The POPAN parameterization models survival and capture probabilities in a similar way to JS, but comes at recruitment and abundance estimation from a different direction. POPAN starts with the idea of a 'superpopulation' parameter Nsuper, which can be thought of as a reservoir of animals that may enter the population during the course of the study. Recruitment is then defined in terms of entry probabities penti , so that
Bi = Nsuper*penti .
Abundance is then gotten by application of the JS formula in the other direction
Ni+1 = Bi + Phii (Ni -ni+Ri)
N1 = B0
Because of various constraints (e.g., the entry probabilities have to sum to 1) not all the N's or B's are estimable; in fact, the same ones are estimable as under JS (no surprise- this is basically the same model).
I provide an example from female capsids recaptured by Muir (1957). The R script reads the data from a MARK input file and converts it to RMark format, then runs several models with varying assumptions about time dependency in Phi, pent, and p. Note that in the data there are several negative frequencies. These refer to animals that were captured and not released on the last occasion, which is needed for JS (but not CJS).
This is a simple example with no grouping variables or covariates; if these were present they obviously could be modeled as well. The script produces model averaged real parameter estimates, as well as derived abundance estimates under the time specific model.