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Hi,

I've posted here previously (viewtopic.php?f=21&t=3857) about how to deal with transience in POPAN models, and the feedback I received was extremely helpful, but after discussion with my PI, I am starting a new analysis (and subsequently I have a new problem). In short, I have a 16-year CMR dataset of birds marked as chicks and adults. As part of a larger analysis involving estimating the population's growth rate and predicting population trends, I'm trying to estimate the initial population size for the study using a POPAN model. My capture history file only includes birds captured as adults and chicks recaptured as adults (i.e., the 2nd time they were captured, not when they were banded as adults), so only breeding birds are included. GOF tests reveal I have a trap dependence issue, which I've dealt with before via creating a trap dependence (td) function (see RMark Appendix C page C-77) for CJS models.

However, I'm unable to get models with p(td) to run, and after some digging I think I figured out why. Trap dependence is a time-varying individual covariate, and based on the responses from Jeff Laake to these posts (viewtopic.php?f=21&t=3806&p=12553&hilit=POPAN#p12553) (viewtopic.php?f=21&t=3631&p=11877&hilit=popan+individual+covariates#p11877), you shouldn't use individual covariates with POPAN models because we can't know the covariate values for individuals never seen again.

Which leads me to my issue: I'm unable to find any information on how to incorporate trap dependence in a POPAN model. A recent post (viewtopic.php?f=1&t=3864&p=12766&hilit=popan+trap&sid=9f78bf5ae90ddb21a9fa195894c35529#p12766) asks a similar question but as of yet the issue hasn't been addressed. In one of the previously linked posts, Jeff stated "To do it (individual covariates) correctly you would need to develop a likelihood that includes a distribution for the covariate in the population because if as shown p depends on the covariate," but I'll be honest, I have no idea on how to go about doing that. I'm assuming that properly specifying my p() models is important for estimating abundance, so I can't ignore this issue. Any suggestions or feedback would be appreciated.

Thank you.

This post isn't really specific to RMark and is a general analysis question about the popan model. I don't think there is a good solution to the problem because the capture information from marked animals is used for unmarked newly captured animals. My comment about a covariate distribution isn't something you can implement in MARK and would require coding a particular model.

Hi Jeff,

Given that there isn't a good solution to this issue, do you have any recommendations moving forward? The only other options I can think of are either 1) ignore the trap-dependence issue and run the POPAN model to get my estimates of N, or 2) use the number of birds captured in the first study year as my initial population size. I don't think either solution is great, but I don't see another way to get those population size estimates.

Not sure what to suggest. Are your critters trap shy or trap happy. If the latter then your estimate may be too low and if the former it may be too high. Maybe others can make suggestions. With polar bears I used the CJS model with a trap dependence term that was from one occasion to the next. If caught in year 1, would be more likely to be caught in year 2 and if not caught in year no dependence. td is a 0/1 variable. In this case, not a response of the bear but maybe a function of the bears location and memory of researcher. In that case with td=0, you can use p to estimate N for newly caught bears (and those previously caught but not in prior year) and for td=1 a separate p for those caught the previous year. You can construct an estimate of N from the number caught divided by p. I think much of that code is in RMark utilities functions. Look in help index. Has been a long time since I did that work. Not sure if this could be implemented with POPAN. My guess is that you can't. Hope that helps.

--jeff

My birds are trap-happy, so raw count data would probably be too low. Thanks for providing the example with your polar bear research. I've used the td variable before when estimating annual adult apparent survival, so I'm familiar with the coding. I'll play around with my data and look through the help index. Even if I can't implement this with a POPAN model, having an estimate of N via a CJS model (rather than from raw count data) might be okay. Once I figure this out, I'll post an update here for anyone else having this issue.

Hi everyone, I am currently in a similar situation as sharrod. I used POPAN models to estimate population parameters of dolphins in two different islands, each with two different groups clustered by site fidelity. In one of the island, I found that there was a significant trap-hapinness effect for both groups, which I tried to take into account in the estimations with the script of RMark found in the RMark Appendix C. Unfortunately, that script did not work so good with my POPAN model. I know realize that it might not only comes from my lack of experience, particularly in Rmark, as I am not the only one facing that issue.
Also, sharron, I wanted to know if you found a way to implement trap-dependancy in POPAN or if you used a CJS model for estimate your parameters. Thanks.

As far as I know there isn't a really good way to handle trap dependence other that what I have said above. However for better or worse, here is another approach I used. If I was you I would do some simulation to see how it performs in your situation. I performed that whale analysis as a favor and didn't have time to explore its performance under different scenarios. It may be completely different than your situation because the whales were migratory. A robust design would have been a better option but it was not designed that way.

https://www.researchgate.net/publication/228110127_Abundance_and_survival_estimates_of_the_Southeastern_Pacific_humpback_whale_stock_from_1991-2006_photo-identification_surveys_in_Ecuador