Incorporating "seen but umarked or unidentified" animals

[jnwaite]

Is there a way (or a benefit) to incorporating individuals that were seen/detected, but known to either be unmarked or their mark was not identified, into secr models?

Some examples:
1. An individual leaves a sample in a hair snare but it cannot be genotyped to a unique individual (DNA quality and/or quantity problems).
2. An individual is known to be present (via a camera pointed at the hair snare), but either does not make contact with the hair snare, or makes contact but does not leave a sample.
3. Multiple animals are known to have made contact (with or without leaving samples) with the hair snare (based on camera data), but not all of them can be genotyped or identified.

These last two examples are especially common with pack animals, such as wolves. Over the course of a few years, there have been several instances when we know that multiple individuals were in the immediate area (i.e., within feet of the hair snare) based on camera data, but only one (or maybe two) of them actually contacts the snare and leaves a sample. Just as problematic is when LOTS of them roll but not all of them can be genotyped (there are only so many single-hair analyses you can do when left with a fist-sized ball of mixed hair from multiple individuals).

At the very least, this should influence the minimum number of individuals in the population size estimates (a bound on the lower confidence interval), and I would think that it would affect the baseline probability of detection.

Thanks!

[murray.efford]

Hi - Good questions, and worthy of investigation, but my first thoughts for what they're worth are mostly negative:

Data from unmarked individuals carries relevant information, but often it's very weak. Technically, yes it can improve estimates a little, but in practice I wonder when it's really worth it.

There's literature on using unmarked animals in Bayesian SECR models, and some limited capability in 'secr' not yet configured for synchronous marked + unmarked sampling. I don't relish the challenge of providing a general interface for complex mixtures of marked & unmarked (rather like the mostly undocumented SECR + telemetry capability in 'secr'). My main interest is in joining large-scale 'unmarked' sampling and intensive capture-recapture.

Strictly, I doubt you should be using standard SECR for wolves in the first place - independence among animals is a core assumption. Presumably detecting one animal of a group is often associated with detecting other animals, leading to overdispersion. In distance sampling one can take refuge in counting groups, multiply by estimated group size, but (usually) passive detectors don't let us estimate group affiliation and group size. I'd like to see someone solve this problem! However, your particular worry that you will miss some animals when you get a whole lot at once has something in common with single-catch traps - catching one precludes others - and that doesn't seem a big deal if we have a lot of trap sites.

It's a fact of life that most detectors have less than 100% efficiency, and we live with that. Whether increasing efficiency is going to much improve precision of density estimates depends on whether RSE(a-hat) is limiting, as opposed to RSE(n). And acknowledging unmarked animals can only go a small way to increasing efficiency.

I think your 'lower bound' argument applies only to realized (not expected) density or N, which is not to say it's wrong. It's true that 'total N must be at least as large as the maximum number of different animals recorded at any one detector', but I wonder how often that really helps...

Perhaps someone else has ideas.
Murray

[jnwaite]

Thank you for the insight.

You bring up a point that actually has been bothering me for some time now, and that is the (presumed, but very likely) lack of independence between animals. Unfortunately, distance sampling is not very effective here--visibility from the air is extremely poor due to the dense vegetation and canopy cover in our study area. Collaring animals in this area has also proved to be extremely difficult. This is the primary reason we've added the passive hair snares to our arsenal (though detection is still extremely low, especially when amplification and genotyping failure is factored in).

We can get some measure of pack affiliation based on similarity among several of the genetic markers we are looking at. Interestingly, if I include this pack affiliation measure as a covariate in a secr model, it ends up being significant and fairly informative. It doesn't, however, improve the model fit very much at all.

I was looking for a way to estimate (and correct for) overdispersion in secr, such as the median c-hat statistic in Program MARK. It doesn't look like this is implemented quite yet, but my understanding (at least from how Program MARK works) is that the mean estimates aren't affected nearly as much as the variance of those estimates. Not that this isn't important.

For now, though, these models are the best tool we have for estimating wolf abundance, and our results actually fit quite nicely with expectations based on what we know is happening demographically (reported harvest, estimated unreported harvest, and pup production). Do you have any suggestions for other tools we could be exploring?

[murray.efford]

Interesting that you think SECR is working for wolves - and I agree that overdispersion is a problem for variance estimation (and AIC) rather than the estimates themselves. I just haven't thought much about social animals, and recently deflected a question about another social carnivore. Presumably there will be ways to estimate c-hat, and QAIC and variance adjustments could be done by hand. I can imagine formally including social groups in the model, especially if there is some information on membership... for the future!
Murray