Struggling to understand the theory behind the POPAN model.

Backstory: I am trying to get a population estimate of fish that could potentially move past a large barrier on a river. Am using the POPAN model since it is an open population. 18 sampling events over 36 day period.

The 'best' model is p(t), phi(.), pent(t). AICc Weight 0.99863 -- Number of parameters 24. The next model p(.), phi(.), pent(t). has a delta AICc of 13.4, Weight 0.00121 -- Number of parameters 15.

So my question comes down to the confounding of the parameters. Because I'm using time dependent probability capture, I have confounding variables in N1 and Nk right? In the MARK book: 'If confounding takes place, the estimated super-population number may be suspect....This confounding implies that careful parameter counting may have to be done when fitting POPAN models'.

Does the model take into account the confounding variables when outputting the final N? I started out with 37 variables (18 p, 1 phi, 17 pent, 1 N), but ended up with 24 in the model output. Do I have to manually go back and do 'careful parameter counting', or does POPAN do that for me?

I know I can't use the next model that doesn't have confounded variables because the delta AICc is greater than 10, and has no support.

All I need is a half decent population estimate, and I want to make sure that the theory behind getting it is legit.

Sidenote: From a previous 2005 comment by Cooch on N - 'Estimating population size in open populations is not trivial, and is (more often than not) not overly precise'.

I don't need it to be overly precise, but is there a better way to estimate N? If it is useless then I might as well not even send it out for peer-review.