Juveniles not released in Spring

[louise.fairless]

Hi all,

I have a TSM model with females and males falling into groups 'Marked as adult' and 'Marked as Juvenile' depending on the age at which they were marked, therefore 4 groups in total. My global model is phi(a2*s*A*t)p(s*A*t) where s=sex, A=age and 'a2' accounting for transience highlighted in GOF analysis in U-CARE.

A TSM model, by separating individuals marked as juveniles and adults, should 'to some extent', although not fully, be able to separate transience and initial juvenile survival.

My capture seasons are in May and September, yet Juveniles are only found and marked in September. As such, there are no new juveniles released in May and therefore survival is not estimable for cohorts starting in the May capture period as no juveniles are captured or released, they are only captured in September. This obviously leads to parameter estimability problems in the juvenile groups due to no juveniles being released at every other capture event.

I therefore thought it would be viable to introduce an arbitary parameter for the juvenile survival periods from May to September and keep this constant, this would reduce the number of parameters I am asking the model to calculate and as long as I keep this constant throughout all models in my candidate set, I can ignore this parameter in analysis of parameter estimates.

Therefore the first diagonal for the survival PIM for 'marked as juvenile' would be:

1
11
2
11
3
11
4
11
5
11
6
11
7
11
8
11
9
11
10
11

where juvenile survival from September to May corresponds to parameter coding 1,2,3.....10 and is fully time dependent
and May to September survival (which is not possible for juveniles) is coded for in the juvenile PIM by the arbitary parameter 11 which will be kept constant throughout models and ignored at the end and it is useless. Am I going the right way about this to solve this issue? This must be a common issue when the juvenile period is short and there are multiple recapture events within a year.

On the other hand, does it not matter the model cannot calculate these parameters and should I just leave full time dependence in the initial time period for juveniles, even though half cannot be calculated and again ignore the May-September survival parameters at the end?

Thanks in advance for your help. I hope this question is not trivial, I am after piece of mind!

Louise

[louise.fairless]

*peace of mind!!

[louise.fairless]

With further thought...would I be right to fix the juvenile parameters that are not estimable to equal 1 in the run window... ie may to september survival in the initial survival period... so the model does not have to estimate these parameters which are unestimable anyway.

Louise

[louise.fairless]

To say it another way, if you have a two age class model with four groups (juvenile males, juvenile females, adult males and adult females) with two capture occasions in May and September, but due to the seasonality of parturition, juveniles are not represented at every other release occasion. Therefore juvenile survival is not computable for the May release occasions of new captures as by this time they are adults and therefore there are no 'new' juveniles in the population,therefore there are 'empty' cohorts in the juvenile groups, so how do we solve this?

a) Can you fix the parameters to 0 for those parameters which you know are not estimable as not juveniles are released in certain cohorts? i.e. in the first diagonal of the juvenile PIM, fix each 'empty' cohort May release event to 0.

b) If so, can you ignore these parameters in your total number of estimable parameters. i.e. if you fix 32 initial survival intervals for juveniles on occasions where no juveniles were released, can you ignore these parameters and therefore right your final number of estimable parameters as the total estimable before fixing parameters minus the number of parameters which have been fixed. i.e. if the total number of estimable parameters should be 300, but you fix 32, should I report the total number of estimable parameters as 268 as these are the parameters estimated by the model.

c) Should I ignore the effect of initial juvenile survival and combine the adult and juveniles into one group for each sex and use a TSM model. I would like to look at juvenile survival and hence I included it in the initial model, but if the problems outlined above cannot be addressed this may be my only option?

I hope this makes it clearer and any comments you may have will be much appreciated.

Louise

[Morten Frederiksen]

Louise,

The solution you suggest should work fine. You can fix the parameters with no data to any value you want (between 0 and 1), it won't affect the estimation process. It is also immaterial whether you first give all these dummy parameters the same number in the PIM, but housekeeping becomes simpler if you do. Regarding the correct number of identifiable parameters in the model, you should indeed subtract the dummy parameters (in fact, any fixed parameters) as they're not estimated from data. Note that if p is also time-specific for the first age-class, the first p for each of these non-existent cohorts will also be unidentifiable as no animals were available for recapture/resighting. So in that case you may as well fix these p's and not count them towards the total.

Morten

[louise.fairless]

Morten,

Thank you very much for reading my message and taking the time to reply, you have answered all my questions and now I can battle on!

Best wishes,

Louise