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Hello,

I've been working for some time on a variety of capture recapture and occupancy models. I'm trying to wrap my feeble brain around detectibility. I took a class a several years ago and I remember the professor mentioning that detectibility was a "nuisance" parameter. Some the models estimate that lets us get at what we are really interested in, such as abundance, survival, or occupancy.

In the literature, there seems to be some focus on detectibility, but in the context of increasing detectibility (or recapture rate) to improve the accuracy and precision of the survival or occupancy.

Does detectibility have any biological significance? In of itself, is detectibility interesting? Or do most folks recognize that detection is imperfect and treat it as a nuisance parameter?

Thank you.

Bryan Hamilton wrote:Hello,

I've been working for some time on a variety of capture recapture and occupancy models. I'm trying to wrap my feeble brain around detectibility. I took a class a several years ago and I remember the professor mentioning that detectibility was a "nuisance" parameter. Some the models estimate that lets us get at what we are really interested in, such as abundance, survival, or occupancy.

In the literature, there seems to be some focus on detectibility, but in the context of increasing detectibility (or recapture rate) to improve the accuracy and precision of the survival or occupancy.

Does detectibility have any biological significance? In of itself, is detectibility interesting? Or do most folks recognize that detection is imperfect and treat it as a nuisance parameter?

Thank you.

Sure - detectability p is in fact (minimally) the product of two things: the availability to be detected, and then, given available, were you detected. See fig. 15.1 in Chapter 15. The former is usually where the 'interesting biology' lies. See the *many* papers by Bill Kendall and colleagues on application of the robust design as a tool to partition p into component parts.

The basic point is -- *why* isn't an animal detected. Sometimes, the reason(s) relate to interesting biology. Perfect example is for species where all detections occur during breeding -- as such, non-detection relates to non-breeding at some level. Which is biologically interesting.

Thank you.

Isn't the availability to be detected also a function of abundance? So that could confound interpretation of detectibility across studies.

I'm partially asking to try to understand how translatable detectibility is across studies. If you and I are both studying sage grouse occupancy in Nevada and Colorado, would differences in detectibility be due to differences in breeding timing or differences in abundance? Is that the kind of paritioning the Kendall papers discuss?

Isn't the availability to be detected also a function of abundance? So that could confound interpretation of detectibility across studies.

I think you are confusing the probability of detecting at least one animal with the probability of detecting an animal. The first is a function of N and the second is not. It is the second that is being estimated.

If is the probability of detecting an animal then assuming independent detections and constant p for all animals, then the probability of detecting at least one animal is

jlaake wrote:

Isn't the availability to be detected also a function of abundance? So that could confound interpretation of detectibility across studies.

I think you are confusing the probability of detecting at least one animal with the probability of detecting an animal. The first is a function of N and the second is not. It is the second that is being estimated.

If is the probability of detecting an animal then assuming independent detections and constant p for all animals, then the probability of detecting at least one animal is

...which of course is part of the conceptual basis underlying the Royle-Nichols model, which got (gets?) everyone all excited. A patch is occupied if there is at least 1 individual. Probability of detecting at least 1 individual is a function of how many individuals there are (the exponent in Jeff's expression), and the per-individual detection probability (the p in his expression). Given all that, there must be an algebraic relationship between p (as estimated from occupancy studies) and N (overall abundance). Clever people (aka Andy and Jim) worked out said algebra, and presto-chango, you can (under some 'rather strong' assumptions) go from occupancy -> abundance.

As an interesting anecdote -- within 2-3 weeks of that paper being published, I had no fewer than 27 emails (I actually kept track after the initial flurry), asking why the 'Royle-Nichols' model wasn't in MARK? Gary resisted putting it in MARK for quite some time, since (as I believe the story goes) said model gives the appearance of getting everything for virtually nothing ('abundance from only having to detect one? Bag all that capture and mark individuals silliness then. Too time consuming, and too expensive...'). The method rests on some strong assumptions, and with some careful thought, the approach may in fact be useful for some situations. But, it is not uncommon for people to read the abstract, see the 'abundance from occupancy' bit, and stop any think, let along anything close to 'careful'. [In the end, the model, and various permutations, were fully implemented in MARK].

What was notable about the 27 emails is that 100% of them came from 'agency folks', who are often charged with trying to tell robust stories over large landscapes for which individually marking is often (generally?) impractical. So, first comes occupancy (use Psi as a mean-field approximation to 'abundance' -- but the administrative types don't know how to interpret -- they keep asking for 'how many are there?'). Then, Royle-Nichols comes out and...you could almost hear the collective 'Yee-haw...'.

OK. Its starting to slowly come together for me. Thank you both for talking me through it.

I think you are confusing the probability of detecting at least one animal with the probability of detecting an animal.

I think I was confusing terms. Most of the papers I've been reading refer to detectibility as p, but p is calculated differently in different kinds of models? I just found out that detection in secr is closely related to distance sampling.

In a capture recapture model, p is the probability of detecting AN ANIMAL. Sometimes referred to as capture and recapture probabilities. Is p sometimes referred to as 'detectibility' in capture recapture models? Imperfect detection is often given as a reason to use capture recapture models and occupancy.

In occupancy modeling, detectibility (also p) is a function of abundance. This comes from the Royle Nichols 2003 paper. In an occupancy framework, detectibility could differ between two studies becasue there are a different number of animals or because the probability of detecting AN ANIMAL differs between studies.

I did not realize that you could estimate abundance from occupancy models. Is this done much? I've been reading a lot of papers and I haven't picked up on it yet.