Pradel Model with Juvenile Data - Trying to figure it out

questions concerning analysis/theory using program MARK

Pradel Model with Juvenile Data - Trying to figure it out

Postby PBurr » Tue Oct 15, 2019 1:41 pm

A data set, along with a rough manuscript draft and the beginning of an analysis was handed off to me to finish up. The data is straight forward: Every year, for 12 years, 500 chicks were captured and marked on an island used by a nesting colonial waterbird. “Recaptures” were done using re-sightings of those chicks as adults (>1 year) in subsequent years.

The analysis the co-authors would like to do is the Pradel model ‘Survival and recruitment’ in MARK, along with estimating the derived lambdas (Chapter 13 in the MARK book). The main question being: How have the annual population dynamics of this colony changed on this particular island?

I’ve spent some time reading through the MARK book along with other papers that describe and/or use variations of the Pradel model. While I understand the basic concept, conceptually these is a lot going on for me. I want to make sure the analysis is appropriate and I understand the results. Forgive my ignorance, I’m still trying to wrap my head around all of this.

1) Is there an issue with all marked individuals being first year (juvenile) birds? I know Pradel models use reverse time of the full encounter history, but in the case of this data any zeros before the initial banding are true zeros.

2) We know there are differences in survival between juveniles and adults, but the Pradel model does not allow for such effects. Chapter 7.1 in the MARK book describes how to do this with the CJS model and I understand that. How will this influence the final results of the Pradel model?

3) Would creating a grouping variable based on each cohort make sense or be informative? Perhaps it would do something to address the above?

4) If I were to run the Pradel ‘survival and recruitment’ model on all the data, with full time (year) dependency, what would the resulting estimates tell me? In the MARK book “lambda from time-symmetric models is the realized growth rate of the age class from which the encounter histories were generated”. Does this mean growth rates (and recruitment rates) are only specific to juveniles in the population, and not the colony itself? This statement confuses me because juveniles do grow into adults as the study progresses. There is a good chance I am not interpreting correctly.

Any guidance and feedback is very much appreciated! Population modeling is somewhat new to me, and I’m learning as I go. Thank you.
PBurr
 
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Re: Pradel Model with Juvenile Data - Trying to figure it ou

Postby cooch » Tue Oct 15, 2019 2:02 pm

PBurr wrote: Every year, for 12 years, 500 chicks were captured and marked on an island used by a nesting colonial waterbird. “Recaptures” were done using re-sightings of those chicks as adults (>1 year) in subsequent years.


Basic data design -- but you don't mention whether or not adults were tagged at the same time?

1) Is there an issue with all marked individuals being first year (juvenile) birds? I know Pradel models use reverse time of the full encounter history, but in the case of this data any zeros before the initial banding are true zeros.


Although perhaps that answers my 'design' question. And, for tagged as young, there are no 'sampling zeros' before the initial tagging event. The only such zeros would be structural, based on staggered entry of ech new marked cohort.

2) We know there are differences in survival between juveniles and adults, but the Pradel model does not allow for such effects. Chapter 7.1 in the MARK book describes how to do this with the CJS model and I understand that. How will this influence the final results of the Pradel model?


There is no age-specific Pradel model, in the sense of giving you an overal estimate of realized population growth, perhaps even partitioned by contributions from juvenile and adults portions of the population...this has been something that has been 'sought after' for some time.

4) If I were to run the Pradel ‘survival and recruitment’ model on all the data, with full time (year) dependency, what would the resulting estimates tell me? In the MARK book “lambda from time-symmetric models is the realized growth rate of the age class from which the encounter histories were generated”. Does this mean growth rates (and recruitment rates) are only specific to juveniles in the population, and not the colony itself? This statement confuses me because juveniles do grow into adults as the study progresses. There is a good chance I am not interpreting correctly.


It means what it says. A Pradel model fit to encounter data from inividuals marked as adults gives the realized growth rate for the adult segment of the population. Period. If the adult segment of the population dominates the dynamics (trajectory) of the population as a whole, then that migh be sufficient (thats essentially what the spotted owl rely on). I suspect you could concoct something that would give you the growth rate of the juvenile segment of the population, but if all babies are born at the colony, it isn't a particular informative measure.

Any guidance and feedback is very much appreciated! Population modeling is somewhat new to me, and I’m learning as I go. Thank you.


You've clearly done a lot of work, so no appolgies/caveats needed. My gut hunch is that with only marked as juveniles (and there are precious few studies that have that condition -- the vast majroty of studies have either marked as adult only, or both juveniles and adults), there will be real limits to what you can do in terms of Pradel models. I've done work using the 'marked as juveniles only' segment of 'my data', but then only to look at variation in recruitment rate, which is easily and robustly handled in a Pradel model.

I'll give it some more thought, though...my short term approach (which I haven't fully fleshed out) is a permutation of the robust design Pradel model, but there are issues there since the Pradel model doesn't allow for temporary emigration.
cooch
 
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Re: Pradel Model with Juvenile Data - Trying to figure it ou

Postby PBurr » Mon Oct 21, 2019 12:10 pm

Hello Dr. Cooch,

Thank you for your input!

cooch wrote:Although perhaps that answers my 'design' question. And, for tagged as young, there are no 'sampling zeros' before the initial tagging event. The only such zeros would be structural, based on staggered entry of ech new marked cohort.


I understand the zeros before the initial capture would just be structural as you describe. I was worried there might be an issue using the reverse modeling with Pradel. For example, a bird marked as a chick in year 4 of a 6 year study might have a history = 000101. Reversing that would be 101000, but those last three 0's are true zeros. This might not be an issue, or I'm just over thinking it, or I just don't understand it well enough yet. :?

cooch wrote:It means what it says. A Pradel model fit to encounter data from inividuals marked as adults gives the realized growth rate for the adult segment of the population. Period.


So in my case this would not work then? As individuals are marked as chicks and are re-sighted as adults. Would removing the first encounter (marked as chick) and only keeping re-sighting’s as adults be a work around of sorts? For example, changing an encounter history such as 101101 to 001101.

cooch wrote:My gut hunch is that with only marked as juveniles (and there are precious few studies that have that condition -- the vast majroty of studies have either marked as adult only, or both juveniles and adults), there will be real limits to what you can do in terms of Pradel models. I've done work using the 'marked as juveniles only' segment of 'my data', but then only to look at variation in recruitment rate, which is easily and robustly handled in a Pradel model.


I’m familiar with your paper on snow geese, if that is what you’re referring to. We may very likely explore variation in recruitment rate if nothing else can really be done with the data.

Let’s say I run the Pradel ‘recruitment and survival’ model on the data as is, with all individuals marked as chicks and re-sighted as adults in subsequent years. The model output will provide me with yearly estimates of recruitment, survival, and lambda. Would these estimates be representative of the colony? For example, if between 2007 and 2008 the model estimates a lambda of 1.2, can I claim the colony on this island was growing with a realized lambda of 1.2 for that time period? Or would this not be appropriate in my situation. Also the same for recruitment and survival?
PBurr
 
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Re: Pradel Model with Juvenile Data - Trying to figure it ou

Postby cooch » Tue Oct 22, 2019 9:26 pm

The problem you have is that the Pradel model conditions on the first encounter for estimating phi, but uses the leading 0's (prior to the first encounter) to model recruitment. With marked as young, there is nothing to estimate before the first encounter, since there is nothing before the first encounter (unless there are age classes before babies, which of course there aren't). Further, with marked as young, you'd not be able to partition age from time effects, since they'd be collinear.

Feel free to try your hand at simulating data ('when in doubt, simulate'), and fitting Pradel (or general J-S models), but I suspect you'll demonstrate for yourself the underlying reason why I can't think of a single paper applying J-S-type models to marked as young only data.
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