Program POPAN-5 provides a parameterization of the Jolly-Seber model (Schwarz and Arnason 1996) that is particularly robust. The POPAN data type in MARK emulates this model. Schwarz and Arnason (1996) parameterized the Jolly-Seber model in terms of a super population (N), and the probability of entry (pent in MARK, beta in the paper). The POPAN data type implements this model in Program MARK.
Four PIMs are created for each group: phi (apparent survival), p (capture probability given the animal is alive and on the study area, i.e., available for capture), pent (probability of entry into the population for this occasion), and N (super-population size). For t occasions, there are t - 1 phi estimates, t p estimates, t - 1 pent estimates, and 1 N estimate. The t - 1 pent estimates correspond to the probability of entry for occasions 2, 3, ..., t. The probability of being in the population on the first occasion is equal to pent(0) = 1 - sum(pent(i)). The MLogit link function provides a constraint that makes the sum of the pent parameters <= 1, with the probability of occurring in the population on the first occasion as 1 - sum(pent(t)). An example of how to constrain parametes within a MLogit link is also provided. Convergence of this model is problematic unless the MLogit link function is used with the pent parameters.
The number of animals in the population on occasion 1 is N(1) = pent(0) times N. The number of new animals (births, B) entering the population prior to occasions i = 2, 3, ..., t is B(i) = pent(i - 1) times N. The population size on occasion i = 2, 3, ..., t is N(i) = (N(i - 1) - losses on capture) times phi(i - 1) + B(i). Estimates of the B(i) and N(i) are provided as derived parameters from models with the POPAN data type. In addition, the N(i) dereived parameters can also be used with model averaging and variance components analyses.
One limitation of the POPAN data type is with the use of individual covariates. Because the super-populations size (N) estimates the number of animals never captured, this parameter includes animals for which the individual covariate is not known. Thus, modeling N as a function of individual covariates is inappropriate. Further, the B(i) and N(i) parameters are functions of N, as well at the pent(i) and phi(i). Thus, if the pent(i) or phi(i) are modeled as functions of individual covariates, the derived parameters will also be functions of these individual covariates, creating a illogical estimate. The best strategy for use of individual covariates with the POPAN data type is to use the mean values of the individual covariates for providing the estimates of the real and derived parameters.
Link and Barker (2003) reparameterized the Schwarz and Arnason (1996) parameterization in the Link-Barker data type, with the pent parameter replaced by the recruitment (f) parameter. Burnham's Jolly-Seber model is also a competing model available in MARK. None of these 3 models have the same likelihood, so AIC values are not comparable among these models. Note, however, that the Link-Barker data type and the Pradel recruitment data types do have the same likelihood, so AIC values are comparable among the Link-Barker and Pradel data types.