Pooling data across grids

[wievern]

Hi. I am a graduate student analyzing a data-set of small mammal trapping data from 1997 to present. I have three grids that were trapped simultaneously in the fall of each year, and one additional grid that was trapped inconsistently. Grids were trapped for three days (setting in evening, checking in the morning). Virtually no animals survived between years, and the time between trapping periods was greater than a generation length, so survival over the study period is inconsequential. Each grid was distant enough from other grids that no animals could move between grids.
My plan is to use the three trapping days as occasions for a Jolly-Seber model, and estimate abundance for each year. I will then compare abundance to my other variables (climate, environment). My question is, should I combine the data from all grids for a single year into one model, and estimate abundance from that, or estimate abundance separately for each grid, and either combine the estimates or leave them separate and use each as a different data point. The grids are a bit different from each other, with some species only present on certain grids (i.e. voles only present at the more moist grid, mice present at all grids) and some variation in habitat.
My second query concerns small sample sizes. I read in some papers about small sample size corrections for J-S. There is some variability in number of individuals caught, ranging from 4 to 100+ per grid. I have seen it referenced, but haven't found anything on how to actually do these corrections. If anyone could link a reference for me to pursue, that would be much appreciated.

[murray.efford]

I strongly advise you to ditch Jolly-Seber and check out modern spatial capture-recapture methods. There is quite a lot to learn, but the payoff is large. Spatial methods take care of a large chunk of the heterogeneity that dogs J-S. Density is a more credible parameter than grid-specific 'abundance'.

In the R package 'secr' you would treat each year as a 'session' and apply annual covariates as session covariates. Failure to sample the fourth grid in some years can be handled via the usage attribute. Weak data from some grids in some years can be handled by 'sharing' parameter values across grids (i.e. not fitting a fully gridxyear-specific model for the detection parameters). As I said, there's a lot to learn. One place to start is the (slightly dated) tutorial at https://www.otago.ac.nz/density/SECRinR.html, followed by the secr-multisession.pdf at the same place. You might also try the web version at https://www.stats.otago.ac.nz/secrapp/.

There are other approaches to spatial capture-recapture (e.g., Royle & Converse MEE 2013), but in my biased opinion 'secr' is the most accessible.

[wievern]

Thank you very much! I will look into that!