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Sorry to beat this already dead horse but I was confused by Gary's statement above that reads: "What you shouldn't do is have a time-varying phi and a constant or trend model on lambda, because you are forcing the f values to meet the constraint of lambda = phi + f. If you have the same constraint on both phi and lambda, then the model would be valid (in that f would now have the same constraint)."

When I read the Franklin (2001) paper on Pradel models he seems to say the opposite "Because lambda, gamma, and f are the parameters of biological interest in the Pradel models, it is often best to model phi and p as completely time-dependent (e.g., as phi(t), p(t) and apply constraints of interest on lambda, gamma, or f."

Am I missing something? Thanks!

Joe

When I read the Franklin (2001) paper on Pradel models he seems to say the opposite "Because lambda, gamma, and f are the parameters of biological interest in the Pradel models, it is often best to model phi and p as completely time-dependent (e.g., as phi(t), p(t) and apply constraints of interest on lambda, gamma, or f."

Am I missing something? Thanks!

Joe

- sixtystrat
**Posts:**115**Joined:**Wed Jun 01, 2011 9:19 am

Franklin espouses the Nichols view, and Jim is (for the first time in history) wrong.

Very simply -- almost never a good idea to impose a constraint on lambda, since that imposes an implicit constraint on the sub-parameters phi and f. This is in fact a RTFM moment - chapter 13, section 13.4.1.

Very simply -- almost never a good idea to impose a constraint on lambda, since that imposes an implicit constraint on the sub-parameters phi and f. This is in fact a RTFM moment - chapter 13, section 13.4.1.

- cooch
**Posts:**1628**Joined:**Thu May 15, 2003 4:11 pm**Location:**Cornell University

Gary says that "If you have the same constraint on both phi and lambda, then the model would be valid (in that f would now have the same constraint)". So are you saying that is an invalid model as well? Section 13.4.1 was confusing (I RTFM) which is why I went to the Franklin (2001) paper and then to phidot in the first place. Thanks for clarifying.

Joe

Joe

- sixtystrat
**Posts:**115**Joined:**Wed Jun 01, 2011 9:19 am

sixtystrat wrote:Gary says that "If you have the same constraint on both phi and lambda, then the model would be valid (in that f would now have the same constraint)". So are you saying that is an invalid model as well? Section 13.4.1 was confusing (I RTFM) which is why I went to the Franklin (2001) paper and then to phidot in the first place. Thanks for clarifying.

Joe

I never apply constraints to lambda. Period. Suppose lambda has a trend? Whoo-pee. The question of interest is *why* is there a trend - which means, what is the pattern of variation/covariation in the processes (survival, recruitment) that influence lambda. If one is stationary, and the other trends, then guess what? lambda will trend also. I apply constraints to those lower-level parameter. Period.

As to Gary's approach, not one I prefer. Pick whatever one you want. Just don't apply a constraint to lambda alone, and then try to tell stories about phi and f.

- cooch
**Posts:**1628**Joined:**Thu May 15, 2003 4:11 pm**Location:**Cornell University

This topic is more general than MARK, right? So I'll chip in.

Open population models always include phi, but there is a whole menagerie of ways to include (allow for) recruitment, and lambda is one of these. Others are gamma, f, time-specific relative population size, entry betas (PENT), etc. Don't use more than one. Constraints can be applied only to parameters in the model, all else is secondary. This is a good reason to avoid models with PENT: no constraint makes biological sense. Which parameterizations of recruitment are available is a software issue: in theory they are interchangeable. And all are compatible with the conditional (Pradel-Link-Barker) formulations.

It's fine to compute derived estimates of alternate recruitment parameters after fitting the primary model (for example lambda = phi + f) but remember where these came from.

Open population models always include phi, but there is a whole menagerie of ways to include (allow for) recruitment, and lambda is one of these. Others are gamma, f, time-specific relative population size, entry betas (PENT), etc. Don't use more than one. Constraints can be applied only to parameters in the model, all else is secondary. This is a good reason to avoid models with PENT: no constraint makes biological sense. Which parameterizations of recruitment are available is a software issue: in theory they are interchangeable. And all are compatible with the conditional (Pradel-Link-Barker) formulations.

It's fine to compute derived estimates of alternate recruitment parameters after fitting the primary model (for example lambda = phi + f) but remember where these came from.

- murray.efford
**Posts:**686**Joined:**Mon Sep 29, 2008 7:11 pm**Location:**Dunedin, New Zealand

Thanks Murray. By "Don't use more than one" are you saying not to constrain more than 1 parameter (i.e., lambda, f, phi) in any particular model, but they are otherwise interchangeable? In other words, lambda~1, phi~t is okay and lambda~t, phi~1 is okay but lambda~1, phi~1 is not.

- sixtystrat
**Posts:**115**Joined:**Wed Jun 01, 2011 9:19 am

I meant only that it doesn't make sense to include more than one recruitment parameter in a model. I don't see why (phi~1, lambda~1) should not be an acceptable model (it is the default for 'PLBl' models in openCR). Derived f will also be constant. The 'problem' comes with (phi~t, lambda~1) which implies derived f varies inversely with phi: you can do it, but is it a biologically sensible model?

- murray.efford
**Posts:**686**Joined:**Mon Sep 29, 2008 7:11 pm**Location:**Dunedin, New Zealand

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