Geoscience Reference
In-Depth Information
d
3
P
4
P
1
P
3
d
1
d
2
P
2
45°
SX
45°
FIGURE 6.4
Wandering quarter sampling (Catana, 1963).
S
is a randomly selected point.
P
1
is the near-
est object to
S
within a quarter determined by the direction of the transect (indicated by the
arrow), having
S
as the starting point for searching. The nearest object to
P
1
(i.e.,
P
2
) found in
the next quarter determines the first measured distance
d
1
used in the formula for density
estimation. The procedure continues in a similar fashion, producing additional distances
d
2
,
d
3
, . . . . See text for further details.
be the mean distance between items. If items in the study region are ran-
domly dispersed, the density is estimated as
ˆ
DAd
/
2
,
(6.6)
wq
where
A
is the unit of area, and
d
2
is interpreted as the mean area of all
items. For a clumped spatial distribution of items, Catana (1963) developed
an estimator of
D
wq
based on methods suggested by Cottam et al. (1953, 1957),
that is,
ˆ
wq
DNN
=×
itc
,
cl
where
N
cl
is the number of clumps per unit area, and
N
itc
is the number of
items per clump. However, here only the estimator of
D
wq
for randomly dis-
persed items is considered.
As noted by Diggle (2003), the wandering-quarter method is an ingenious
method whose slow adoption may be because of the use of longer chains of
object-to-object distances that would produce distances with increasing like-
lihood of boundary problems (i.e., reaching the end of the region in less than
n
steps either because Catana recommended
n
= 25 or because of encounter-
ing the side boundary). Another reason why Catana's method is not so popu-
lar is the lack of an easy-to-compute standard error of the estimate. Hall et al
.
(2001) proposed a bootstrapping procedure for a generalized version of the
wandering-quarter method, but the density estimator is different from that
suggested by Catana (1963).
