaks in Lansing Woods ( n = 25 )
^
D
T
=928.83
1.0
20
10
15
5
25
0.8
19
14
24
8
9
4
0.6
23
Y
13
18
3
17
0.4
12
22
7
0.2
2
11
16
6
21
0.0
1
0.0
0.2
0.4
0.6
0.8
1.0
95% CI for DT
T
= [ 694.25,1402.86]
X
FIGURE 6.2
T
T-square sampling of oaks in Lansing Woods. Twenty-five points (+) in a 5 × 5 grid were ran-
domly positioned in the unit square, and the nearest oaks to the random points (the point on
each circle) were located. The squared points indicate the nearest oaks to the former oaks.
Byth's estimate of the density
D
ˆ
T
and the 95% confidence interval for
D
T
are also shown.
