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is assumed to take a multiplicative form,
c
ij
= φ
p
i
e
j
(where φ is the behavioral
response effect), and the heterogeneity effects
p
i
are characterized by their
mean and CV (Chao and Huggins, 2005b). The estimating equation method
is applicable for all of the Otis
et al. (1978) models, and CARE-2 includes
these last methods and a bootstrapping approach for the estimation of popu-
lation sizes and their standard errors.
Before considering model selection for mark-recapture data gathered in
multiple samples, the first task is to test whether the population to be mod-
eled is truly closed. Since the unifying work by Otis et al
.
(1978), a procedure
(suggested by Burnham and Overton) was implemented in CAPTURE to test
the null hypothesis that the individual capture probabilities are invariant
over time against the alternative that some individuals (that were captured
at least twice) were not present in the population at the beginning or the
end of the study or both. This test is not appropriate in cases of temporary
emigration for which individuals present at the start of the study then left
the study for a time and returned before the end of the study. Improved tests
of closure have been given by Stanley and Burnham (1999) that provided an
overall closure test based on a chi-squared statistic together with component
tests on whether the population experienced additions or losses during the
study. In particular, these component tests compare the null hypothesis of a
closed-population model M
t
versus the alternative that losses or additions
are governed by the open-population Jolly-Seber model that is described in
Chapter 8. Computations for all these tests and for Burnham and Overton's
test described previously can be performed in the CloseTest program (Stanley
and Richards 2005).
Example 7.2 The Snowshoe Hares
These data, collected by Burnham and Cushwa, were analyzed in
Cormack (1989) and Agresti (1994). Using the same data, Baillargeon and
Rivest (2007) illustrated the application of capture-recapture analyses
based on log-linear models and their implementation in the R package
Rcapture. Under this approach (given that model comparison was pos-
sible by means of AIC, Akaike's information criterion), they showed
that there is little evidence of a behavioral response, and the best-fitting
model was heterogeneous, corresponding to a particular version of
model M
th
(called M
th Poisson2
), producing a population size estimate of 81.1
with a standard error of 5.7 and a 95% confidence interval of 71.8 to 93.8.
For this example of snowshoe hares, the data were reanalyzed using the
programs CAPTURE, CloseTest, and CARE-2.
CAPTURE and CloseTest were run first to test the assumption of
closure for the sampled population of hares. This indicated that the
assumption of closure holds (see overall closures in Table 7.1). Additional
(and more detailed) tests produced by CloseTest also suggest no addi-
tions or losses during the study (see the information on the component
tests of Stanley and Burnham's Closure Text in Table 7.1). The CAPTURE
program was run for model selection based on the procedures described
