Geoscience Reference
In-Depth Information
TABLE 7.2
Estimated Number of Snowshoe Hares (Cormack, 1989) for Two Heterogeneity
Models M
h
and M
th
Computed by CARE-2 (Chao and Yang, 2003), Using Several
Estimation Approaches
Bootstrap
SE
Asymptotic
SE
95% CI
(log-transf)
95% CI
(percentile)
Model
Estimate
CV
M
h
(SC1)
89.1
9.18
8.77
0.48
(77.31, 115.71)
(78.43, 107.56)
M
h
(SC2)
80.6
7.53
7.33
0.38
(72.28, 105.23)
(71.82, 96.97)
M
h
(JK1)
88.8
6.01
6.18
—
(79.97, 104.27)
(82.17, 96.33)
M
h
(JK2)
93.8
9.14
9.40
—
(81.12, 118.59)
(80.17, 109.83)
M
h
(IntJK)
88.8
8.47
6.18
—
(77.68, 112.86)
(81.33, 107.48)
M
h
(EE)
85.3
7.34
—
0.48
(75.82, 106.43)
(75.64, 98.36)
M
th
(SC1)
89.4
8.88
8.85
0.49
(77.82, 114.75)
(79.24, 106.39)
M
th
(SC2)
80.9
7.91
7.41
0.39
(72.28, 107.04)
(71.73, 98.89)
M
th
(EE)
84.7
7.11
—
0.49
(75.53, 105.20)
(74.36, 97.09)
Note:
SE, standard error; CV, coefficient of variation; CI, confidence interval; log-transf, log-
transformed interval; SC1, SC2, sample coverage approaches 1 and 2, respectively (Lee
and Chao, 1994); JK1, JK2, jackknife approaches 1 and 2, respectively (Burnham and
Overton, 1978); IntJK, interpolated jackknife (Burnham and Overton, 1978); EE, estimat-
ing equations approach (Chao et al., 2001).
interval because “more general models produce wide intervals with a
better coverage probability” (Chao and Yang, 2003, page 10). Selecting
the approach based on estimating equations (Chao et al
.,
2001), it is esti-
mated that there are 84.7 or about 85 hares in the population with an esti-
mated bootstrap standard error of 7.11 and an associated 95% confidence
interval of (74, 97) hares, based on the percentile method.
7.3.4 Huggins's Models
One of the major improvements in the mark-recapture analysis of closed popu-
lations is the use of a regression-type parameterization of covariates for estimat-
ing capture probabilities, with generalized linear modeling. Because capture
probabilities must be within the range 0 to 1, it is sensible to build this constraint
into a model. One way that this can be done involves replacing
P
ij
with a logistic
function. For example, in the time-varying model M
t
, the probabilities of capture
and recapture are given by
P
ij
=
e
j
, and these can be modeled as
P
ij
=
e
j
= exp(
a
+
c
j
)/{1 + exp(
a
+
c
j
)}.
This equation is equivalent to log{
e
j
/(1 −
e
j
)} =
a
+
c
j
, which is a particular
case of what is called the logit transformation; in generalized linear model-
ing terminology, this transformation is the logit link function. The logit is
the most commonly used link function for modeling capture and recapture
