Number and arrangement of traps varies across occasions

[Eric H]

Hello,
We are analyzing data from a 39-occasion camera trapping study using closed CR models. Cameras sometimes failed or were damaged, and were frequently moved, such that the number and spatial arrangement of traps differed across occasions. Fortunately, we can assume that the population at risk of detection did not change with changing trap numbers and layouts (picture a functional island where all individuals use the whole island). However, we need to account for the resulting variation in capture probability across occasions. I was considering using a temporal covariate specifying the number of cameras operating on each occasion (and ignoring any effects of the spatial distribution of traps). Does this seem reasonable, or is there a more explicit way to model variation in p associated with variable trap layouts.

Thanks in advance,
Eric

[JDJC]

Eric,

An SECR model is probably the best and most sensible framework to deal with the issue you describe. The issue with your proposal is that all individual animals are not likely to be subjected to the same differences in p due to camera failure; in fact, individual p should depend on the location of your cameras, and which ones failed when.

Cheers,

John

[Eric H]

Thank you John,
I agree! We are interested in presenting (another!) comparison of SECR and CR models, and I'm trying to parameterize them as similarly as possible (while taking advantage of the extra recaptures allowed by SECR).

I understand your argument about different individuals being affected differently by removal of different traps. However, we expect home ranges of all sampled individuals to have 100% overlap, with similar centers. They form a single community with a single shared territory. We expect some overdispersion due to non-independence of detections, but that's a separate issue.

Eric

[JDJC]

Hmm...I guess what you propose makes sense--or at least, I can't think of anything immediately that makes more sense.

It would be interesting to see if some of the proposed N-mixture adapations (e.g., http://onlinelibrary.wiley.com/doi/10.1111/j.2041-210X.2011.00113.x/full) for non-independence could be applied within a SECR framework

[murray.efford]

I don’t think this is at all relevant. Eric has data on which cameras were active when, and the problem is how to include that in the model. The traditional method is to use a covariate, estimating its coefficient. It is also possible to use a hard-wired adjustment for effort in the nature of an offset (defined as a covariate with known coefficient). We pointed this out in MEE in 2013 (and provided some comparisons in the context of SECR), but the idea is not ours alone (it crops up with minimal comment in other code I’ve seen). The catch is that, as far as I know, it is not a canned option in the non-spatial software.

One trick to consider, Eric, is turning the SECR detection model into a nonspatial model by fixing sigma to a large number in ‘secr.fit’. You should still be able to include detector-specific variation in effort (‘usage’). Interesting to try, in any case.

On JCDC’s point: if you are concerned about individual heterogeneity of detection parameters (g0, lambda0, sigma) in SECR you can fit finite mixtures (Eric is something of an exponent!). It is argued that these 3-parameter discrete random-effect models (theta1, theta2, pmix for the 2-class case) are more flexible than the 2-parameter beta-binomial, and therefore better, as they implicitly represent variation in both skewness and variance, whereas the skewness of the beta-binomial is fixed for given mean and variance. I’m sure this is formally correct, and the finite mixture models are easier to implement, but I’m keeping an open mind on when they should be used.

Murray

[Eric H]

Thanks to you both for the comments and suggestions.

I have proceeded with the covariate defining the number of traps operational on each occasion for now.

Murray, your comment about fixing sigma to a high value is intriguing, because with this data set (trap arrays are slightly smaller than the [communal] home range, and individuals were detected at traps the maximum distance apart) we get little information regarding the decline in detection probability with distance, estimates of sigma are high, density estimates are sensitive to the size of the region of integration, but abundance estimates are not... It's as though we achieved the non-spatial model you described via lack of information about sigma resulting from the sampling design. I think it will be interesting to write up, if only as cautionary example! I think articles by Royle, Marques, and others from ~2011 discussing the appropriate or minimum size of a trapping array or search area relative to home range size will be relevant.

Cheers,
Eric

[murray.efford]

It may even be worth checking the simulations in Efford 2011

[Eric H]

I will, thanks!
Eric