Closed capture model selection and model estimates

[Bill]

Dear forum
Please forgive what may be a stupid question however I have pored over chapter 14 of the manual, have read the relevant sections of ‘Handbook of capture-recapture analysis’ and White (2006): Closed population estimation models and their extensions in program MARK.

I am using program MARK and the AICc values provided in the results browser to assist with closed capture model selection for 10 night capture-mark-recapture surveys of a native carnivore. I am including models M(0), M(b), M(t), M(h) and their combinations including M(tbh). I have used the appropriate constraints as per the handbook and White (2006) to make time and/or heterogeneity models estimable.
My concern is the model outputs that arise from the models I specify in program Mark are different from those obtained from running program CAPTURE through program MARK. For example:
Model M(th) additive mixture effect as per White 2006 popln est = 93 (SE 48 95%CI 62-323) whereas the Chao M(th) model run via program CAPTURE popln est = 69 (SE 5.8 95%CI 63-87). Similarly M(h) specified as per the manual and White (2006) in mark popln est = 97 (SE 58 (95%CI 62-384) compared with M(h) jackknife run through CAPTURE popln est = 92 (SE 15 95% CI 73-137) and M(h) Chao run through CAPTURE popln est = 81 (SE 14.7 95% CI 66-130). On the other hand the popln estimates for models such as M(b) using both MARK and CAPTURE are not identical but similar.

I understand that some of the models in program CAPTURE have been specified differently than those I am using in MARK even though they are ostensibly accounting for the same sources of variation in capture and recapture probabilities. Is it reasonable to rank models in program MARK and then use the estimates produced under ‘similar’ models in CAPTURE? Or are the models presented in CAPTURE too simplistic and I haveto live with the relatively large uncertainty in model outputs from those I have constructed in MARK. Generally capture probabilities for the carnivore in question are low (less than 0.3 in many cases under M(h)jackknife).
Many thanks for your consideration.

[cooch]

Quick replies since I'm late. Gary might weigh in at some point -- he's forgotten more about program CAPTURE than I'll ever know, and can speak to some specifics.

Dear forum
I am using program MARK and the AICc values provided in the results browser to assist with closed capture model selection for 10 night capture-mark-recapture surveys of a native carnivore.

Model selection, and not model averaging? In 99% of applications of closed population estimation, the objective is to get the best estimate of abundance. Meaning, you model average over your candidate model set. See below...

I am including models M(0), M(b), M(t), M(h) and their combinations including M(tbh). I have used the appropriate constraints as per the handbook and White (2006) to make time and/or heterogeneity models estimable.

In other words, everything but the kitchen sink. If you used Huggins models, and had individual covariates, you could use those also.

This is pretty normal -- abundance estimation is about as close to 'acceptable data dredging' as you can get. Occasionally, you learn something of interest in terms of model support (for example, trapping arrays almost always induce a form of individual capture heterogeneity, and finding that heterogeneity models - say, based on finite mixtures -- fit better than models without mixtures might be a confirmation of your hypothesis.) But, generally, the interest is in abundance estimation. Model averaging...and you can't robustly average over conditional estimates in CAPTURE. In fact, one of the motivations for recasting everything in a likelihood-based framework in MARK is because it lets you use AIC, and AIC weights, to do model averaging.

My concern is the model outputs that arise from the models I specify in program Mark are different from those obtained from running program CAPTURE through program MARK.

But, you next questions tips off what you're really concerned about...

... and I have to live with the relatively large uncertainty in model outputs from those I have constructed in MARK.

Which explicitly suggests that the estimates of conditional uncertainty in MARK are 'too big', and that the estimates of same from CAPTURE are 'correct' (or more satisfying, in terms of wanting precision).

2 issues:

1\ there are technical differences in how MARK is estimating things, and I'd personally have more faith in output from MARK than CAPTURE, at this stage.

2\ if you don't want to accept that MARK is more likely to be correct, then the question comes down to -- would you rather have too big a CI around the estimate, or too small an estimated CI? For most conservation management perspectives I can think of, given the precautionary principle, there is a fair argument that too big is better than too small.

To get a good feel for comparisons, if you're interested, try simulating data in MARK, and then running the simulated data through both MARK and CAPTURE.

[gwhite]

All the heterogeneity models in CAPTURE except Mbh are not likelihood-based, so give quite different estimates than what you would get with MARK. In addition, for likelihood models, CAPTURE returns the estimate from the integer that maximizes the likelihood, not the floating point value that maximizes the likelihood.

All models in MARK are likelihood-based. The estimate reported is the floating point value that maximizes the likelihood. The heterogeneity models you used are probably based on the Pledger mixture models. I have also added another heterogeneity model for the Huggins estimator based on a normal distribution on the logit scale.

Gary

[Bill]

Thank-you very much for your replies. I will indeed try simulating some data in both programs. From a management perspective we ‘want/need’ to be able to detect a 10% change in population abundance (among other things) of this species within monitored sites over 5 years, and we are particularly interested in detecting a 10% or more decline. We have 8 spatially independent sites that we have been monitoring on and off for over 10 years (some more often than that). As a result I think the lower bound of the confidence interval, and any changes in this over time, is of the most interest to us. It may be that both programs produce similar patterns in lower bounds over time. We commenced our analysis using program CAPTURE so that our estimates were directly comparable with previous work, and also because it is unlikely that our models that include individual heterogeneity for sites that have been hit the hardest by disease and hence have relatively few individuals left, would converge using a likelihood based approach. Your replies have been very helpful in developing our understanding of how closely estimates from our data reflect what is really going on out there. Thanks again.