S or Phi with CJS robust design

[sixtystrat]

The documentation for the robust design models says that survival and permanent emigration cannot be separately estimated, yet the parameter listed in the output is S and not Phi. Which is it?

Also, portions of our sampling area flood during some years. I can use water gage data as a covariate on p and c, but would my estimates of N (and phi) be biased because not all of the population is sampled in some years? I am assuming that the robust design CJS models would be better for this purpose than robust design Pradel models but comments are welcome. Thanks!
Joe

[ehileman]

Hi Joe,

CJS does not allow for temporary immigration or emigration, which is why the model estimates apparent survival (Phi). Robust design models explicitly estimate temporary migration, and therefore estimate survival (S). However, permanent emigration is still indistinguishable from mortality.

In my experience, survival estimates are generally robust to modest violations, especially if you have good covariates to address them. I would think that flooding events may induce temporary immigration and emigration if you are not surveying these areas during flood years, but this won’t likely be an issue for survival estimates, assuming that you consider models that include temporary migration and that flooding doesn't cause permanent emigration. The closed model during secondary occasions, however, has strict assumptions regarding demographic and geographic closure, and non-random temporary immigration/emigration can cause bias in derived estimates of abundance (See Kendall 1999). It depends on the extent of the flooding and where the animals go during (and after) these flooding events, but good covariates that explain spatial and temporal variation in capture and recapture may help. Regardless, I suspect you will have larger error for estimates of N in flood years. Hope this helps!

Cheers,

Eric

[sixtystrat]

Thanks Eric. I was thinking that survival and PERMANENT emigration combined was phi, not S. Just curious about the MARK notation. I get it that temporary emigration can be estimated but, according to Fig. 15.1 in the mark book, the temporary emigration parameters have more to do with availability for capture (p) than S. Apologies for the all caps.

[ehileman]

I think I missed that part of your query was more about the naming convention. I know that Thompson et al. 2009 attempted to provide guidelines on this topic to reduce confusion and ambiguity. Not sure the reason for the convention in the MARK book. Unless true survival is known (e.g., known fate) or the model explicitly include a fidelity parameter (e.g., L/D recovery), you are estimating S x fidelity as you indicated.
Cheers,
Eric

[sixtystrat]

Got it. Thanks again Eric.

[Bill Kendall]

I don't have much to add to what Eric has provided. I just have a few additional comments/questions.

You are right to understand the temporary emigration parameters in the RD model to be about availability for capture. If the availability process is completely random (i.e., just driven by an environmental process like flooding), then in the CJS model effective capture probability is the product of availability and capture probability given presence. In that case you could model p as a function of flooding and probably deal with it that way. If that availability for capture is Markovian, then both p and phi are affected, and that's where the robust design mitigates a lot of the problem.

If you have robust design data, as Eric confirmed it helps with temporary emigration but not permanent. As he also pointed out, you have to pay attention to the closure assumption. If flooding is occurring in such a way that individuals move out of the study area but some come back when it recedes, you could model the p's within the primary period as a function of flooding.

My last thought on this is that if flooding is the only source of emigration, and you know which parts of your study area are affected by this, you could simply put dots in the history for those individuals affected, or if the flood doesn't chase all of them out, use a flooding as a time-varying individual covariate.

Finally, if there is temporary emigration that needs to be dealt with at the primary period level, don't use the robust design Pradel model. That model does not permit emigration, but is simply intended to use the secondary sampling periods to add precision to the estimators and be able to estimate all parameters.

[sixtystrat]

Thanks Bill! Can you elaborate a little about your last paragraph? I am assuming the temporary emigration occurs between primary periods and the secondary periods are closed. I know that Pradel models are sensitive to changes in the size of the study area, and I have tried to stick with the CJS robust design models. I am using the one with random effects though (CJS-Robust Design with Huggins p and c with random effects). I was thinking about using the number of hair traps in the study area each year as a covariate for the flooding. That number is probably more relevant than stream gage data, but would that be improper? Thanks again.
Joe