Robust Design or Closed Higgins?

[kate12]

In short, I want to make sure I'm doing my analysis correctly- I am interested mainly in estimating abundance, capture and recapture probabilities (via CAPTURE). I had 3 sites and 3 field seasons (medium carnivores- low sample sizes and recapture rates). However, site one was the only site I trapped at over all three years (3 trap sessions). Site two I trapped over two years ( but had 4 sessions), and site three over one continuous field season (1 session). My question for you is, is it correct to use Pollock's Robust Design to estimate abundance, pi, and ci for site 1 and 2? Obviously site 3 would need to be closed. Or would I be better of considering each of these closed since there are so few sessions? Any advise would be great. Thanks.

[abreton]

If you haven't done so already, you'll want to read-over Chapters 15 (closed models) and 16 (robust design) in the MARK manual (http://www.phidot.org/software/mark/docs/book/). Given what you summarized in your post, it is clear that a straightforward application of your data to either a closed model or the robust design is not going to be available. For example, in order to estimate the minimum set of parameters provided by the Robust Design (see Fig 16.3, Page 16.5, MARK Manual), data must be available from three primary (your seasons) sessions or occasions; and nested within these primary occasions, must be at least two secondary occasions (your trapping sessions). I suspect that you trapped >=2 times each season at each site, but note that only one of your sites provides data from three primary occasions. Certainly, inclusion of the site with only one primary occasion is not possible under the Robust Design; and, at minimum, additional assumptions will be required to accomodate the site with only two primary occasions.

Assuming you were able to include two of your sites in a robust design analysis, you're likely to run into convergence problems due to sparse data ("medium carnivores- low sample sizes and recapture rates"). As you may know, when a model 'fails to converge' the numerical search procedure applied by program MARK (or CAPTURE, SURGE, etc...) fails to locate estimates for some (or all) of the parameters specified by the model - complete convergence failure generally causes program MARK to crash. Given sprase data (the norm, unfortunately), the best you can do is start with the simplest model possible and consider fixing parameters if appropriate. Subsequently, use the estimates from the simple model as starting values for a slightly more complex model - repeat this process until you experience partial or complete convergence failure (e.g., watch for large SEs associated with betas).

Regarding closed models (note that the Robust Design combines open [primary sessions] and closed [secondary sessions] data types), if you can assume roughly no inputs (births, immigration) or outputs (deaths, emigration) into/from the sampled population and you have at least three sessions per trapping period (season) then your data are likely appropriate for 'closed models' (12 options in program MARK). And following a review of Chapter 7 (MARK manual), you should be able to specify a model parameterization to accomodate your multi-season design. However, 'sparse data' will certainly force you to be clever...and modest.