I'm having some trouble conceptually understanding what exactly constitutes a violation of closure vs. something that can be modeled as a behavioral response, in the context of my study.

We set up a robust-design style experiment where we capture aquatic salamanders in a small, relatively confined area, where all the habitat on the surface can be exhaustively search within a few hours. We do the secondary sampling for three days in a row. There is some opportunity for the animals to move in and out of the study area during the survey (the site is a concrete enclosure, with some entrance and exit points), but we initially assumed this occurs randomly and at a relatively low rate due to the short time interval between surveys. Births and deaths were also assumed to be negligible for this period of time.

However, we found that on the 2nd and 3rd days there were many animals absent compared to the first day. Because of our ability to exhaustively search all of the available cover in this small area, we assume these absences are due to animals taking refuge just underneath, or alongside the sample area in these crevices that cannot be searched. So this looks to me like a behavioral response to capture, that can be modeled using a closed population type model, such as p(.) c(t), which seems reasonable (edited to add, this appears to have the lowest AIC score among several competing models). However it also looks like a violation of the closure assumption, if animals can move just outside the sample area. The bulk of the population in the immediate vicinity is assumed to be at the surface (i.e., in our sample area).

I should also note that we have done two primary sampling sessions so far. I ran closure tests on both sessions, individually. The first one we did not have any strong indication (statistical or otherwise) of closure violation, other than being a bit surprised we were not recapturing as many animals as we had expected. For the second primary sampling it was very clear from the closure tests and the data that animals were exiting (as described above) in large enough numbers to cause concern.

Is it reasonable to treat this as a behavioral response in a closed-population, or must I conclude that this is a violation of the closure assumption, and therefore, cannot under any circumstances, use closed-population models to analyze this data?

One alternative to this sampling design I was thinking about were to space out the secondary sampling (a few days, perhaps) to allow the "tray-shy" effect to wane, and either model the secondary samples as an open-population (with apparent survival representing the emigration rate)...

Or, alternatively, continue with the closed-population assumption even though it can never be perfectly closed. I think births and deaths would still be negligible over the short timer period and even if any movement between the observable and unobservable states occurred, I would assume it to be random, thus potentially negating concerns about bias in the survival estimate. I would then be interpreting N as a super population estimate (both of which I am interested in). Ultimately I'm interested in N (super), survival, as well as temporary emigration parameters, in that order of importance.

I would very much appreciate any insight into this. Am I thinking about this correctly? Are there other sampling designs we should consider? Are there different statistical approaches I should consider? Thanks in advance.

Nathan