Losses on capture in Pradel models

[Joel Schmutz]

I am interested in using Pradel models to look at survival and recruitment simultaneously. In this data set, all observed unmarked animals are uniquely identifiable (e.g., on spatially distinct nests), but they are not physically captured and marked. Thus, in a reverse-time perspective, they are captured, but then released without marks, and thus are losses on capture. Hines and Nichols (2002) identified this as a significant source of bias that must be dealt with, but program MARK does not explicitly address this sampling issue. I am wondering if there is nonetheless a way to deal with this within MARK. For instance, consider the following line in a 6 occasion, 1 group encounter history:
001000 -124;
This represents that 124 animals marked on occasion 3 were than removed from the sampled population (i.e., losses on capture). In this example, if 124 is the number of unmarked animals on nests (whereas there may also be a 001000 45; line to represent 45 animals with marks seen or captured on nests that occasion but not subsequently seen, despite not being 'removed' from the sample population), then this would seem to provide the information needed to appropriately deal with losses on capture of the type described by Hines and Nichols (2002) in the reverse time sense. However, I am unsure if the adjustements to lamda (e.g., their equation 6) really relate to how MARK deals with above type of coding of losses on capture, which typically has been applied to just forward time analyses. Any thoughts on how to appropriately model - with accessible software - phi, gamma, and lambda with losses on capture?

[gwhite]

Joel:
When I first coded the Pradel models into MARK, I left out the losses on capture part of the likelihood that Roger had in his paper. Hence, the approach you describe will not work.
However, when I put the Link-Barker model into MARK, it does handle losses on capture correctly. So, specify a Pradel model when you start the analysis, but then immediately switch to a Link-Barker model, and you should get correct results.
The difference is that f in the Link-Barker model is estimated outside of the encounter history, whereas the f in the Pradel model is estimated within the encounter history. You get exactly the same estimate, but the likelihoods look very different (although they are the same).

Gary

[Joel Schmutz]

Thanks, gary. So, in terms of telling MARK about the losses on capture for the Link-Barker parameterization, would I use the kind of syntax that I mentioned? That is, for all those unique unmarked animals seen on nests but not marked, code them as, say 001000 -124; if I had seen 124 unmarked individuals in that third year?