by jlaake » Thu Oct 02, 2008 12:25 pm
I can understand your confusion. It always confuses me as well. The model names in RMark correspond to those that MARK uses and they are as follows:
Pradel, Pradsen, Pradlambda and Pradrec
Their descriptions in the MARK help file are listed below in the order of the model names above. As you can see the Pradel model is called the Pradel recruitment only model but has the seniority and gamma parameters. So both sources are correct -- just confusing. In that regard if you find discrepancies between the help files and the appendix, let me know. It is hard to keep up with all the files. The most current info is typically the Appendix and the What's new in RMark file. Some of the material in the latter has not made it's way to the help files yet.
On another point, RMark is simply an interface to MARK. They both use the same mark.exe for estimation. RMark is simply a tool for building models. All of the model fitting is done by Gary's MARK program. If there is a discrepancy then it is a difference in how the models were constructed. You can compare the input and output files created via the MARK and RMark interfaces to see where those differences occur. Differences can occur from the link function and the DM construction because there are many different ways to specify the same model with different DMs. If the data are sufficient, the result should be the same but sometimes you can get lack of convergence or small numerical differences. The biggest differences can occur based on the choice of the link function.
regards --jeff
Pradel Recruitment Only Model. Pradel (1996) developed a model to estimate the proportion of the population that was previously in the population. Thus, this model, labeled 'Pradel Recruitment Only', estimates recruitment to the population. The parameters of this model are the seniority probability, gamma (probability that an animal present at time i was already present at time i - 1), and recapture probability r. Only LLLL encounter histories are required for this model. This model can be estimated by reversing the time sequence of the live encounter histories (Pradel 1996), an idea suggested by Pollock et al. (1974:85-85), and even mentioned by R. A. Fisher in about 1939 or so (Box ????).
Pradel Survival and Seniority Model. Pradel (1996) extended his recruitment only model to include apparent survival (phi). In MARK, this model is labeled 'Pradel Survival and Seniority'. Parameters of the model are apparent survival (phi), recapture probability (p), and seniority probability (gamma), which is the probability that an animal in the population at time i was also in the population at time i - 1 (i.e., the animal did not enter the population during the interval i - 1 to i. Only LLLL encounter histories are required for this model.
Pradel Survival and Lambda Model. Pradel (1996) also parameterized his model with both recruitment and apparent survival to have the parameters apparent survival (phi), recapture probability (p), and rate of population change [lambda(i) = N(i + 1)/N(i)]). This model converges quite readily compared to the Burnham parameterization of the Jolly-Seber model described above. Only LLLL encounter histories are required for this model.
Pradel Survival and Recruitment Model. Pradel (1996) also parameterized his model with both recruitment and apparent survival to have the parameters apparent survival (phi), recapture probability (p), and fecundity rate [f(i) = number of adults at time i + 1 per adult at time i]. This model converges quite readily. Only LLLL encounter histories are required for this model.