Burnham life and dead encounter model questions

[matobler]

I am trying to estimate fledging success in California Least Terns using a Burnham life and dead encounter model. Terns were equipped with a radio transmitter right after hatching and monitored several times a week. All chicks were in large enclosures that prevented emigration from the survey area until they fledged. Dead recovery can be both from inside and outside the enclosures. The area surrounding the enclosures was regularly searched for transmitters from depredated individuals that were moved out of the enclosures by raptors. Fledging could generally not be observed.

While the general model structure and data format is clear I have some questions regarding missing data and varying survey effort. There were several enclosures and not all enclosures were surveyed at the same time. Furthermore survey intervals could vary. Bellow three example capture histories in the LD format where ".." indicates a day when the enclosure was not surveyed. Unfortunately it seems like the Burnham model does not allow for missing data coding. How would I enter this kind of data? I would like to test for age-dependent survival.

10..00..00....00..00..00....00..01
..10..00..10..00..00..01..00..00..
10..00....00..10..00..10..00..00..

To complicate things even more the survey effort (number of people searching and time searched for chicks) varied across days and I would expect p to be dependent on survey effort. How would I include survey effort in this model when effort can vary by day and enclosure (e.g. Day 1 Enclosure A: 40 person minutes, Day 1 Enclosure B: 30 person minutes)?

Given that the live encounter area can be assumed closed until the chicks fledge I would think that I can model F as age dependent where F=1 up to a certain age and then shapely declines and 1-F could be interpreted as the probability of fledging? Any suggestions on how to model this data are appreciated. I am running all the models through RMark.

Happy holidays,

Mathias

[G3isMe]

I hate to be the guy to tell you to RTFM, ... ... but I am have a similar challenges with my mussel work using the Burnam model. There is a very good write-up on differing sampling intervals in chapter 4. Page 25 of chapter 4 sidebar begins a discussion on how to model uneven time intervals. I think it will behoove you to read this section as I know it helped me in building my models. Best of luck with your models.

As far as missing animals. Look at my question in this forum and you can see how I coded animals that were not found either in a given year or throughout the study. I had the luxury of each animal being uniquely marked so I knew if a given animal was not found on a particular recapture event and hence I could code it as such.

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[matobler]

I saw the information in chapter 4, however, with the data I have the sampling intervals and survey effort vary by enclosure and I want to pool data across enclosure to test whether survival varies by enclosure (and to increase overall sample size). I probably have to get creative with fixed values for p and effort as a covariate for p as suggested by Jeff Laake. Is there a Bayesian formulation of the Burnham life and dead encounter model? That could make things easier.

[Jochen]

In MARK this should not be a big issue - create PIMs for p and r with one parameter for each enclosure*occasion, and then constrain with your effort statistic in the DM. There you can also constrain your survival parms in many ways.
Where effort is 0, you also don't need the ".." in the encounter history - reasons for avoiding dots were discussed elsewhere on this forum.
For specific questions how to do this in RMARK you might want to switch to the RMARK subforum.