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probabilities and is, for example, the default in the R package mra (McDonald,
2012), but other links are also possible. The use of generalized linear models
for the probabilities of capture and recapture has the advantage of making it
easy to incorporate the effects of covariates into the model, as it is done with
logistic regression. For example, assuming no individual heterogeneity, if R j
is a measure of the effort put into recapturing animals in sample j , then it may
be considered appropriate to model the probabilities of capture by
e j = exp( r 0 + r 1 R j )/{1 + exp( r 0 + r 1 R j )}.
Using logistic functions in this way allows a good deal of flexibility in the
modeling process. Several covariates can be used, and capture probabilities
can be allowed to vary with time, the age of animals, an animal's group, and so
on. In all cases, the likelihood is maximized with respect to the parameters in
the logistic models (e.g., the c j 's or the r j 's in the two models shown previously).
Once these parameters have been estimated, the logistic functions can be used
to determine estimated capture probabilities for any animal, as proposed for
closed populations by Huggins (1989, 1991) and Ahlo (1990).
Huggins's method involves the modeling of the capture probabilities P ij ,
assuming that measured covariates can account for unequal catchability
on different capture occasions and that the covariate values for uncaptured
individuals are not known (Huggins, 1991). This assumption then requires
estimation of parameters by maximization of the conditional likelihood
based on the data for captured individuals. As a consequence, the estima-
tion of N is more complicated for models including individual covariates
(e.g., age, sex, body weight, etc.) or capture occasion covariates (e.g., the pre-
cipitation on each capture occasion, the effort on each capture occasion,
etc.) as described by Chao and Yang (2003) in their manual for the program
CARE-2. The general logistic model for P ij used in this program is
logit( P ij ) = log( P ij /(1 − P ij )) = a + c j + vY ij + β W i + r R j ,
( 7. 5 )
where a is the intercept; c 1 , . . . , c k -1 account for the capture occasional or time
effect, with c k = 0; W i ' is a vector of the s covariates measured on each indi-
vidual i ; β ′ is the vector of effects for these covariates; R j is a vector of g
covariates for the j th capture occasion; and r ′ denotes the vector of effect
for these covariates. The Y ij are dummy variables indicating whether the i th
animal has been captured at least once before the j th occasion ( Y ij = 1) or not
captured before that occasion ( Y ij = 0), and v is the corresponding effect of
this behavioral response.
Huggins's method can be used with the eight Otis et al . models described
previously. Thus, under the Huggins method, model M 0 is given by
logit( P ij ) = a ,
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