This type of data structure can arise from any situation where encounters occur that are mixed between ordinary live recapture or re-sighting, and dead recovery. It is not extremely common to find data sets that work well with joint analysis-- often, there are too few of one type of encounter to make the complexity of these models worth it. However, situations do arise where there are significant number of both live encounters (typically, recaptures) and dead recoveries (e.g., from hunters or anglers).
The LDLD structure is appropriate for organizing these data, where again the first column of the pair indicates release or live recapture (1=release or recapture), and the second indicates recovery (1=recovery). For obvious reasons an encounter history such as 1011 can be possible (released first period, recaptured live second, then recovered) but not 1110 or 1101 (the animal already was encountered dead in the first period, so it cannot be subsequently re-encountered, either as alive or dead.
An advantage of the joint live-dead models can be the estimation of parameter not available under either live only (CJS) or dead recovery (e.g, Seber/ Brownie). Under CJS live recapture models, the parameter Phi provides an estimate of apparent survival, which is really the product of demographic survival and the absence of permanent emigration ("fidelity")
Phi = S x F.
However, S and F are not separately estimable with CJS data. By contrast, if animals can potentially be recovered and reported anywhere (the usual assumption with hunted birds or angled fish), tag recovery data can be used to estimate S (under Seber or Brownie parameterizations). If we have both types of data, we can estimate both S and Phi -- and therefore derive F.
Both MARK and RMark implement variants of the joint live-dead data and model structure (See MARK book chapter 9). Two are noteworthy:
Burnham model (essentially described above).
Barker model (extends the analysis to situation involving live recaptures, live re-sightings, and dead recoveries).
Here I provide code that simulates joint live-dead data structure (Burnham, so recaptures and recoveries) and runs 3 analyses:
Joint live-dead (providing estimates of survival S, fidelity F, recapture p and reporting r)
Live (CJS) only (estimates of Phi and p)
Dead recovery only (estimates of S and r)
The code performs these analyses in RMark, but also produces *.inp files that can be read into MARK.
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