Phi(g) or Phi(.)? - Joint analysis of independent datasets

[butterphi]

I studied a rare butterfly in different years and at different unconnected sites. Individuals die after one season and are not available for being captured in the next year, i.e. I have multiple independent datasets.

I analyzed the datasets individually with CJS- and POPAN-models in MARK. Model selection was sometimes in favor of sex-dependent apparent survival, Phi(g), whereas equal survival between sexes, Phi(.), was suggested for other datasets. Probably it is not the biological truth that Phi is sex-dependent in some situations but not in others. It may be a matter of information which is in the individual datasets (remember, I studied a rare species and the number of recaptures was low in some datasets).


I wondered if it is possible to combine the different datasets into one single analysis. Is there a convenient way to do this?
So far, I tried to expand my input-file, i.e., I took all individuals across years and sites and added dots (missing occasions) to the capture histories when individuals were in fact not available for being captured. However, I am not sure how MARK deals with all the dots and the strongly unequal time intervals (1-4 days within seasons, 330 days between seasons).

[jlaake]

I'm assuming your main interest here is survival and my comments are for CJS. Not sure about POPAN.

If you have used the same model set for each analysis you CAN just add the AIC values across the independent data sets for each model and then compare models but this isn't terribly efficient because it assumes all of the parameters differ across data sets.

Stitching data together like you are proposing is certainly possible but you said you don't have butterflies living across years (seasons?). If I understand correctly, there is no need to have a correct time interval for the gap or add dots. Let's say you had 2 years with 4 occasions on the first year and 5 occasions for the second year. If you had a butterfly with capture history 0101 in year 1 and another butterfly with history 10010 in year 2, you could construct the stitched histories histories

010100000
000010010

CJS starts at the first 1 (release), so the leading 0's are irrelevant. However, trailing 0s like in the first history are modelled. The easiest thing to do is to set phi=0 for the interval between occasion 4 and 5 - which is what you described that nothing survives between years. You would have to do that for each year you stitched together. The time interval between years (occasions 4 and 5) here can be any value as it will not be used since you are fixing phi=0 for those intervals. The survivals you will be interested in will be those between occasions within year. You can then model them as constant, year (data set) varying, sex varying etc and it will use all of your data in one analysis.

[murray.efford]

If Jeff's suggestion doesn't appeal or work, you could try the R package openCR that now has a 'stratum' structure for combined analysis of independent data. Then you may model phi~1, phi~stratum, phi~stratumcov1 etc. (where stratumcov1 is an arbitrary year covariate). Works (but is relatively untested) across CJS, POPAN (JSSA, PLB) and spatial models. Of course you would have to grapple with a different data format and miss out on the bells and whistles of MARK & RMark.

[butterphi]

Many thanks to both of you for your helpful suggestions!
Jeff, what you described is very appealing and is exactly what I was asking for. Still, I have one follow-up question on how to combine data from multiple sites when sites are unconnected and trapping days (and intensities) differ between sites.

Let's assume the following situation:
I conducted a 13-day survey at 2 different sites. The survey has started on the same day for both sites. Butterflies were captured every other day at site 1 but every third day at site 2. How would you suggest stitching the data together. Could it work as follows?

butterfly 1 (site 1, 7 occasions, CH: 0100100): 01.001.00
butterfly 2 (site 2, 5 occasions, CH: 11010): 1.1.0.1.0

[jlaake]

Yes that will work.

[butterphi]

Thanks a lot!