Fixing fecundity to 0 in ZiUnIDPoissonMR models

[kaitlynvega]

Hello everyone,

This is my first post on the page, so I hope I'm not repeating a previous post and that I provide adequate information to get some help with my issue.

This summer, we have been doing transect surveys to estimate abundance of bighorn sheep in our study area. We had 5 primary occasions (survey rounds) and 37 "secondary occasions" (transects), and each round of surveys took between 7-10 days (multiple transects could be done in a day). We occasionally saw sheep on multiple transects within a survey round, we have some marked individuals that can't always be identified, individual sighting rates are not independent of each other across surveys, and we have individuals marked from 3 years of captures that may or may not actually be alive and available for resighting. For all of these reasons, I chose the ZiUnIDPoissonMRacross model for my analysis.

I set up my capture histories so each primary occasion has either a count the number of resights of each individual during the transects, a "-0" for individuals that were not sighted during a survey round (and, as such, I do not set any "Known Marks" in my counts list of the process.data step), or a ".." for individuals that were known to have died during the survey rounds. The models are running both without and with covariates (sex-age class or subherd, those these covariates aren't important for my current question) and are giving me about the results I expected.

The problem I am having is that the surveys were started in late June after the lambing season, so no individuals should be added to the population, I also fixed my Gamma parameters to 0 because we know that no animals have emigrated out of the study site or immigrated in, or at least not in a way that would affect the population extimate we are interested in. However, the derived population estimate increases during the first 3 survey rounds. I futilely tried to fix "f" to 0 in my model parameters since it appears that "f" is used as a fecundity parameter in other RMark models, but this of course doesn't work because the ZiUnIdPoissonMR models do not have an "f" parameter.

The short version of the question: is there any way to force RMark to not allow population increases when calculating a ZiUnIDPoissonMR model?

Thanks in advance for any help!

[bmcclintock]

As described in Chapter 19 of "The Book", abundance (N) in this model is derived as N = U + n* / p* for each primary occasion, where U is the estimated number of unmarked individuals, n* is the total number of marked individuals resighted at least once and known to be in the population, and p* is the overall probability of being sighted at least once. If you are indeed correct that the population cannot be increasing during the period of sampling, then the fact that you're estimating an increase could be indicative of problems with the data and/or model. For example, have you tested for time dependence in the detection rate parameters (e.g. alpha) or are you assuming they are constant? If the model and data seem OK (which, under the assumption of a constant population size, should not result in "big" differences in estimated N between primary occasions) then it seems you could just constrain the "U" parameter to be constant (i.e. `model.parameters=list(U=list(formula=~1,link="log"))`), but this of course is not guaranteed to keep N constant (there could still be fluctuations depending on n* and p*).