Geoscience Reference
In-Depth Information
It is necessary to be careful with the units when plotting histograms and
doing calculations. The units for the length of transect
L
must be the
width of one class in the histogram. In the duck nest example,
ˆ
(0) 0.148/
f
=
ft
, and
L
= (1600)(5280) ft.
If the width of a class were 0.5 ft, then
ˆ
(0) 0.148/2 0.074
per 0.5 ft,
f
=
=
ft
and
D
ˆ
(534)(0.074)(2)/{2(8448000)} 0.000004678
n e s t s/f t
2
.
=
=
A common mistake made when plotting histograms and fitting the func-
tion
f
(
x
) occurs when classes for grouped data are of different widths. In this
case, the height (and area) of the histogram bars must be adjusted to yield a
histogram with total area of 1.0 for all bars. If this is not accomplished, then
incorrect impressions will be drawn concerning the detection function.
4.4 Estimation from Sighting Distances and Angles
As noted, it is less satisfactory generally to record sighting distances
r
and
angles θ than it is to record distances from the transect line
x
, as shown in
Figure 4.1. But, if it is for some reason necessary to use
r
and θ, then estima-
tors of density are available. One approach is Hayne's (1949) method, which
assumes a circular flushing envelope.
The basic estimator is
n
1
2
∑
1
ˆ
D
Lr
=
.
i
i
1
=
Thus suppose that five sighting distances
r
i
in meters (5, 3, 1, 2, and 4) are made
on a transect of length
L
= 1000 m. Then, the reciprocals 1/
r
i
are 0.200, 0.333,
1.000, 0.500, and 0.250, respectively, with sum 2.283, and the estimated density is
D
ˆ
=
{1/(2 1000)}(2.283) 0.00114
obje c t s/m
2
.
×
=
4.5 Estimation of Standard Errors in Line Transect Sampling
Currently, with the versatile options implemented in the Distance program,
there are many choices for obtaining the most suitable detection function for
