Geoscience Reference
In-Depth Information
TABLE 5.1
Comparison of Population Estimates Provided by Two Approximate
Methods Compared to Estimates Provided by CAPTURE Program
95% Confidence Interval
N
ˆ
Lower Limit
Upper Limit
Zippin (1956)
400
347
453
Soms (1985)
394
338
450
CAPTURE
394
362
453
the CAPTURE program were apparently adjusted for nonnormality of the
estimate (Table 5.1).
EXAMPLE 5.1 Estimation of a Crab Spider Population Size
Soms (1985) illustrated his method of estimation using data on crab spi-
ders. In one case, six samples were taken, and 46, 29, 36, 22, 26, and 23
spiders were removed. The calculations for this example are shown in
Table 5.2. The proportion removed on each sampling occasion is esti-
mated as 0.115, with standard error 0.040, and the estimate of the popula-
tion size is 350, with standard error 87.6. Soms also described a test for
the goodness of fit of the removal sampling model. With the spider data,
it provides a chi-squared value of 4.06, with four degrees of freedom.
This is not significantly large and therefore gives no reason to doubt the
assumptions made.
Running the interactive CAPTURE program shows that the maximum
likelihood estimate of the population size is
N
ˆ
= 324 with standard
error = 69.03 and with the approximate 95% confidence interval 240 to
TABLE 5.2
Results for the Removal Sampling of Crab Spiders
Quantities Needed for
Variance Calculations
Regression Data
Sample
i
Removed
z
X
y
c
s
c
2
/s
1
46
0
3.829
−0.143
0.115
0.177
2
29
1
3.367
−0.086
0.102
0.072
3
36
2
3.584
−0.029
0.090
0.009
4
22
3
3.091
0.029
0.080
0.010
5
26
4
3.258
0.086
0.071
0.104
6
23
5
3.135
0.143
0.062
0.327
Total
182
0.699
Note:
The fitted regression equation is
y
= 3.683 − 0.122
x
. Hence,
ˆ
= 1 − exp(−0.122) = 0.115,
ˆ
= 0.885, and
N
ˆ
= 182/(1 − 0.885
6
) = 350.3. From Equation (5.5), with
N
and
q
replaced by
their estimates Var(
N
ˆ
) ≈ 7801.2 and SE(
N
ˆ
) = 87.6. Similarly, from Equation (5.6), Var(
ˆ
) ≈
0.0016 and SE(
ˆ
) ≈ 0.040.
