Reverse-time multi-state and Nichols et al. 2000 (Ecology)

[royworth]

Dear forum and c-m-r superiors,

I am attempting to apply the methods described by Nichols et al. (2000) to estimate the contribution of in situ recruits, immigrants, and survivors to population growth rate for three age/size classes of a fish population. I was hoping some of you may have experience with this approach using MARK and could clear a few things up for me.

Upon reading the Nichols et al. (1994, 2000) papers, "the book", and some suggestions I came across in this forum, I feel I correctly structured my .inp file and have an obtained the "correct" output for a robust design, reverse time, multi-state model detailing the time-dependent survival (seniority) and transition parameters. Thus, I think I have all of the output I need to make some of the calculations detailed in the Nichols (2000) paper. Those calculations are, for instance, for a large adult class, the contribution of adult survival ("gamma^22"), small adult (in situ) recruits ("gamma^21"), and true immigrants ("1 - "gamma^22" - "gamma^21") to large adult population growth. Similarly, for the small adults, I would like to estimate the contribution of small adult survival, juvenile recruits, and small adult immigrants to the population growth rate of this class. For the juvenile class, I'm not interested in separating immigrants and recruits.

The questions I would like to pose to you folks are, with the first one being rather blunt, yet simple:

1) Have I screwed up already in my approach to the problem using the reverse-time, multi-state apprach in MARK or in any other manner?

And

2) if not, could someone enlighten me to the meaning of the survival estimates (i.e. seniority estimates) using the backward-time, multi-state approach in MARK in comparison to the calculations made in the Nichols et al. (2000) paper using MS-SURVIV. Primarily, after rummaging through "the book", I understand, or at least I think I understand , that MS-SURVIV does not separate survival and transition, while MARK does. I assume this plays some role in those calculations using MS-SURVIV (as in the paper) versus MARK for this particular problem? Can anyone familiar with the approach point me in the right direction here? More directly, and perhaps for those more intimately familiar with the Nichols et al. (2000) paper, where exactly do I get "gamma^22" and "gamma^21" from columns 5 and 6 of Table 4 in that paper using my reverse-time, multi-state, MARK output? Thus far, I have warily assumed, for example, that I need to take the product of survival (i.e. seniority) and 1-Psi^21 for "gamma^22" and the product of survival and Psi^21 for "gamma^21". Am I hot or cold?


Thank you sincerely for any suggestions, comments, and/or reprimand

Roy Martin
PhD Candidate
Wildlife and Fisheries Resources
West Virginia University
Morgantown, WV 26505
royworth@gmail.com

Nichols, J. D., et al. 2000. Estimation of contributions to population growth: a reverse-time capture-recapture approach. Ecology 81(12): 3362-3376.

Nichols, J. D., et al. 1994. Estimating breeding proportions and testing hypotheses about costs of reproduction with capture-recapture data. Ecology 75: 2052-2065.

[cooch]

Primarily, after rummaging through "the book", I understand, or at least I think I understand , that MS-SURVIV does not separate survival and transition, while MARK does.

No - not quite. MARK and MS-SURVIV both provide estimates of psi and S. Only MS-SURVIV provides estimates of phi (where phi = S * psi). This is what is noted in "the book". And yes, it if you read the Nichols paper carefully, you'll see that they 'get there from here' in part by using phi, which you can't get directly in MARK. Which, of course, is why that section in that chapter includes 'problems for MARK...' in the title.

[royworth]

Which, of course, is why that section in that chapter includes 'problems for MARK...' in the title.

Thanks so much, Dr. Cooch. It appears that I overlooked that section

Best,

Roy

[cooch]

Which, of course, is why that section in that chapter includes 'problems for MARK...' in the title.

Thanks so much, Dr. Cooch. It appears that I overlooked that section

Best,

Roy

No problem. I'll ignore the transgression of using the 'Dr' bit.

[darryl]

Which, of course, is why that section in that chapter includes 'problems for MARK...' in the title.

Thanks so much, Dr. Cooch. It appears that I overlooked that section

Best,

Roy

No problem. I'll ignore the transgression of using the 'Dr' bit.

You prefer Prof Cooch?

[cooch]

Which, of course, is why that section in that chapter includes 'problems for MARK...' in the title.

Thanks so much, Dr. Cooch. It appears that I overlooked that section

Best,

Roy

No problem. I'll ignore the transgression of using the 'Dr' bit.

You prefer Prof Cooch?

Nah - no titles at all.

[royworth]

[/quote]

No - not quite. MARK and MS-SURVIV both provide estimates of psi and S. Only MS-SURVIV provides estimates of phi (where phi = S * psi). This is what is noted in "the book". And yes, it if you read the Nichols paper carefully, you'll see that they 'get there from here' in part by using phi, which you can't get directly in MARK. Which, of course, is why that section in that chapter includes 'problems for MARK...' in the title.[/quote]

No - not quite. MARK and MS-SURVIV both provide estimates of psi and S. Only MS-SURVIV provides estimates of phi (where phi = S * psi). This is what is noted in "the book". And yes, it if you read the Nichols paper carefully, you'll see that they 'get there from here' in part by using phi, which you can't get directly in MARK. Which, of course, is why that section in that chapter includes 'problems for MARK...' in the title.

Evan,

Thanks again for pointing me in the right direction. However, before I completely abandon my MARK results and prepare myself to tackle MSSURVIV, I had one more question. In the relevant section in "the book", it is stated that:

"Since MARK does not allow you to estimate the combined ‘survive and move’ parameter (i.e., φ) in the multi-strata case, you can’t use MARK to estimate the immigration rate (i.e., γXA in the preceding). This limitation may be fixed in future versions of MARK (specifically, φ could be estimated as a ‘derived parameter’). At present, the option of using MS-SURVIV is available."

Does this imply that I could perhaps estimate a 'derived parameter', γ, 'by hand' using the results from the reverse time multi-state model results I obtained in MARK? I recall from another section of 'the book' that estimates of φ, in forward time, can be estimated simply as the product of the proper combination of S and Psi, which results in estimates similar to those using MSSURVIV (Section 8-12, pp. 303-304). Thus, can I not take the product of the reverse-time estimates of S and Psi to get the various estimates for γ I am interested in (i.e. contributions of survival, recruiment, and immigration to lambda)? Is this entirely illogical in the reverse-time case?

Thanks again and I hope everyone had a nice Thanksgiving,
Roy

[cooch]

Does this imply that I could perhaps estimate a 'derived parameter', γ, 'by hand' using the results from the reverse time multi-state model results I obtained in MARK?

In theory, yes, but that would require a fair bit of work.

I recall from another section of 'the book' that estimates of φ, in forward time, can be estimated simply as the product of the proper combination of S and Psi, which results in estimates similar to those using MSSURVIV (Section 8-12, pp. 303-304). Thus, can I not take the product of the reverse-time estimates of S and Psi to get the various estimates for γ I am interested in (i.e. contributions of survival, recruiment, and immigration to lambda)?

Sure, but you'd need to derive SE's by hand, and since phi wouldn't appear as a structural parameter in the model, you'd have to be 'clever' in constraining the linear model (since phi is a product of other parameters, you could - in theory - get there for here by applying clever constraints to one or both underlying parameters - S and psi - used to generate phi). Again, all possible, but some work.

Of course, if Gary put phi into MARK in some fashion, this becomes moot.

[royworth]

[/quote]

Sure, but you'd need to derive SE's by hand, and since phi wouldn't appear as a structural parameter in the model, you'd have to be 'clever' in constraining the linear model (since phi is a product of other parameters, you could - in theory - get there for here by applying clever constraints to one or both underlying parameters - S and psi - used to generate phi). Again, all possible, but some work.

[/quote]

Excellent! Thanks again!

[/quote]
Of course, if Gary put phi into MARK in some fashion, this becomes moot. [/quote]

I haven't asked for anything for Christmas and I've been extremely good this year, for what its worth

Best,
Roy