Geoscience Reference
In-Depth Information
TABLE 7.1
Closure Tests for the Snowshoe Hares Data, Produced by the CloseTest Program
(Stanley and Richards, 2005)
Test
Statistic
df
p
Overall Closure
Burnham and Overton
a
z
= −0.311
—
0.3779
b
Stanley and Burnham (1999)
Chi
2
= 3.174
8
0.9229
b
Component Tests of Stanley and Burnham Closure Test
Test
Chi
2
df
p
Additions to population
No recruitment vs. Jolly-Seber
c
1.421
4
0.8406
d
Time effect vs. no mortality
1.976
4
0.7402
d
Losses from population
Time effect vs. no recruitment
1.754
4
0.7810
d
No mortality vs. Jolly-Seber
c
1.199
4
0.8783
d
a
Described in Otis et al. (1978) and present in the CAPTURE
program
.
b
Low
p
values suggest population not closed.
c
A model for open populations (see Chapter 8).
d
Low
p
values suggest there were additions to the population.
e
Low
p
values suggest there were losses from the population.
by Otis et al
.
(1978), showing that the appropriate model is probably M
h
,
followed closely by models M
0
and M
th
. CAPTURE produces an interpo-
lated jackknife estimator (Burnham and Overton, 1978) for the popula-
tion size of 87, with a standard error of 6.76 and an approximate 95%
confidence interval of 78 to 105 snowshoe hares.
Applying the estimation approaches implemented in CARE-2, it is
possible to include various estimators for the population size for M
h
and
M
th
and gain more information about the heterogeneity in capture prob-
abilities. The corresponding estimations are summarized in Table 7.2.
Thus, the estimated coefficients of variation of the capture probabilities
for all estimation methods range between 0.38 and 0.49, which provides
evidence of heterogeneity. The CARE-2 program produces two stan-
dard error estimates: the asymptotic estimate and the bootstrap stan-
dard error. The asymptotic standard error for the models considered in
Table 7.2 (where heterogeneity is assumed) were obtained by the delta
method (Casella and Berger, 2001). In the case of the estimating equation
approach (EE in the table), the asymptotic standard error is not comput-
able for models M
h
and M
th
because of their complexity. The output also
shows two types of 95% confidence intervals constructed using boot-
strap standard errors. One is based on the log-transformed estimates of
N
, as described in Chao (1987), and the other is derived using the percen-
tile method (Efron and Tibshirani, 1993; Manly, 2006).
Comparing the confidence intervals for models M
h
and M
th
under
the sample coverage 2 estimator (SC2), it can be seen that the confi-
dence interval for M
th
is wider than that for M
h
because more param-
eters are included. In capture-recapture models for closed populations,
it is common to find that a simpler model has a narrow confidence
