Multispecies models with single-catch traps?

[Phil Chapman]

Hi all,

I'm trying to get my head around the use of SECR to extract densities for multiple small mammal species, which are detected using a grid of live traps. The grid is run for 7-day trapping periods over multiple years, and the ecological result of interest is how the densities of each species change over the years. There are multiple grids in my study (each grid comprises a 4x12 array with two traps at each point, for a total of 96 detectors).

Having read my way through the secr package guidance, as well as parts of the textbook Spatial Mark-Recapture, I've decided to take the following approach.
Each grid is run as a separate multi-session model, with sessions corresponding to sampling years. Species is put in the capthist object as a factor covariate, then I specify the model as D~g*session, with the groups defined as the covariate "species".

The models seem to take nearly 4 hours to run on my laptop, but I do get a species- and session-specific density estimate.

My question is this:

Does this seem computationally the correct thing to do? If not, how else should I construct the models?

I basically followed this approach in the manual's advice for analysing sex-specific densities, and applied it to species groups. However I decided against one of the options, namely dividing the model into one session for each sex (or species), because the nature of single-catch traps is that the probability of catching species A at a detector is not independent of the probability of catching species B: Once a trap has caught an individual of B then it cannot catch an individual of A living in the same area. This is obviously not true for other detector types like camera traps which can (effectively) catch A with the same probability whether or not it has caught B.

I'm not 100% convinced I've really got round this by encoding species my way: is there any other way of doing this?

[murray.efford]

Hi Phil

Your approach seems formally OK to me*, so the question comes down to whether there are faster ways get to the same place.

Your motivation for jointly estimating all species is good, but it is defeated by the limitation that we do not have a detection model that includes competition among animals for traps (the elusive single-catch likelihood); we rely on the multi-catch likelihood and the observation that density estimates+ are pretty much unbiased when this is applied to single-catch data. This leads me to think that as you really care about individual species, each with its own density and detection characteristics, you would be better to estimate each separately. Separate analyses will be a lot faster.

You can also speed things up by using a coarser habitat mask - make.mask(..., nx = 32) is often OK if the buffer is tuned (not too large or too small).

Murray

* assuming you allow for species differences in detection with e.g., g0~g, sigma~g
+ but not g0 estimates

[Phil Chapman]

Murray,

Thanks a lot for the reply and advice. I'd forgotten to account for species-specific differences in detectability, so I'll amend the models accordingly. I was aware of the issue of using the multi-catch likelihood method for single-catch traps, but had been suitably lulled by the literature I'd read suggesting that in practice it doesn't much bias the results.

Back to your suggestion about splitting the model by species (i.e. modelling each species separately). As far as I can see the big problem remains as I outlined it? Essentially you'd be treating every trapping occasion outcome which isn't a capture of your focal species as an empty trap, even if it's actually a trap which is closed and contains a different species. Therefore the number and spacing of traps treated as "available" by the model isn't actually correct. As far as I can see, this is a problem where you have two individuals of different species sharing approximately the same home range area: clearly the trap is unavailable to Species B if A already occupies it, and you end up underestimating the detectability, and thus density of each species accordingly. Thinking about it, this bias would disproportionately affect "rarer" species with lower encounter rates, because a greater proportion of the traps not containing your focal species would actually be occupied with a non-focal species rather than empty.

My catch rates are fairly low ( generally <20% of total daily effort), and I've had it suggested to me that this might mean that it doesn't really matter much. This seems like it would be hard to defend to a paper reviewer or PhD viva, though!

Someone else has suggested marking all the traps with non-focal species in as "out of use" in the capthist file, thereby adjusting the effort to account for the number of traps actually available to your focal species. While I like this idea, it still simplifies the situation greatly, by assuming that all the traps with non-focal species are unavailable at the beginning of the trapping occasion, and remain so for the duration. Most of my animals are nocturnal, and are active at about the same time, so this is a pretty unrealistic assumption.
I notice that secr now lets you assign non-binary "effort" values to individual detectors. Do you think it would be reasonable to try assigning a decimal value, say 0.5, to a trap with another species in? The trouble is that this is a bit of an arbitrary number!

Sorry for the long reply, but hopefully I've made myself a bit clearer. Am I missing something by worrying about this?

[murray.efford]

Yes, I understand the problem, and I stick to my original answer. You have individuals competing for traps both within and between species, but the problem is still that we do not have a likelihood for this case, and will have to rely on some approximation.

Your intuition may be correct (and you do state it very clearly) that there is a particular bias in the case of stratified (multi-species) population, but I wouldn't bank on it. This would be fairly easy to check by simulation (come to think of it, someone should extend and update the simulations in Efford, Borchers and Byrom 2009). That should satisfy and even impress an examiner. Note the specific conclusion of EBB that D-hat is unbiased whereas g0 is biased when the multi-catch likelihood is applied to single-catch data.

secr now lets you assign non-binary "effort" values

...since Jan 2013. Varying effort by both occasion and trap might save you, but it is also ad hoc and needing validation by simulation.

Your trap saturation is so low I do think you're wasting time on this. However, a few simulations might put your mind to rest.

Murray