Geoscience Reference
In-Depth Information
on capture, and
L
3
is the component that contains all the recapture infor-
mation conditional on the numbers of marked animals released at different
times and the parameters for capture and survival probabilities.
L
3
is the likelihood that was originally derived by Cormack (1964). One
way to view estimation in the full JS model is that capture and survival prob-
abilities are estimated from
L
3
only. This is then what is called the CJS model.
Once capture probabilities are estimated, the size of the population at the
time of sample
j
can be estimated from
n
j
≈
N
j
p
j
, leading to
ˆ
/
ˆ
Nnp
j
,
(8.9)
j
j
which turns out to be the same as the JS estimator.
Accurate estimates can only be obtained from the JS model if the data are
extensive because so many parameters are involved. For this reason, alterna-
tive models with fewer parameters, such as those with a constant survival
rate per unit time, are of interest. Generalizations of the JS model allowing
for trap response, the analysis of data from several cohorts of animals, and
age-dependent survival rates are also available.
Before and after the JS model was introduced, various special cases and
generalizations were developed and included in the computer program
JOLLY. The deaths-only model is useful if there is no immigration and
recruitment is not occurring. The births-only model is useful if there is no
mortality or emigration. Versions of the model with constant survival or cap-
ture probabilities are also available in the JOLLY program. Some generaliza-
tions of the JS model that allow for temporary effects on survival and capture
rates have also been developed and are available in the programs JOLLY or
MARK. Although the JS model is intuitive and can be applied in some situ-
ations, most real-world multiple-occasion surveys will want to apply more
sophisticated models described later in this chapter.
EXAMPLE 8.1 Estimation for a Moth Population
To illustrate the use of mark-recapture methods, consider Manly and
Parr's (1968) data obtained from sampling an isolated population of the
burnet moth
Zygaena filipendulae
(Table 8.1). This was an open population
so that any analysis should allow for ingress and egress. The JS esti-
mation equations are therefore applied to the data. Because the study
involved five samples taken on 19, 20, 21, 22, and 24 July 1968, this per-
mits the estimation of the population size on 20, 21, and 22 July; survival
rates for the periods 19-20, 20-21, and 21-22 July; and the number of new
entries to the population for the periods 20-21 and 21-22 July.
From these data, the values
m
j
,
R
j
,
z
j
, and
r
j
needed for Equations (8.3)
to (8.6) can be obtained, and hence estimates of population param-
eters with their estimated standard errors are obtained as shown in
Tables 8.2 and 8.3. The 95% confidence intervals shown in this table are
