The basic Jolly-Seber (JS) model is a straightforward extension of CJS that allows estimation of recruitment and abundance (in addition to survival) by explicitly modeling the unknown parameters Ni and Bi (abundance and recruitment). The steps in JS can be thought of informally as:
Estimate Ni at each occasion by captures of previously marked and unmarked animals, in a manner very similar to Lincoln-Petersen
Estimate Phii (survival between i and i +1) from recaptures of marked animals by CJS models
Estimate Bi by difference between next period's N and survivors from this period:
Bi = Ni+1 - Phii (Ni -ni+Ri)
where -(ni -Ri) is included to account for the difference between number of animals caught and those released (so trap loss or sacrifice). For a k - sample CMR study the following parameters will be estimable:
Abundance (N): occasion 2 to k-1
Survival (Phi): occasion 1 to k-2
Recruitment (B): occasion 2 to k-2
Recapture (p) : occasion 2 to k-2
The standard implementation of this model in MARK and RMark is the "Burnham parameterization", which re-parameterizes the basic Jolly-Seber relationship as
Ni+1 = NiLambdai
with recruitment no longer an explicit parameter (but apparent survival remaining). Recruitment rate fi can then be obtained (theoretically) as derived parameter by the relationship
Lambdai = fi + Phii.
I say "theoretically" because this parameterization is notoriously difficult to run and usually fails for lack of numerical convergence (see comments on page 12-31 of MARK book). The JS model is incorporated into MARK and RMark with this parameterization but because of the above issues we will move on to the alternative super-population (POPAN) parameterization of JS.