The initial 2 is the probability associated with the bird surviving from period
2 to 3, (1p 3 ) corresponds to the bird not being captured in period 3, 3
corresponds to the probability of surviving from period 3 to 4, p 4 denotes
capture probability in period 4, and (1 4 p 5 ) is the probability that the bird
either does not survive until period 5 or survives but is not captured then
(i.e. both possibilities are included in this term). Note that a key difference
between the modeling of capture–recapture data and radio-telemetry data
concerns the modeling of trailing 0’s (0 entries that occur following the last 1).
In the modeling of telemetry data for which detection probability is 1, 0’s that
occur following death are not modeled, as there is no uncertainty associated with
them. However, trailing 0’s in capture–recapture studies must be modeled, as
their meaning is ambiguous.
The capture–recapture data (consisting of a capture history for every bird
marked during the study) and the probability model (each history has an
associated probability, constructed as in the above example) are then combined
into a likelihood function, and the parameters of the model are estimated.
Computation of estimates, their variances, and covariances, under different
models and computation of test statistics and model selection criteria are usually
accomplished using computer software such as MARK (White and Burnham
1999). The CJS model outlined above can be modified in numerous ways for
various reasons. For example, reduced-parameter models in which parameters
are assumed constant over time provide estimates with smaller variances than
those produced by time-specific models. The logistics of capture–recapture
sampling, combined with animal behavior, may result in the need to model
parameters as a function of the previous capture history in order to deal with
such phenomena as trap response in capture or survival probabilities. A special
kind of capture–history dependence, especially useful in avian capture–recapture
studies conducted at certain times of the year, involves incorporation of a tran-
sient parameter, reflecting the possibility that an unknown number of unmarked
birds are transients with no chance of returning to the study area (Pradel et al.
1997). Parameters are frequently thought to be age-specific for birds, and such
variation can be included in the modeling. As with the analysis of telemetry data,
interest will often be focused on covariate relationships in which survival is
modeled as a function of environmental or management covariates (e.g. using the
linear-logistic relationship in equation (5.1)) or even individual bird covariates.
A key step in these analyses again involves the selection of the most appro-
priate model from a set of competitors. Recent descriptions of capture–recapture
modeling are provided by Burnham et al. (1987), Lebreton et al. (1992) and
Williams et al. (2002).
126 |Estimating survival and movement