Multistate questions ? Assumptions and GOF

[DMills]

My project involves assessing the survival of lobsters reared in captivity which are returned to the wild. To help with the problem of emigration Vs survival I am doing this by comparing relative ‘survival’ estimates for tagged captive-reared lobsters and tagged wild controls. Preliminary experiments suggested higher survival of controls. However, I also performed searches on a second reef (reef B) some distance from where all the lobsters were released (reef A), and found that there were many more captive-reared lobsters there than controls – it seems that at least part of the apparent ‘survival’ difference is due to movement. So, my questions are as follows:

1) I have only released tagged lobsters on reef A. I can constrain movement from B to A to zero for time interval 1, but have I violated any assumptions of the models ? Are there any other precautions I should take ?

2) Probability of encountering a control lobster on reef B is very low, leaving little data for GOF testing. Even numbers for captive-reared are quite low. I have stumbled my way through GOF testing with U-care, but have found little in the way of instructions about how to accomplish this (March edition of Biometrics isn’t on-line or on the shelf yet!). While the test outputs seem to make sense, and indicate good fit, for tests 3G and M, I find many rows in the output tables have ‘NaN’ for Sta and Pval. Is this telling me that there is insufficient data in these cells, or is it to do with data pooling ?

3) Is there a way of calculating c-hat for multistate models form the output of U-care?

Thanks
Dave Mills
Tasmanian Aquaculture and Fisheries Institute

[cooch]

1) I have only released tagged lobsters on reef A. I can constrain movement from B to A to zero for time interval 1, but have I violated any assumptions of the models ? Are there any other precautions I should take ?

Nothing obvious. It is not always the case that the most general model is the fully time-depedendent one. It often is, for the practical neccesity of GOF testing - GOF methods for time-dependent models are (in many cases) available, but not for constrained models. Most people argue that the time-dependent model should be the most general model, but this is not always reasonable (biologically), or practical (usually due to data limits).

2) Probability of encountering a control lobster on reef B is very low, leaving little data for GOF testing. Even numbers for captive-reared are quite low. I have stumbled my way through GOF testing with U-care, but have found little in the way of instructions about how to accomplish this (March edition of Biometrics isn’t on-line or on the shelf yet!). While the test outputs seem to make sense, and indicate good fit, for tests 3G and M, I find many rows in the output tables have ‘NaN’ for Sta and Pval. Is this telling me that there is insufficient data in these cells, or is it to do with data pooling ?

Perhaps the larger issue should be one of - do you need to do a MS analysis. Have you considered other approaches - perhaps treating encounters on reef B as 'recoveries' (you could code them as such in your data), and using a combined recapture/recovery model? Perhaps worth a thought.

3) Is there a way of calculating c-hat for multistate models form the output of U-care?

Yes, for fully time-dependent MS models, assuming you have the newest version of U-CARE (which has options for the MS GOF tests). The canonical reference for this is a paper 'in press' with Biometrics, written by Roger Pradel and colleagues. Since the paper isn't out yet, I suggest you contact Roger Pradel (concerning his paper, and the theory) and/or Remi Choquet (who manages the development of U-CARE). Both are associated with CEFE in France

[DMills]

THe idea of using combined recapture/recovery model is an excellent one ! - I will give it a go.

Thanks for the prompt reply.
Dave