Effect of Markovian migration on N in closed RD

[Eurycea]

I'm fitting a series of closed robust-design models (11 primary sessions(i), 3 secondary per) and I am trying to understand why, when I specify Markovian temporary migration, I will get different estimates of N for some i (but not all). This is in comparison to straight closed population models or close RD models with random migration. I've read a good portion of the relevant chapters in the MARK manual, and also numerous papers etc., but I feel like I am missing something obvious or doing something wrong- because I am not expecting N to change according whether I have specified Markovian migration or not. Does this have something to do with the maximum likelihood estimate of p* when I am also estimating gamma, vs. estimating p* with both gamma' and gamma''? Any explanation, or direction to the appropriate literature would be most appreciated.

Nate

[Eurycea]

Ok no responses yet... Let me try this....

Is this true or false: In RD, the temporary emigration and survival parameters are not linked to the mathematics of population size estimation.

True or false: In RD, within primary session parameters (p*, N) are estimated independently of the open population parameters.

True or false: Estimates of N will be the same for a closed population analysis as they will for a RD analysis, (assuming N is all you are interested in).

Please help.

[Bill Kendall]

Just a quick answer. I'm not sure how different your answers for N are, and whether you are using the conditional (Huggins) models or the full model. First, N-hat is linked intimately to p* (the effective capture probability) for that primary period. Because there is information on p* coming from between primary period data (think of the straight multistate or Jolly-Seber models), modeling of temporary emigration and survival should have some influence on N. Under conditions I've evaluated in the past, the closed model part dominated. I would think there would be less influence of the between periods information when there is temporary emigration (especially non-Markovian), but it can get complicated. I would also guess that if you are using the full model (with N estimated as a parameter), rather than the Huggins version, and you have sparse data, your results would get a little stranger. For small data sets I prefer the conditional (Huggins) model as more stable.

[Eurycea]

Thank you for the reply, it helps very much. I was using the full model, however I have tried Huggins as well. I do not think the dataset is small, but it is not huge either (I'm new to this- we get recaptures rates around 30% with new marks around 100+ per primary session). The closed model part does appear to dominate (based on comparison of closed model vs. RD closed model), and it is only several primary sessions in particular where the emigration type appears to have a appreciable effect on N. For instance, the 1st period (3 secondary sessions) of the dataset does not change much at all (as might be expected) regardless of Markov, random, or just plain closed model (no RD). However in periods where N is differs according to the emigration type, it is not by a huge magnitude (usually on the order of 10-20% max). I just needed to confirm, that indeed, the open design model DOES in fact have an impact on your estimates of N.

One more question- say, hypothetically, that I was only interested in estimating the population size, N. Would RD be the best way to achieve these estimates, or should I stick to a simple closed model (thus eliminating the influence of phi and gamma on my estimates of p*)? My intuition is that Occam's razor might be the way to go here?

[Bill Kendall]

You do have the option to treat the years as groups in a closed model analysis. If you do, just don't fall into the temptation to model the N's (if you use the full model). Remember that N is not really a parameter here. Instead, it is the number of individuals that have not been captured, f(0).

[Eurycea]

It'd be months (not years) in my case. I have not tried this grouping option (actually have not used the closed model analysis very much), but I will investigate it, thanks. At this point I'm trying to determine whether it still makes sense to do a full robust design analysis at all, if all I'm (hypothetically) interested in is estimating the population size.

Long story, but it's a project (and data) I inherited, and since then, the goals of the project have also changed. They set up as a robust design to estimate survival, and temp. emigration, but at this point, I am mostly interested in calibrating a double-sampling effort, whereby I use the MR results to build an observation model, and then use those results to help interpret direct count data. Thus, the most critical piece of information is N, for each primary session.