Recall that with CJS live data, the estimate Phi confounds true survival and "fidelity", the probability that an individual will not permanently emigrate and thus remain at some point available for recapture: Phi = FS. By contrast, tag recovery models, since reencounters arrive from potentially the entire distribution of the animal, estimate S directly. Joint analysis of live and dead recoveries is implemented in an MLE framework in MARK and RMark, with the Burnham joint live-dead model being typically implemented to allow joint estimation of true survival (S), fidelty (F) . reporting, (r) and live recapture (p).
Kéry and Schaub (2012) have recast the joint live-dead problem as a multi-state model, in which the states are "alive, inside population", "alive, outside", "recently dead" and "dead" (I guess that's "very dead"). See pg. 295-296 and the state and observation matrices. Transitions from one of these states to the others (including the same state) are then expressed in terms of S and F. For instance, going from "alive in" to each of the 4 states has probabilities
SF S(1-F) 1-S 0
for alive, outside
0 S 1-S 0
for recently dead and dead
0 0 0 1
0 0 0 1
Encounter (recapture or recovery) outcomes fall into 3 states:
Seen alive (1) recovered dead(2) not seen or recovered (3)
and the probability of each depends on the state the animal is in; for each of the 4 states these are
alive,in p 0 1-p
alive,out 0 0 1
rec dead 0 r 1-r
dead 0 0 1
Kéry and Schaub have written code that 1) simulates the joint live-dead data as a multi state outcome, with the capture histories being coded by 1 -3 for each state (0 is reserved for indicating that the animal has not been released as marked and so is not yet in the sample. For example,
0 0 0 0 0 0 1 1 3 1
indicates the animal was released at occasion 7, recaptured live at 8, not seen at 9, and recaptured at 10
0 0 0 1 2 3 3 3 3 3
indicates the animal was released at occasion 4, recovered dead at 5, and (obviously) not seen again.
whereas
0 0 0 1 1 3 3 3 3 3
indicates the animal was released at occasion 4, recaptured alive at, and not seen again (but could be alive and in or out of the population).
Code here simulates these data for specified number of occasions and parameter (S, F, r, p) values and runs them through a Bayesian model formulation written in JAGS.
One important take home here (which should be clear from the transition matrices) is the fundamental difference between temporary emigration (modeled by gamma in the Robust Design) and permanent emigration (modeled by 1-F). Animals that go to the state of "outside" in temporary emigration may come back; animals that permanently emigrate by definition never come back (probability of going to "in" from "out" =0).