(e.g. once each week), listening for radio signals and identifying birds as alive or
dead. Such status identification sometimes requires actually locating and observ-
ing the bird, although some transmitters are equipped with “mortality sensors,”
based on either temperature or motion, that indicate whether the bird is alive or
dead and that so do not necessarily require location of the bird.
If all radioed birds are detected when alive and are also detected as dead during
the first sampling period following death, then the data needed for each bird are
simply the sampling occasion of initial capture and release with a radio, the last
sample period of detection as a live bird, and, in the case of death, the sample
period during which the bird was encountered dead. We can also summarize the
data for each marked bird as an encounter history, using codes 1marked and
alive, 2marked and newly dead (i.e. the bird died following the previous
sample period and before the current period) and 0not yet marked or died
during a previous period. The encounter history is a row of these codes, with an
entry for each sample period. Thus the encounter history 0 1 1 1 2 0 would
denote a bird marked in period 2, detected alive in periods 3 and 4, found dead
in period 5, and so not detected in period 6 of a 6-period study. These data can
then be modeled in either of two basically equivalent ways, using either binomial
survival models or models based on time at death (Williams et al. 2002).
We will illustrate the binomial survival modeling approach (also see Heisey
and Fuller 1985) and define sias the probability that any bird alive at sampling
periodiis still alive at sample period i1. We would model the above capture
history, 0 1 1 1 2 0, as:
P(0 1 1 1 2 0 | release in 2)s 2 s 3 (1s 4 ).
Thus,s 2 denotes the probability associated with the bird surviving from week 2
until week 3, and s 3 denotes the probability that the bird survives from week 3 to
week 4. The (1s 4 ) term indicates the probability that the bird did not survive
the interval between weeks 4 and 5 (we found the bird dead in week 5). We would
have a similar probability for each observed encounter history. The product of
these probabilities over all birds in the study would constitute the model for the
entire data set and could be used to estimate the model parameters, the si. Nesting
studies described in Chapter 3 use similar encounter histories and similar survival
models to estimate daily nest survival probabilities and success.
In general, we could obtain estimates under various models of this sort using
a software package such as MARK (White and Burnham 1999). Program MARK
can also be used to fit competing binomial models (e.g. interval survival varies over
time and sample period or is instead constant; survival differs for two groups
of birds such as males and females or is instead the same for both sexes) and to
Survival rates| 121