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of sample j and the time of sample j + 1 that are still alive at the time of
sample j + 1.
Estimation of the population size is possible because it is expected that
n j N j p j . Thus, the estimator given in Equation (8.9) is applicable
ˆ
(
Nnp
/ ˆ )
j j j ,
with ˆ j given by Equation (8.10). This then has a sample variance that can be
estimated by
·
ˆ
ˆ
2
Var(
NNCcncc
)
=
(
)(
)/
(8.11)
j
j
j
j
j
j
j
(Manly, 1969).
Estimation of the survival rate is based on m j , j +1 , the number of animals
seen in both sample j and sample j + 1. It is expected that m j , j +1 n j ϕ j p j +1 , sug-
gesting the estimator
ˆ
ˆ )
φ=
mn p
/(
.
(8.12)
j
j j
,1
+
j
j
No variance equation has yet been produced for this equation.
Having estimated N j and ϕ j , there is the obvious estimator
ˆ
ˆ
ˆ
ˆ
BN N
=
φ
(8.13)
j
j
1
j
j
+
for B j .
The use of the idea behind the Manly-Parr method has been extended to
when animals have known ages (Manly et al., 2003). Given the validity of
certain assumptions, this leads to a relatively simple analysis of data using
logistic regression to allow for the effects of covariates on capture probabili-
ties. Survival rates do not have to be modeled with this approach.
8.4 Recoveries of Dead Animals
It is sometimes possible to obtain information about where and when some
marked animals died by using a suitable marking or tagging system. This
information can then be employed to estimate survival rates and to study the
movement of the animals. The main application of studies of this nature has
been with banded birds, with schemes set up to encourage anyone finding
one of the bands (on or off a bird) to return it to an address on the bands.
A major contribution to the analysis of the data obtained from the recov-
eries of dead animals is provided by the handbook of Brownie et al . (1985),
in which a series of models with different assumptions about survival and
recapture probabilities is described. These models allow for animals to be
banded as adults only, as young and adults, or as young, subadults, and
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