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...'.