When age class lengths differ

[jbauder]

I have question about how to format PIMs and the design matrix when modeling age-specific survival with a CJS model when members of one age group are not available on all sampling occasions. I found a similar post (viewtopic.php?f=1&t=1717&p=5044&hilit=cobra#p5044) but it's reply did not fully answer my question.
I am modeling rattlesnake survival rates and have five groups for different age classes, neonates, 1st - 3rd year juveniles, and adults. We mark and recapture snakes in the spring and fall at their dens and all juveniles and adults are available for capture during this time. However, neonates (by definition) are only available for capture/recapture during the fall they born in. The next spring they become 1st year juveniles. When setting up a PIM I used the following format to try to account for this:
S F S F S F S F S F S F
0 0 1 1 2 2 3 3 4 4 5 5
__0 1 1 2 2 3 3 4 4 5 5
____0 0 1 1 2 2 3 3 4 4
______0 1 1 2 2 3 3 4 4
________0 0 1 1 2 2 3 3
__________0 1 1 2 2 3 3
____________0 0 1 1 2 2
______________0 1 1 2 2
________________0 0 1 1
__________________0 1 1
____________________0 0
______________________0
Zeros represent neonates and since each subsequent age class lasts one year, their survival parameters are paired (one for the spring sampling event and one for the fall). Is this an appropriate way to code for neonates? Would I need to set p to "0" since there are no neonates in the spring available for capture?
If this approach is correct, could someone explain how to set up this type of coding in the design matrix.

Thank you very much for your help
Javan

[jlaake]

If I correctly understand what you are saying, this is not an issue because in a CJS model you don't model the initial capture but only subsequent recaptures. So there is no recapture probability for neonates in spring because they don't exist; they'll have the recapture probability for a 1st year. Before I go any further please explain how you have time starting (spring or fall) and whether what you gave was a PIM for p or Phi. I assume it is for p but if they are a first year the following spring then it should start with 1 and not 0. More details needed here.

You should also consider whether you should be using CJS and maybe you really want a JS or POPAN approach for what you are doing.

--jeff

[jbauder]

Thanks for responding Jeff and I apologize for not being clearer about my PIM. The PIM that I sent was intended to be for survival for individuals marked as neonates. We started our sampling in the spring of 94 and continued sampling each subsequent fall and spring. So the first cell in column 1/row 1 should be summer survival for a neonate marked in the spring of 94, which cannot happen since neonates can only occur in the fall of any year and become first year juveniles the following spring. My PIM structure has individuals stay within a given age class for one year (a spring and fall sampling occasion) and then transition to the next age class immediately prior to being recaptured the following spring. Would it be appropriate to format my PIM for phi in this way under these circumstances?
I see your point about the recapture PIM for neonates starting with a 1 and not a 0. To make sure I understand you correctly I have made a PIM for individuals marked as neonates for recapture probability. The first cell in column 1/row 1 in this case would be recapture probability in fall of 94 (with spring 94 being the first capture occasion). Ones are recapture probability for first year juveniles.
F S F S F S F S F S F
1 1 1 2 2 3 3 4 4 5 5 5
__1 1 2 2 3 3 4 4 5 5 5
____1 2 2 3 3 4 4 5 5 5
______1 1 2 2 3 3 4 4 5
________1 2 2 3 3 4 4 5
__________1 1 2 2 3 3 4
____________1 2 2 3 3 4
______________1 1 2 2 3
________________1 2 2 3
__________________1 1 2
____________________1 2
______________________1

I have considered using a Pradel model to estimate lambda or POPAN to estimate abundance. Both would be useful to my project. I am not sure if our data meet the assumption of equal catchability between unmarked and marked animals, since rattlesnakes are known to show a "spook-factor" response after being captured and marked. But I will continue to look into the possibility of using other JS models.

Thanks again for your help
Javan

[jlaake]

I prefer to make it clear in the PIM that there are no data for certain cohorts. So below I use NA where there are no data -- you had no releases of neonates in spring because there are none by definition. You can use any index in those locations because they will be unaffected as there are no data for that cohort. I tend to use a separate index for the NA and fix that parameter value as it cannot be estimated but that is up to you. I think if you view it this way it will make more sense. I set up both Phi and p pims under the basis that they remain in that stage for 2 occasions afterwards but it is a bit odd that you are calling them neonates in the fall and then first year juveniles 6 months later even though you continue their survival forward to a full year. In the p PIM, index 6 is the recapture probability of first year juveniles so in their p pim for a first year juve caught in spring would have a 6 for fall and then a 7 for following spring.

--jeff

Neonate PIMS
Phi StoF FtoS StoF FtoS StoF FtoS StoF FtoS StoF FtoS StoF FtoS
S NA NA NA NA NA NA NA NA NA NA NA NA
F 1 1 2 2 3 3 4 4 5 5 5
S NA NA NA NA NA NA NA NA NA NA
F 1 1 2 2 3 3 4 4 5
S NA NA NA NA NA NA NA NA
F 1 1 2 2 3 3 4
S NA NA NA NA NA NA
F 1 1 2 2 3
S NA NA NA NA
F 1 1 2
S NA NA
F 1

p F S F S F S F S F S F S
S NA NA NA NA NA NA NA NA NA NA NA NA
F 6 6 7 7 8 8 9 9 10 10 10
S NA NA NA NA NA NA NA NA NA NA
F 6 6 7 7 8 8 9 9 10
S NA NA NA NA NA NA NA NA
F 6 6 7 7 8 8 9
S NA NA NA NA NA NA
F 6 6 7 7 8
S NA NA NA NA
F 6 6 7
S NA NA
F 6

[jbauder]

Thinking about each row as a release cohort seems to make more sense to me and I think I understand how to code the neonate PIMs and why.
Thanks for all your help
Javan