Abundance estimates from CJS

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Abundance estimates from CJS

Postby SoConfused » Thu Nov 09, 2017 7:11 am

A general and basic question here. It is my understanding that abundance estimates based on CJS recapture rates are simplistic and shouldn't be used. However, I seem to have trouble finding a concise, cite-able explanation as to why. Can anyone point me to one? I'm sure there's a sidebar in the Gentle Intro dedicated to this that I'm missing...

Thank you!
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Re: Abundance estimates from CJS

Postby jlaake » Thu Nov 09, 2017 1:44 pm

So where did you get that understanding? Abundance estimates from CJS are not fully efficient because they don't use the entry of unmarked animals but it is my understanding that if you use pent(t) then all of the information about p comes from the marked animal recapture rate. I have seen a paper by Judy Zeh that proposed that survival rate estimates for long lived bowhead whales were improved with JS over CJS but I believe that is because she didn't use a fully time dependent model. Others thoughts?
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Re: Abundance estimates from CJS

Postby SoConfused » Thu Nov 09, 2017 2:34 pm

Maybe it's my misunderstanding then? Among other things, it was a comment of Dr Cooch on here ("I'll restrict further comment on the 'utility' of deriving abundance estimates from an open CJS model in the first place"). The lack of worked R examples or built-in tools (similar to the popan.derived) seems to also be a hint to not engage in such activities :-)

What does "not fully efficient" mean in terms of estimates or their CIs?
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Re: Abundance estimates from CJS

Postby jlaake » Thu Nov 09, 2017 3:16 pm

Fully efficient means that it is not using all of the available information and thus cv may be larger but like I said I think that is only the case when pent is not time dependent. I have not done extensive simulation on this subject and it is probably a worthwhile task for someone.

There is precedent for constructing abundance estimates from CJS. You can look at some papers that I helped author on polar bears and also I believe Trent McDonald has used this approach as well so a search on his name should turn up some papers. With regard to code, ?pop.est in RMark will bring up a help page describing code I used in those polar bear papers and citations for them.
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Re: Abundance estimates from CJS

Postby cooch » Thu Nov 09, 2017 4:06 pm

The basic point is this -- the canonical estimator for abundance is 'count/detection'. With an open CJS model, there is minimum information for p, so the uncertainty for your estimates of N as 'count/detection' is considerable (to the point where many estimates from open models verge on silly). This is the motivation for the many models for estimating abundance from closed populations. Because N is a constant over the closed samples, you can do a much better job modeling the encounter process, and thus your estimate of 'detection' is much better. And thus, so is your derived estimate of abundance. If all you needed to do to get abundance that you had faith in was take number counted at a sampling occasion and divide by the CJS estimate of p, then life would be much simpler. But, alas, life isn't that simple. Short of strong assumptions (which are often the basis of the classic J-S and POPAN-based open models that generate abundance estimates), I generally look at simple 'count/detection' (as per original post) as an index to abundance, but not much more.
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Re: Abundance estimates from CJS

Postby jlaake » Thu Nov 09, 2017 4:58 pm

Clearly I'm not as pessimistic as Evan but I have been fortunate to have worked with datasets with largish p.

As I understood your query it was about cjs vs js. I believe Evan is saying that abundance estimates from either are not useful. I happen to disagree with him but to get to your original query, I am unaware of any pub that says abundance from open model ate not useful. Clearly you can obtain better inference with a robust design but closure is oftenot a risky strong assumption.
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Re: Abundance estimates from CJS

Postby gwhite » Thu Nov 09, 2017 5:05 pm

One reason I'm skeptical of CJS estimates of population size is behavioral response to first capture. The p estimates in CJS and JS are all recapture probabilities, and cannot account for any behavioral response.

Secondly, we know that individual heterogeneity is generally the biggest reason for biased estimates, and the CJS p estimates cannot fully account for individual heterogeneity. However, if the data are really good, fitting the individual random effects p model (logit normal model) can be very useful.
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Re: Abundance estimates from CJS

Postby darryl » Thu Nov 09, 2017 5:21 pm

You also sometimes have researcher behavioural effects where their study design means they target previously marked individuals, perhaps unintentionally, by focusing on areas within their area of interest where they captured animals before (e.g., where they captured them last time, always going back to the same known nest or den sites, etc). Like the behavioural effect Gary mentioned, this also means that the probability of first capture will be different to the probability of recapture, which will therefore give biased estimates of abundance if based upon the recapture probabilities (which is what CJS gives you).
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Re: Abundance estimates from CJS

Postby cooch » Thu Nov 09, 2017 7:20 pm

Darryl and Gary have fleshed out my basic concern -- abundance estimation is really a problem is estimating p. With a CJS model, there are limits to what you can do. J-S (and derivative) estimators are fine, so long as you're willing to live with the heroic assumptions (the most egregious of which is -- that unmarked animals in the population have the same probability of capture as marked animals in the population. This is likely (generally?) a problem in the presence of any heterogeneity in p (which is also likely to be a general reality)). If you imagine a simple mixture of high-p and low-p individuals. Animals with high-p likely to be caught, and part of marked population (M in JS models), whereas low-p in unmarked (U in JS models).
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Re: Abundance estimates from CJS

Postby jlaake » Thu Nov 09, 2017 7:41 pm

Both are possible problems. The first for animals that capture themselves and the second is correctable with a good design. However if you are going to make a general statement it would be that robust designs with closure is preferable and not that all cjs/js abundance estimates are not useful. But closure can often be suspect as well.
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