Output from Robust model - what is N?

[JonL]

Actually, I assume that the N-values given in the "estimates of real parameters" (N) and "estimates of derived parameters (N-hat) outputs are the same and both represent estimates of the number of animals available for capture within any one primary capture session. I infer this from http://welcome.warnercnr.colostate.edu/ ... robust.pdf and from the fact that the estimates in my case are similar to those from the POPAN model for each separate year.

However, this leaves the question, which is the size of the superpopulation? That is, the sum of animals available for capture and those that temporarily have emmigrated from the trappable population (and are alive) in year t.. This should be a derived parameter. Can I find iit somewhere in the output from the MARK run?

If not, I assume I can compute it myself as Nuper(t) = N(t)/gamma. In this case I assume random migration, gamma' = gamma''. However, I guess this approach assumes recruits (born, animals entering mature age and/or immigrating from outside world) are seen as part of the superpopulation even if they never have been available for capture. In one context this means that with gamma = 50% animals may be defined as mature at 2 years of age but still only 50% of the 2y and 75% (actually a little less?) of the 3y have ever bred. Any more complex formula I can think of depends on knowing the superpopulation in year t-1 so II get stuck. This should (?) actually be an estimated parameter.

This is indeed difficult enough to handle conceptually/biologically but what about the robust model?

Comments and help, please!

[TGrant7]

The estimated N in closed cap and RD is the superpop. It's the number of animals ever available for capture (well, for RD, in each primary occasion). Think for a second about the animals that can be captured. Anything that can be captured is the superpop. If it is never subject to capture, how can it be part of the superpop? And how can those that only temporarily emigrate be distinguished from those that don't? They can't, or aren't, in the model, so after some thought I think you'll see that the estimate has to be the superpop. (For RD, it's the superpop for each primary occasion). But some of the superpop may undergo temporary emigration, part of the motivation behind RD. There is a paper or two by Kendall and others in 95 or 97 that talk about temporary emigration and it's violation of assumptions. Maybe you have read it because you are talking about whether the emigration is random or Markovian.

The above may help, but on second look at your post, I see you are thinking about the "superpop" for the whole study. This is not the sense that superpopulation is used. You are talking about the changes in population over time.

I don't think the superpop you are thinking about is estimable from the model. And more importantly why would you want to know? What does it mean? I think I see what you are thinking, but you can't go there. All inference is in regards to the population that can be captured during any primary occasion.

You talk about estimating those that have temporarily emigrated, but you don't know they have temporarily emigrated until they come back...

Then when you say you want to calculate the superpop for whatever time period, (Nuper(t)), but the superpop for each time period is N(t)...

So I think your question is, how many animals are out there that were subject to sampling before, but aren't this time? We could call this the the "did-population". You also seem to be touching on how many are out there that will be available for sampling in a future occasion, whether they were available for sampling before or not. We could call this the "will-population". This is kind of the converse of the other question. There would be some overlap between these groups, of course.

I suppose you could estimate by Ndid(t) by N(t-1)*gamma(whichever one is emigration, I forget)*S. But what does it mean? You have no area to apply it to. I don't think it means much. I don't think you can estimate Nwill(t) unless you assume immigration is constant, because you have to know what immigration rate is to estimate how many there are that will be available in the future. Then you'd want some parameter for how they relate, but I'm reaching the end of my rope on this.

I hope this helps. I'm kind of thinking out loud, so I hope I don't embarrass myself. But I think you're barking up the wrong tree, so to speak. You want to know more than it can tell you and/or what you are intuitively reaching for is not what you think it is.