GOF when some capture histories cannot exist by design

[jennyh]

I am using a CJS to do a survival analysis of juvenile coho salmon in which we have four occasions. The first two occasions occur in the fall and two groups of ~650 individuals are marked at each occasion. The last two occasions occur at a downstream migrant trap located at a permanent weir where we capture outmigrating individuals. The latter two occasions at the weir are the primary focus of this post.

At the weir we capture the fish we marked in the fall and give them a secondary mark (small upper caudal fin clip) and release them upstream of the trap approx. 0.20 river miles. These fish are then subsequently recaptured at the same trap and are then released downstream (if they have an upper caudal fin clip). These are “weir efficiency” trials in which we are trying to estimate recapture probability of the fish were previously marked in the fall. A major assumption here is that phi=1 between the first recapture and second recapture at the trap.

Given this study design encounter histories 1101, 1001 and 0101 are not possible because fish that are not captured on occasion three are not released above the weir and therefore cannot be captured on occasion four. The parameter of interest here is between occasions two and three (phi2). Because fish that were never captured at the third occasion have a p=0 for the fourth occasion and because we are not running a fully time dependent model (p3=p4) I cannot use RELEASE or bootstrap procedures provided in MARK.
I see two ways of working with our data at this point.

1.Only use the first three encounter histories (the first two occasions in the fall and third occasion at the trap). We could then use our estimate of recapture probability from the above occasions 3 and 4 (assuming phi=1 between the release upstream and subsequent recapture at the trap) to fix p3 which would result in an estimate of our parameter of interest (phi2). I understand that my survival probabilities are completely conditional on what I fix p3 to; however, we are using an estimate of p3, not just pulling a number out of a hat and therefore have some justification for what we are choosing to fix p to. Would this be completely inappropriate? If I bootstrapped data with a fixed p, does the bootstrap procedure use the value that I fixed p to? Also, I had read in a previous post that one individual accounted for the error in their estimates of p by fixing the p to the upper and lower 95% CI and using the estimate he got from this to bound their estimates of phi. Would this be a correct way to bound estimates of phi?

2.The second way is to create two groups in which all individuals with encounter histories 1100, 0100 are in group 1 and encounter histories 1110,1111,0111,0110, 1011 ,1010 are in group 2. In the PIMs we set all parameters equal for both groups except for p4 at the weir for group 1. We then fix phi3=1 for both groups and p4=0 for group1, all other parameters are “free.” We did run simulated data under this model, but unfortunately in RELEASE we do not have “sufficient” data for TEST 2 or TEST 3. Again, I cannot bootstrap the data given the model-constrained capture histories. Would the deviance plot of residuals be an appropriate test of model fit under the circumstances of “missing” capture histories?

Perhaps the most important question I have is which method seems most appropriate?

[abreton]

Hi Jenny --

I'm having trouble deciphering your encounter histories. If you can clarify I might be able to provide some advice. For your encounter history 11-- (I'm ignoring the 'weir' captures),

11 = fish was caught in the 1st AND 2nd fall seasons?

Are we talking about two different years?

The following encounter histories make more sense to me,
01-- = fish caught in 2nd fall of the study
10-- = fish caught in 1st fall of the study

Since these are salmon (semelparous), they're only making one (fall) downstream migration so "11" is impossible?

No doubt I'm missing something, thanks for the clarification.

andre

[jennyh]

Hi Andre,

That is a good question and my apologies for not explaining it in the first post. There are two fall capture occasions in one year...meaning we did in fact have two different "mark" groups in one fall season. You are correct that salmon do only make one migration; however, in our case (with coho salmon) that migration occurs in the spring (which is where we recapture them at the weir).

The first occasion was late-Sept to mid-Oct 2010 and the second was mid-October to the beginning of November 2010. The reason for doing this was to account for any PIT-tag induced mortality (see Brakensiek and Hankin 2007 for more details). The first tag group/cohort would provide an apparent overwinter survival estimate (Phi2) that is uncontaminated with PIT tag mortality. The second release group's overwinter survival would be contaminated with any PIT tag mortality.

So just to clarify an individual with 11-- (ignoring "weir" captures) means that the fish was marked at the first occasion in the fall of 2010 and then recaptured again on the second occasion (approxmately 21 days later) in the fall 2010.

An individual with 10-- means that the fish was marked on the first occasion in the fall and not recaptured on the second occasion (which was 21 days later)

An individual with 01-- means that the fish was marked on the second occasion.

Please let me know if you need more information. I hope that helps to clarify how to interpret our encounter histories.

Thank you very much for you help!

Jenny

•Brakensiek, K., and D.G. Hankin. 2007. Estimating overwinter survival of juvenile coho salmon in a Northern California stream: accounting for effects of PIT-tagging mortality and size-dependent survival. Trans. Am. Fish. Soc. 136:1423-1437

[abreton]

Here's a simple idea that could be accommodated by the CJS design and single-state GOF testing in U-CARE: Consider two groups, group (1) are all those fish that were eventually caught at the weir on occasion 3; group (2) are those that were not.

For group (1) you could have,
1011
1010
1111
1110
0110
0111

For group (2) you could have,
1001
1000
1101
1100
0101
0100

Note all zeros for the second group, and all ones for the first group on occasion 3. Therefore, for the second group, fix detection probability (p) on occasion 3 to zero -- these fish were not encountered on this occasion. For the first group, fix p = 1 on occasion 3 -- these fish were all encountered on this occasion at the weir. The fixing that I'm referring to would occur in program mark of course when specifying your CJS models. Regarding GOF, group (1) provides four occasions of data, and group (2) just three. Perhaps a simple single-state GOF solution is to assess these groups separately in U-CARE...import the first group as a four occasion study and the second as a three occasion study. If the data are not too sparse this strategy should work...

Nonetheless, I keep imaging Paul Doherty's voice in the background saying..."gosh, I'd want to think about this more." And I agree with him. My instincts are suggesting that a multi-state design might be more efficient and effective when it comes to modeling the data. I'll keep thinking about the problem and get back to you if I have any other thoughts...

andre