Closed population modeling with two sampling times only

[phettinga]

Hello,

I am doing closed population modeling using sampled genetic information from an ungulate population across two sampling times. I am not using the Lincoln-Petersen model because of issues of unequal capture probability and have instead been using the Mb and Mt models in MARK which appear to give N-hat estimates more consistent with what is known about this population (and verified using mark-resight techniques).

My problem is that when I select the 'appropriate' model option in CAPTURE it appears that the Mh, Mb and Mt models all yield statistically different results from the Mo model with the strongest of these being the Mh model. Unfortunately I cannot use the Mh model in MARK so it seems by only considering those models I can construct in MARK (even after using model-averaging) I am somewhat missing the boat as I can't account for this Mh model which seems the best-fitting of them all (and with a nice set of confidence intervals too!).

Is there anyway of weighing the models used in CAPTURE and somehow weighing those estimates instead of the ones I am getting in MARK? Should I just accept that the models I can build in MARK are a good enough representation of the sampled population?

On another yet related note, and still considering sampled genetic information over two sample times, I heard that the Mh model N-hat estimate should be substituted in situations where the Mo model is selected for as the best fit model. I am assuming this was in reference to CAPTURE, but was wondering if in situations where the Mo model is selected as the best fit model in MARK (with a high AICc weighting) if I should instead be selecting the Mh jackknife estimator from CAPTURE.

Also if anyone has any general comments on the use of mark-recapture modeling to estimate population abundance using two sampling times only I would likely be very interested in what they have to say.

Thanks in advance.

[dhewitt]

First, I'm not versed in closed captures models, but if the below quote from Paul Lukacs' current chapter 14 in the GIM book is correct, then you are missing something about model availability in MARK and CAPTURE:

"All of the likelihood-based models from Program CAPTURE can be built in MARK plus numerous models that have been developed since then."

That aside, if you have substantial (or sometimes not even so substantial) heterogeneity in capture probabilities, then two capture occasions give you little information to understand that variation. And thus, your abundance estimates are pretty shaky. Do you have any sense of what proportion of the population you are getting your "hands" on? If that proportion is large, you *might* be OK. The big discrepancies in N estimates across models doesn't bode well though.

So what's the likelihood of you being interested in this comment?

[cooch]

First, I'm not versed in closed captures models, but if the below quote from Paul Lukacs' current chapter 14 in the GIM book is correct, then you are missing something about model availability in MARK and CAPTURE:

"All of the likelihood-based models from Program CAPTURE can be built in MARK plus numerous models that have been developed since then."

If its in the book, its correct.

Actually, in all seriousness, the statement in the book is correct as written - all of ML-based models in CAPTURE can (and should) be built in MARK. At this point, there is no compelling reason to use CAPTURE (sorry, ease of use does not constitute 'compelling'), and a number of reasons why you should use MARK.

That aside, if you have substantial (or sometimes not even so substantial) heterogeneity in capture probabilities, then two capture occasions give you little information to understand that variation.

I'm guessing its actually 3 occasions - initial 'marking' event, plus two subsequent encounters - yes? If not, then you're not doing much more than an LP anyway. The rule of thumb promulgated by some of the 'smart folks' is that you really need 5 or more encounter occasions to really do much in closed abundance estimation - if you've got 'annoying' levels/patterns of heterogeneity, then >8 occasions is suggested.

And thus, your abundance estimates are pretty shaky. Do you have any sense of what proportion of the population you are getting your "hands" on? If that proportion is large, you *might* be OK. The big discrepancies in N estimates across models doesn't bode well though.

So what's the likelihood of you being interested in this comment?

Clever!

My suggestion is you (i) ditch CAPTURE, (ii) ready/study/work through the closed abundance chapter, (iii) pay close attention to how model averaging is handled, and (iv) when in doubt, consider simulating your sampling situation in MARK to check/confirm estimator performance for yourself (simulations are covered in Appendix A). But, if you only have two occasions, then there is not going to be a lot you're going to be able to do.

[phettinga]

Bunch of comedians! In response to the previous posts...

We are only using two sampling times (not three). Each sampling time used noninvasive genetic sampling so no need to "mark" anything on a first go-around. It is just that the number of samples collected at the second sampling time was much less than that collected in the first (thus selection for the Mb and Mt models in MARK instead of the Mo model). I know there is not much I can do with two sampling times only but then there is no excuse to have not tried everything (which is why I would still appreciate people answering my original post if they have additional comments).

I am familiar with the gentle introduction manual. I thought that the only heterogeneity model built into MARK for closed population modeling was the Pledger model and because of the small number of sampling occasions used in my study it's use was not an option. Typically capture probability is high (50-70%) but has varied as this study has been ongoing. There has been situations where the genotypes sampled have instead been used as a basis for forming census estimates but that is not what concerns me here.

My concern is that I can have a best-fit model when using CAPTURE and then when I go to test this same data in MARK I am to essentially forget about it (two sampling occasions or not). While model-ranking in MARK may have a strong mathematical basis the selection of models by users of MARK can be entirely subjective (or seemingly so based on how good their programming skills are). There may not be a compelling reason to use CAPTURE but there is a compelling reason to believe that the models it has espoused for the past thirty years have some basis in reality and should not be entirely forgotten. Even the gentle introduction handbook says the Mh jackknife model is still valuable. If you want to elaborate on why this model is not important please do (as in response to my second question).

I appreciate the comments thus far and encourage further suggestions.

[darryl]

Comedians or clowns, I'm not sure which the better descriptor...

Part of the issue is that the jackknife is a non-likelihood method, which is why it isn't in MARK. Do you any practical reasons for why you'd expect heterogeneity in capture probabilities? You noted that fewer samples were collected in the second sample; did they cover the same geographic extent as the first sample? I suspect that the bottom line though will be with only 2 samples you're going to have a very hard time estimating heterogeneity.

How different were the various estimates from CAPTURE?

[cooch]

Comedians or clowns, I'm not sure which the better descriptor...

I agree. Oh wait, I thought we were talking about the Otago Highlanders. (Inside joke...)

Part of the issue is that the jackknife is a non-likelihood method, which is why it isn't in MARK. Do you any practical reasons for why you'd expect heterogeneity in capture probabilities? You noted that fewer samples were collected in the second sample; did they cover the same geographic extent as the first sample? I suspect that the bottom line though will be with only 2 samples you're going to have a very hard time estimating heterogeneity.

Hard time approaching impossible. With only two samples, you really can't differentiate much among the various models (sorry, thats a simple reality - there is a very small set of models you can fit with only two sampling occasions) - at which point, your best bet is to model average - which means MARK.