Fixed recapture rate - still returns survival estimate

[megpetrie]

Hello,

I have a multi-year, multi-population data set that I have been working on modelling. There are a couple of years that don't have surveys for certain occasions so I've fixed them at zero so that the encounter histories are the same for all years. The best model estimates Phi for all populations and all years separately. What I don't understand is how I can still get (reasonable) survival estimates on those occasions for which I fixed the recapture rate at zero. How is MARK calculating survival for those periods? They can't be reliable can they?

Thanks,
Megan

[jlaake]

It depends on what model you are fitting. If it is an additive model (population+year) then it can create reasonable estimates. If it is population*year, then the estimates for those years with p=0 are garbage. Because there is no data, the std errors for those parameters should be very large. There is no information in the likelihood for those parameters (it is flat with respect to them) so they will simply float around the starting value if they move at all. MARK will fit any model that you tell it to and will derive estimates. It is up to you to provide it with a reasonable model. The fact that you can't estimate those parameters doesn't mean that the model is not the best model. At present with RMark it will count those parameters so the model is actually being disadvantaged relative to others. You can reduce the parameter count by the number of those non-estimated parameters or you can fix them to 1. For example, let's say you had 4 occasions and you didn't collect data on occasion 3 so you fixed Phi for the interval from 2 to 3 to be 1. Then Phi for the interval 1-2 will actually include survival from 1 to 3. If you have many holes (non-sampled occasions) then it could be that population*year is coming out the best because the annual variation is due to these survival parameters that are really multi-year. If all of the "holes" were in the same place for each population then you could collapse the capture history and use time.intervals to circumvent the problem but that does not sound like that is possible here. An alternative is to fit separate parameters for the multi-year survivals and then ask if the remaining annual rates are constant over time.

--jeff

[megpetrie]

Thanks for your response Jeff.

I just want to clarify:
"For example, let's say you had 4 occasions and you didn't collect data on occasion 3 so you fixed Phi for the interval from 2 to 3 to be 1. Then Phi for the interval 1-2 will actually include survival from 1 to 3."

So when you fix a p at zero because you have no data, you should also fix the corresponding Phi at 1?

Best,
Megan

[jlaake]

Correct. Recognize that the prior Phi is now a multi-year Phi. If you have one missing occasion it is a 2-year survival and if you miss 2 occasions in a row it is a 3-year survival etc. As I mentioned in last posting this does complicate the interpretation somewhat. You can convert them to an annual rate (eg sqrt(Phi) for 2-year survival).

--jeff