Geoscience Reference
In-Depth Information
For this particular model, it is possible to obtain explicit estimates for most
of the unknown parameters based on the principle of maximum likelihood.
The estimator of the recovery rate in year
j
is
ˆ
f RCNT
(
)/(
j
)
(8.14)
j
j
j
j
for
j
= 1, 2, . . . ,
k
, where
R
j
is the total number of birds recaptured from the
N
j
released in year
j
, and
C
j
is the total number of birds recovered dead in
year
j
(Table 8.4). The definition of
T
j
is more complicated, and values must be
calculated from the following relationships:
R
,
j
=
1
j
,
2,3, ...,
T
=
RT C
+−
j
=
k
j
j
j
−
1
j
−
1
TC jk k
−
,
=
++
1, , ...,
l
j
−
1
j
−
1
The estimator of the yearly survival rate
S
j
is
ˆ
j
= (
R
j
/
N
j
)(1 -
C
j
/
T
j
)(
N
j
+1
+ 1)/(
R
j
+1
+ 1),
(8.15)
j
= 1, 2, . . . ,
k
- 1, where the addition of 1 to
N
j
+1
and
R
j
+1
has been made to
reduce bias. The maximum likelihood estimators do not include these
additions.
Approximations for the variances of the estimator are provided by the
equations
·
Var(
ˆ
)
ˆ
2
f
≈
f RNCT
(1//1/ /)
−
+
−
(8.16)
j
j
j
j
j
j
and
·
Var(
ˆ
ˆ
{
}
2
SSRNR NTR T
)
≈
1/
−
1/
+
1/
−
1/
+
1/(
−
) 1/
−
. (8.17)
j
j
j
j
j
+
1
j
+
1
j
+
1
j
+
1
j
Standard errors are estimated by the square roots of the estimated variances,
and approximate 100(1 - α)% confidence intervals are given in the usual way
by estimates plus and minus multiples of the standard errors.
Variations on this model discussed by Brownie et al
.
(1985) include those
for which either the survival rates
S
j
or the recovery rates
f
j
(or both) are con-
stant with time, with the fit of different models to the observed data assessed
by appropriate statistical tests.
