Geoscience Reference
In-Depth Information
The estimate of duck nest density, Equation (4.3), on this basis is
(534)(0.1457)
2(1600)(5280)
D
ˆ
=
=
0.000004605
nest per square foot,
or 128.4 nests per square mile. Note that
L
= 1600 × 5280 ft.
Anderson and Pospahala fitted a second-degree polynomial equation
to the midpoints of the top of the bars in the histogram. Their analysis
procedure was formalized in a slightly different manner, but it is equiva-
lent to the estimation of
f
(0) by
ˆ
(0) 0.1442
, leading to =
D
ˆ
=
127.1
nests
per square mile.
The most widespread approach used to estimate the probability density
function for the observed distances at
x
= 0,
ˆ
(0)
, dictates the use of any of the
parametric and nonparametric methods mentioned. For example, a Fourier
series was traditionally applied in older studies of line transect sampling to
approximate
f
(
x
). Currently, there are plenty of options for density estimation
implemented in Distance (Thomas et al
.
, 2009), a program that has become
standard for line transect analysis (and point transect analysis; see Section
4.8). Although Distance does not have an explicit option called Fourier series,
it can be built with the combination of the uniform key function 1/
w
and an
adjustment given by the cosine series expansion,
∑
m
a
cos( /)
j yw
π
.
j
j
=
1
EXAMPLE 4.2 Sampling Waterfowl Nests (continued)
Assuming a Fourier series to approximating the density function, that the
number of detected objects has a Poisson distribution, that sightings of
nests are independent events, and that distance data are transformed into
eight intervals for analysis, Distance yields
D
ˆ
130.1
nests per square mile. The approximate 95% confidence interval for the
population density of nests is from 114.0 to 148.5 nests per square mile.
Using Equations (4.1) and (4.3), a more intuitive justification for the
estimation formula can be given. The observed density of duck nests is
ˆ
(0) 0.1477
; hence, =
=
ˆ
Dn Lw
=
/(2)534/{2(1600)(8/5280)} 110.14
n e s t s/s q u a r e m i l e.
=
=
The average probability of detection of a nest within 8 ft of the transect
line is estimated to be about 0.8463 by the formula
ˆ
(0)} 1/{8(0.1477)} 0.8463
ˆ
P f
=
1/{
=
=
.
w
Finally, the observed density adjusted for the visibility bias is
ˆ
)}/(
ˆ
Dn Lw
=
{/(2
Pw
) 110.14/0.8463 130.1
n e s t s/s q u a r e m i l e.
=
=
