Multi-state cumulative survival estimates - delta method

[SoConfused]

Hi all,

I have a MS model for a population of hatchery-release fish (known birth years and stocking numbers). Fish are released in age 1. I have 2 strata; survival differs between strata, birth year, and ageclass (2 levels: first year post-release and all subsequent years). Psi is ~stratum + ageclass. My goal is to estimate the current population size, given the known stocking numbers and the estimated S and Psi. Ideally, I'd be able to calculate pop size in each of the 2 strata separately, as well as combined.

Of the similar topics, this: http://www.phidot.org/forum/viewtopic.php?f=21&t=4158 seems to be the closest to what I'm looking for. However, the awesome function Jeff provided calculates S*Psi for each time, whereas I need to propagate my population throughout time. Is there a clean(ish) way to do that? My brain explodes trying to picture specifying manually all the possible stayed-left-survived-died scenarios through a loop.

Thank you!

[jlaake]

I'm a bit confused by your post which is titled cumulative survival but your text says that you want abundance through time and presumably by stratum. If it is abundance that you want, then you may want to consider the MSJS model in MARK but since these are releases you would want to fix the known probability of entries. From what Bill Kendall has told me, it estimates conditional abundance which I took to mean that he uses n/p where n is the number observed at an occasion and in a stratum and p is the probability of capture/ detection. This you can do the same with your MS model. The only issue would be estimating the variances and confidence intervals which is certainly doable. Thus rather than projecting the number still alive, you estimate it. Bill has also suggested to me fitting the data into an MSORD framework. Maybe Bill will have some thoughts on this.

[cooch]

I'm a bit confused by your post which is titled cumulative survival but your text says that you want abundance through time and presumably by stratum. If it is abundance that you want, then you may want to consider the MSJS model in MARK but since these are releases you would want to fix the known probability of entries. From what Bill Kendall has told me, it estimates conditional abundance which I took to mean that he uses n/p where n is the number observed at an occasion and in a stratum and p is the probability of capture/ detection.

Current chapter 14 in the MARK book: http://www.phidot.org/software/mark/doc ... chap14.pdf

[SoConfused]

Thank you for your replies, Jeff and Evan!

Jeff - apologies for the confusion. If I have the cumulative survivals, do I not get the abundance simply by multiplying those by the known release numbers?

I was really hoping to stay within RMark (R user of ~20 years, PIM editing is not my strong suit).

A couple of clarification questions:
1) fixing pent values - do you mean fixing all pent values to 0?
2) Using n/p - does this mean ignoring S and Psi values, and literally using the total # of fish observed at each occasion (a mix of recaps and first-time captures since original stocking) and dividing those by the p for that group/occasion? I'd appreciate any pointers for the CI estimation - both within stratum and across strata.

[jlaake]

MSJS is supported in RMark. If it isn't in the CRAN version ( I believe it is) I can send you a link to my Google drive for the most recent version.

I'm assuming you want abundance by stratum and survival can vary by stratum, then it isn't just cumulative survival.

1. What you set pent values to will depend on your release structure.

2. Yes. Easier to estimate N by stratum by occasion. I have some functions in RMark to use this approach that I used for some polar bear work with CJS models. Can't remember function names at present. Look at help index for RMark. Maybe in utility functions.

[cooch]

2. Yes. Easier to estimate N by stratum by occasion. I have some functions in RMark to use this approach that I used for some polar bear work with CJS models. Can't remember function names at present. Look at help index for RMark. Maybe in utility functions.

There is a short addendum to the robust design chapter (15) in the MARK book that runs through the basics of getting MARK to do the 'heavy lifting' for deriving estimates of uncertainty for abundance estimates for open populations (as an aside, you can also do it as a derived parameter using MCMC in MARK). N as M(t+1)/p* is easy enough, but getting the variances on N is a bit more involved. Not hugely difficult using Delta method. But, not necessary if you get MARK to do the work for you.

[SoConfused]

Jeff - ah yes, the pop.est function to estimate abundance from CJS (which I have used over the years).
I did just find the MS_popan in the RMark help file

Converts data and optionally creates and structures design data list such that population size can be
derived with multistate data. Variance estimate is questionable.

Aside from the variance warning - should I look into that instead of diving into MSJS? Or as a supplement to the pop.est approach?

The CRAN version of RMark doesn't seem to have MSJS unless I missed something. If you're up for sharing, that would be great!

For fixing pents - every year, all 1-year-old fish are dumped into the river. They're not recruiting to gear until a year later. So stocking is a single-day addition of fish, every year, and we only see them in recaps a year later. Would that make pent 1 on the year of release and 0 for all subsequent years, for each birth-year?

Evan - thank you so much for the pointers, I might give it a try if I get stuck with RMark. It's been so long since I worked in MARK itself...

[jlaake]

I wasn't able to get to phidot for awhile so I responded offlist with link to version of RMark with MSJS on my Google drive.

I realized that I didn't answer some of the questions and it would best to look at Chapter 14 as Evan suggested with regards to pent but if it was just straight POPAN you would compute fraction of the fish released each year of the total and set pent to that. Just be aware that proportion in population prior to first capture occasion is computed by subtraction.

But given these are all releases it is probably easiest to stick with pop_est. I provided more details offlist. That said if you decide to go with MSJS you could fit models and it provides abundance estimates and confidence intervals if I recall correctly. You could use Evan's suggestion by exporting model to MARK and then use that model with his suggestion without building the model in MARK interface.