POPAN assumptions

[fhensley]

Question from a beginner (so bear with me please):

Some colleages and I have a 10-year mark-recapture study on turtles, and one goal is to compare population density at our study site with densities reported in the literature. We used CJS to analzye various aspects of the situation, and reviewers liked what we did.

We then used the POPAN procedure to estimate population size. However, our situation is not well suited to the analysis:
a) over 400 sampling visits to the site, but not at regular intervals,
b) only about 200 captures of 60 individuals so the capture history is very sparse,
c) open system (segment of stream) (comparison studies tend to be regarded as closed (ponds) by the authors)

Manuscript reviewers were not satisfied with this:
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We used the POPAN implementation of the Jolly-Seber model in Program MARK to obtain an estimate of population size that is not provided by the CJS model. This estimate allowed us to determine population density for comparison to other studies. Sparse capture histories relative to the number of sampling trips required us to pool our capture data into calendar years in the POPAN procedure, treating each year as a single survey occasion (Rosen and Lowe, 1996; Cooch and White, 2002), which violates the assumptions of the model somewhat, but yields population size estimates that are not otherwise obtainable.
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We thought that if we pointed out up front that we were violating assumptions, readers would look at our numbers with a grain of salt, but be willing to compare them to population densities in other studies. Instead they insist that we quantify how much our violation of assumptions matters, or throw out our population estimates entirely.

The system is open and turtles are known to move in and out, so I doubt any robust estimates are possible. But if I can't make any comparison to other studies, it kills a big chunk of the paper. We think there is a general trend among published studies for population paramenters to be correlated with elevation, and our POPAN estimates seem to fit that trend and are biologically realistic. But reviewers can't see past our honest admission that we don't meet the assumptions of the method.

Any advice to deal with reviewers, or to come up with population estimates they will like? Any sources we can cite that say that poor estimates are better than none?

Many thanks!

-Frank Hensley

[cooch]

I'm running late, but some quick thoughts:

1. estimates of abundance from open populations are generally poor -> worthless (point on continuum between the two being determined by various things). They are generally not recommended.

2. the desire to compare with 'previously published estimates'. Well, what gives the previous estimates any credibility? Just because they're published doesn't mean they're worth anything (if you interest is in comparing your open estimates to other open estimates, the cynical person - occasionally me - might say you're comparing different pieces of rotten fruit to see which one smells different - given some set of interesting environmental circumstances, of course).

3. there are a number of publications which evaluate 'problems' for open estimates (i.e., violation of which assumption will do what to the estimate). One approach is to think hard about which violations might be in your study, and condition your statements based on those. In other words, restrict your caveats and post hoc arm waving about 'possible problems' to those which are plausible, given your system.

4. if your real interest is the trend of abundance with an elevational gradient, then you *can* possibly proceed if you're willing to demonstrate (or hold your nose and assume) that said violations are independent of that gradient. If so, then you could establish trend, which might be your point. If you have a series of estimates, all of which are biased (say), but where the bias is independent of the covariate(s) of interest, then you can still defensibly look at 'trend' (wrt the covariate).

5. alternatively, decompose N (which is poorly estimates) into the 'contributing bits', and tell your story about those. In fact, putting on my 'cynical reviewer' hat - I'd say that 'trend' in N is only partially informative. Suppose N trends with elevation (say). So what? (Although I'm sure there is some adaptationist hypothesis which makes such a trend interesting). What are the processes which contribute to that variation? The reason this might be useful is that not only (i) are the lower-level processes contributing to change in N often more interesting/useful, but (ii) they're often (generally) estimated with greater precision and less bias.


Just some quick thoughts.

[cooch]

... in the POPAN procedure, treating each year as a single survey occasion (Rosen and Lowe, 1996; Cooch and White, 2002)...

Unrelated aside - we generally discourage citing Cooch & White (it is a 'software user's manual', not part of the scientific literature in the usual sense), with one exception (see below). Rather, cite the White & Burnham (1999) Bird Study paper for MARK, and then the primary literature for POPAN (Carl Schwarz & Neil Arnason having jointly contributed the majority of said literature), as needed.

The exception - some chapters in 'the MARK book' have been written by colleagues (Kendall for the RD chapter, Lukacs for the closed abundance chapter, Schwarz & Arnason for the POPAN chapter, Rotella for the nest survival chapter, and so on). In that case, I (personally) think it is entirely appropriate to cite their individual chapter contributions, but in the end, leave that to those authors to decide one way or the other. In other words, its entirely their prerogative. So, if you want to cite the POPAN chapter, ask Carl what he thinks, and go from there.