Pop abundance with specified recruitment

questions concerning analysis/theory using program MARK

Pop abundance with specified recruitment

Postby SoConfused » Thu Mar 23, 2017 7:49 am

Hello,

I'm working on an abundance estimate for a fish species. There are known numbers of hatchery fish being stocked into a river where natural reproduction is essentially zero. However, these are not necessarily the fish from which the encounter histories are generated (since mark-recap occurs separately from stocking). I need to estimate population abundance at each sampling time, while (ideally) specifying number of stocked fish. My p values are time-specific.

Going back to the Gentle Intro and the RMark manuals, it looks like Pradrec may be my best bet for specifying recruitment. Is that correct? However:
1) how do I specify f (probability) based on recruitment numbers?
2) How do I get from Pradel's lambda to pop abundance? Reading through the Intro, I'm not sure that the setup satisfies the assumptions needed to extend the lambda to the population.

Are there options I'm missing? Any help would be appreciated...
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Re: Pop abundance with specified recruitment

Postby jlaake » Thu Mar 23, 2017 11:21 am

Can you differentiate between stocked and non-stocked fish when you do mark-recapture?
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Re: Pop abundance with specified recruitment

Postby SoConfused » Thu Mar 23, 2017 11:37 am

Yes I can. Sorry I didn't specify that earlier.
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Re: Pop abundance with specified recruitment

Postby jlaake » Thu Mar 23, 2017 11:43 am

Then it sounds like what you want is a mark-resight model or something similar depending on whether you individually marked fish that you caught during the mark-recapture component.
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Re: Pop abundance with specified recruitment

Postby SoConfused » Fri Mar 24, 2017 9:30 am

Thank you, Jeff, for your input. Yes, the marks are unique and identifiable - we know each fish we catch.

I spent some time with the Gentle Intro yesterday, reading about the mark-resight options, and still not sure about how to make it work. Would it be the immigration-emigration logit-normal one (due to lack of closure)? We don't really have primary and secondary occasions... Also - are any of them available in RMark? I couldn't find the mark-resight names in the (extensive) RMark model list.
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Re: Pop abundance with specified recruitment

Postby jlaake » Mon Mar 27, 2017 6:25 pm

Can someone else pitch in here? This is a unique situation where you have a known number of individuals introduced to the system with a mark-recapture experiment afterwards. In mark-resight you don't know the unmarked individuals so it isn't quite mark-resight unless I'm unaware of a model that handles that. Thinking off the cuff here, it would seem that maybe you might be able to use POPAN model by adding an occasion before first capture occasion and setting p=pent=0 for non-released individuals and p=pent=1 for released individuals. Then the capture history for released individuals would be supplemented with a 1 in front of their mark-recapture history for their release and all non-released would be given a 0. Any released individual that was never captured would have a 100000 capture history where the number of zeros would be the number of capture occasions. Anyone else have thoughts?
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Re: Pop abundance with specified recruitment

Postby Fish_Boy » Tue Nov 27, 2018 3:21 pm

I have a similar issue with Lake Sturgeon stocking, where the the spawn take year has a p_entry of 1 and subsequent recapture periods have a p_entry of 0. In theory this would allow individuals stocking cohorts to be tracked separately using attribute groups.
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Re: Pop abundance with specified recruitment

Postby Fish_Boy » Wed Nov 28, 2018 10:53 am

So I ran the scenario where p_entry are fixed to 1 in stocking year and 0 in subsequent years. The question of interest is whether survival of stocked fish is equivalent to that of wild fish. which are as follows

1:Phi 0.9526634 0.0419054 0.7650637 0.9920240
2:Phi 0.8598532 0.0687331 0.6673317 0.9494059

Here is what the output looks like for the stocked fish analysis setup exactly as described by Jeff...

95% Confidence Interval
Parameter Estimate Standard Error Lower Upper
-------------------------- -------------- -------------- -------------- --------------
1:Phi 0.9474167 0.3353901 0.3350112E-004 0.9999999
2:Phi 0.8501336 0.3598088 0.0218900 0.9993050
3:p 0.5000000 0.0000000 0.5000000 0.5000000
4:p 0.0049841 0.0039339 0.0010570 0.0231638
5:p 0.0236761 0.0184844 0.0050332 0.1041435
6:p 0.0472054 0.0513772 0.0052525 0.3173475
7:p 0.0322399 0.0466508 0.0017747 0.3843327
8:p 0.5000000 0.0000000 0.5000000 0.5000000
9:p 0.0113531 0.0074187 0.0031340 0.0402570
10:p 0.0133573 0.0131211 0.0019197 0.0869996
11:p 0.0510521 0.0662602 0.0036724 0.4398485
12:p 0.0369532 0.0638512 0.0011383 0.5636947
13:pent 1.0000000 0.0000000 1.0000000 1.0000000 Fixed
14:pent 0.0000000 0.0000000 0.0000000 0.0000000 Fixed
15:pent 0.0000000 0.0000000 0.0000000 0.0000000 Fixed
16:pent 0.0000000 0.0000000 0.0000000 0.0000000 Fixed
17:pent 1.0000000 0.0000000 1.0000000 1.0000000 Fixed
18:pent 0.0000000 0.0000000 0.0000000 0.0000000 Fixed
19:pent 0.0000000 0.0000000 0.0000000 0.0000000 Fixed
20:pent 0.0000000 0.0000000 0.0000000 0.0000000 Fixed
21:N 4517.6647 1639.5375 2346.1737 9142.3020
22:N 5213.9462 2262.3245 2409.4358 11962.067

If we fix the N values to the number of fish stocked the results are as follows:

95% Confidence Interval
Parameter Estimate Standard Error Lower Upper
-------------------------- -------------- -------------- -------------- --------------
1:Phi 0.5356345 0.0448511 0.4475319 0.6215678
2:Phi 0.3711202 0.0393411 0.2977992 0.4509015
3:p 0.5000000 0.0000000 0.5000000 0.5000000
4:p 0.1382633 0.0644139 0.0526791 0.3164446
5:p 0.3088231 0.0791087 0.1776959 0.4802058
6:p 0.6192431 0.0925804 0.4296534 0.7783262
7:p 0.7480586 0.1881076 0.2956751 0.9545466
8:p 0.5000000 0.6465017E-016 0.5000000 0.5000000
9:p 0.3371417 0.0386527 0.2659907 0.4165249
10:p 0.1918228 0.0843819 0.0755052 0.4082096
11:p 0.6197268 0.1057340 0.4034796 0.7970189
12:p 0.9999999 0.6049622E-003 0.1629360E-296 1.0000000
13:pent 1.0000000 0.0000000 1.0000000 1.0000000 Fixed
14:pent 0.0000000 0.0000000 0.0000000 0.0000000 Fixed
15:pent 0.0000000 0.0000000 0.0000000 0.0000000 Fixed
16:pent 0.0000000 0.0000000 0.0000000 0.0000000 Fixed
17:pent 1.0000000 0.0000000 1.0000000 1.0000000 Fixed
18:pent 0.0000000 0.0000000 0.0000000 0.0000000 Fixed
19:pent 0.0000000 0.0000000 0.0000000 0.0000000 Fixed
20:pent 0.0000000 0.0000000 0.0000000 0.0000000 Fixed
21:N 424.00000 0.0000000 424.00000 424.00000 Fixed
22:N 415.00000 0.0000000 415.00000 415.00000 Fixed

Notice the confidence interval for apparent survival estimates are now reasonable, but the estimates themselves are much lower.
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Re: Pop abundance with specified recruitment

Postby jlaake » Wed Nov 28, 2018 1:09 pm

You need to fix initial p to 1 for marked release.
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Re: Pop abundance with specified recruitment

Postby Fish_Boy » Wed Nov 28, 2018 1:31 pm

It does not seem to do anything to the output. POPAN defaults to 0.5 fixed for p1

95% Confidence Interval
Parameter Estimate Standard Error Lower Upper
-------------------------- -------------- -------------- -------------- --------------
1:Phi 0.9474167 0.3353901 0.3350112E-004 0.9999999
2:Phi 0.8501336 0.3598088 0.0218900 0.9993050
3:p 1.0000000 0.0000000 1.0000000 1.0000000 Fixed
4:p 0.0049841 0.0039339 0.0010570 0.0231638
5:p 0.0236761 0.0184844 0.0050332 0.1041435
6:p 0.0472054 0.0513772 0.0052525 0.3173475
7:p 0.0322399 0.0466508 0.0017747 0.3843327
8:p 1.0000000 0.0000000 1.0000000 1.0000000 Fixed
9:p 0.0113531 0.0074187 0.0031340 0.0402570
10:p 0.0133573 0.0131211 0.0019197 0.0869996
11:p 0.0510521 0.0662602 0.0036724 0.4398485
12:p 0.0369532 0.0638512 0.0011383 0.5636947
13:pent 1.0000000 0.0000000 1.0000000 1.0000000 Fixed
14:pent 0.0000000 0.0000000 0.0000000 0.0000000 Fixed
15:pent 0.0000000 0.0000000 0.0000000 0.0000000 Fixed
16:pent 0.0000000 0.0000000 0.0000000 0.0000000 Fixed
17:pent 1.0000000 0.0000000 1.0000000 1.0000000 Fixed
18:pent 0.0000000 0.0000000 0.0000000 0.0000000 Fixed
19:pent 0.0000000 0.0000000 0.0000000 0.0000000 Fixed
20:pent 0.0000000 0.0000000 0.0000000 0.0000000 Fixed
21:N 4517.6647 1639.5375 2346.1737 9142.3020
22:N 5213.9462 2262.3245 2409.4358 11962.067
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