I have encountered some challenges in modelling demographic parameters using an MSORD-SU model with a population that is tagged on irregular secondary intervals, and re-detected continuously. I am wondering if someone could make a recommendation for modelling this type of detection heterogeneity. I am aware that models exist to separate first detection probabilities from all subsequent detection (e.g. Huggins-type); however, the population I am dealing with is open and these models assume closed populations. I also am interested in the structure of a population comprised of 3 states which are unidentifiable at the initial tagging event--hence using the MSORD-SU model.

So the probability of the first tagging is dependent upon an effort covariate related to time spent tagging within each secondary period (most periods have an effort of 0), while re-detection probabilities are quite high because the data is remotely sensed.

I have considered to using the probability of arrival (pent/Beta) parameter to try and separate these two processes (i.e. model p as constant and model pent as a function of tagging effort, where most occasions are fixed pent = 0). My concern with this approach is that I am fitting a biological parameter to study-design data with no biological interpretation and will therefore invalidate any of the derived parameters that this model estimates, including population size and residence-time.

Is this a valid concern and are there better ways of accounting for the effect of initial tagging on detection probability in this type of model?