Geoscience Reference
In-Depth Information
0.3
0.2
f(x)
0.1
0
0
1
2
3
4
5
6
7
Distance from Line
FIGURE 4.3
A curve
f
(
x
) fitted to the relative frequency histogram for observed distances from objects to
a transect line.
in Figure 4.3. Using the previous expression for the estimated probability of
detection
ˆ
w
, it can be shown that the estimated total number of objects
N
ˆ
is
ˆ
/
ˆ
w
,
NnP
(4.2)
where
n
is the actual number of animals detected in the study, which is
sometimes called the encounter rate.
If
n
objects are detected in the strip of width 2
w
and length
L
, then the
observed density is
n
/(2
Lw
). This is then corrected for visibility bias by divid-
ing by the average probability of detection of objects, as given by Equation
(4.1) to obtain
ˆ
(0)
2
D
n w
wf
/(2)
1/(
nf
L
ˆ
=
=
.
(4.3)
ˆ
(0))
Note that the width of the transect strip cancels out of this equation. It is
therefore acceptable to conduct line transect surveys with no upper limit to
the sighting distance. However, it has been found desirable to set an upper
limit on
w
so that a few percent of the most extreme observations are trun-
cated as outliers, using a value of
w
that can be set after the data are collected.
A more general equation for density estimation can be obtained if objects
occur in clusters (see Buckland et al
.
, 2001). The actual number of objects
