Seber recovery age-dependent survival and recovery

questions concerning analysis/theory using program MARK

Re: Seber recovery age-dependent survival and recovery

Postby cooch » Tue Feb 13, 2018 11:55 pm

tlyons4 wrote:I thought my ahy S had been set the same for marking groups (1) and parameter 2 is the survival for the first period for inviduals marked as HY. 3 and 4 refer to the recovery parameters for the different age classes.


So I see it is -- I misread it the first time, because of the way it was formatted (or rather, not formatted) in the post.

No matter. if you have the 'adults' share the parameter across marking groups, then you're fine (which is what Gary and Paul were noting). My response was based on my '(erroneous) assumption that you wanted a separate parameter for HY adults and for AHY adults (which is how I originally interpreted 'includes a difference between HY birds').

Now, if you have a separate parameter for HY and AHY adults (i.e., if you don't assume that all adults are the same), then you have problems with dead recovery data, but not live encounter data. The usual question is (I remember David Anderson asking me this) is 'why would you have a different parameter for HY individuals as adults, and AHY adults? Simple. In many situations, you have no way of knowing anything about adults marked AHY. You simply know they're 'adults'. While adults from HY tagged individuals are necessarily 'born there', adults from AHY markings represent (or, can) an unknown mixture of individuals from different locations, which might influence their survival. If your marking occurs at migration stopover locations, this is often a fairly big deal, as it turns out. So, you might think to address this by having one parameter for 'born there' adults (from HY marked individuals), and one parameter for 'not sure where they're from' adults (from AHY markings). Alas, as noted, this doesn't work.
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Re: Seber recovery age-dependent survival and recovery

Postby tlyons4 » Wed Feb 14, 2018 1:30 am

Ok, sorry for the inappropriate formatting. So if it's not structural, then I guess it is a quirk of the data? I don't think it's a data sparseness issue, I can post it if I know which way you'd all prefer it (long, wide, dput from R?). It's Canada goose data from BBL so I doubt it's too sparse.

Thanks for taking the time to respond, too
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Re: Seber recovery age-dependent survival and recovery

Postby ganghis » Wed Feb 14, 2018 12:20 pm

It's probably a quirk of your data. Where are these guys being marked and where are they being shot?

It might be useful to look at an M_ij array (see early Brownie papers for format) to help diagnose why r is being estimated at it's upper bound. Also, can you provide the MLEs for the 4 parameters (w SEs)?

Cheers, Paul
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Re: Seber recovery age-dependent survival and recovery

Postby egc » Wed Feb 14, 2018 12:53 pm

tlyons4 wrote:Ok, sorry for the inappropriate formatting.


Not inapproriate, just hard to navigate. For future reference, for posting 'formatted' text (say, real estimates, or PIMS), use the *code* tags. If the text is too large (so the formatting is screwed up by lines wrapping around), then you can make it smaller using the *size* tags. See the following example.


Code: Select all
                  Real Function Parameters of {all dot}
                                                               95% Confidence Interval
  Parameter                  Estimate       Standard Error      Lower           Upper
 --------------------------  --------------  --------------  --------------  --------------
     1:S B:breeding          0.6997163       0.0171193       0.6651331       0.7321662                           
     2:S N:nonbreeding       0.7884571       0.0244430       0.7366089       0.8324210                           
     3:p B:breeding          0.6791204       0.0382865       0.5999777       0.7491517                           
     4:p N:nonbreeding       0.6924749       0.0679490       0.5464458       0.8080068                           
     5:Psi B to N            0.4262530       0.0475556       0.3366448       0.5209806                           
     6:Psi N to N            0.1726099       0.0320968       0.1183929       0.2447619                 



To use it, try

Code: Select all
[size=90]
[code]

your text here...

[/code]
[/size]


Here's another example -- suppose you want to show the structure of a PIM. Simply, (i) open the 'full results', find the PIM, and copy it to the clipboard (don't try right-clicking in the PIM to copy to the clipboard - that approach does interesting things to the formatting), then (ii) embed the clipboard contents into the tags as shown above.


Code: Select all
 group=1 Phi rows=6 cols=6 Triang;   
            1   7   8   9  10  11; 
                2   8   9  10  11; 
                    3   9  10  11; 
                        4  10  11; 
                            5  11; 
                                6; 



Correctly formatted, so that evn old farts like Cooch can read it. ;-)
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Re: Seber recovery age-dependent survival and recovery

Postby tlyons4 » Wed Feb 14, 2018 1:15 pm

Thanks!
MLE's

Code: Select all
               estimate        se        lcl        ucl
S:(Intercept)  0.7328106 0.0236898  0.6863787  0.7792425
S:is.hy        1.2884772 0.0388241  1.2123820  1.3645723
r:(Intercept) -0.4838652 0.0202685 -0.5235913 -0.4441390
r:is.hy       19.5125050 0.0000000 19.5125050 19.5125050



Juvenile(HY) M-array

Code: Select all
release `2002` `2003` `2004` `2005` `2006` `2007` `2008` `2009` `2010` `2011` `2012` `2013` `2014` `2015` `2016` NeverRecovered
   
 1     273     20     41     24     14      6      6      3      4      2      2      0      3      0      0      0            148
 2     194            21     16     11     12      7      2      4      1      1      0      1      2      0      0            116
 3     439                   43     42     41     23      9      3      9      4      5      4      2      2      0            252
 4     543                          96     59     37     17     15     11      4      6      3      2      2      3            288
 5     381                                 38     60     20     22      7      5      8      2      0      3      2            214
 6     554                                        71     68     41     24     11     10      8      6      3      2            310
 7     749                                               96     92     42     23     18     13     13      5      1            446
 8     640                                                      73     85     46     24     17     14      3      7            371
 9     701                                                             82    100     51     36     18     19     11            384
10     841                                                                    75    113     74     44     20     14            501
11    1128                                                                          129    172     88     46     33            660
12     738                                                                                 109     93     55     31            450
13     907                                                                                        117    124     82            584
14    1176                                                                                               111    172            893
15     968                                                                                                      116            852




I guess I'm thinking because the raw % for direct recoveries is somewhere north of 10% across all cohorts, it should be estimable.

Geese are banded in NE, recovered anywhere, as long as they're reported to BBL.

I've tried running it through JAGS and using a prior for r that more or less forces it to be <0.6...won't converge yet because I'm trying to run it in the state-space format :\.

Thanks again for the help!
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Re: Seber recovery age-dependent survival and recovery

Postby ganghis » Wed Feb 14, 2018 2:49 pm

Since the model is time-invariant, we can collapse some things and maybe get a little bit of intuition.
So the total number of HY released (omitting the last year) is 9264, and the number of these killed in the 2nd year after release is 1237. So an inefficient point estimator for S_HY can be calculated as

hat(S_HY) = 1237/(9264*(1-S_AHY)*r_AHY = 1.06

So the model is going to "want" to estimate as high an S for HY birds as it can, and it's going to have to maximize r_HY to do so.

To me, this suggests some sort of assumption violation. For instance, it seems likely that adult survival is actually lower for birds marked as young than birds marked as adults (or that recovery rate is higher). Can you think of any explanation as to why this might be? I suppose one possibility is that 2nd year survival is lower than for ages 3+ since the mean age of birds marked as adults is going to be larger than birds marked as young who have lived to adulthood.
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Re: Seber recovery age-dependent survival and recovery

Postby tlyons4 » Wed Feb 14, 2018 3:02 pm

Yeah, I mean I'm trying to work towards a 3-age model, but even allowing for that, anytime HY birds are blocked out separately in S and r, rHY gets bumped to 1.

For example:

Code: Select all
Banded as HY:
S
1  2  2  3  3  3
   1  2  2  3  3
       1  2  2  3
          1  2  2....
Banded as AHY:
3  3  3  3  3  3
   3  3  3  3  3
      3  3  3  3....

r
HY
4  5  5  6  6  6
   4  5  5  6  6....

AHY

6  6  6  6  6  6
   6  6  6  6  6...


4 still comes back as 1

collapsing r for HY birds into the subadult or adult group produces sensible estimates if survival is allowed to follow that 3-age group structure andis sort of the route I'm taking now.

If the answer is that a simpler 2-age S and r model is too constrained for the data, thats fine. It's just that I've never really run into a problem getting estimates for simple models, usually it's the ones that are more highly-parameterized

But yes, I would think that there is some mixture of sub-adults in the group of AHY banded birds
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