Seber recovery age-dependent survival and recovery

questions concerning analysis/theory using program MARK

Seber recovery age-dependent survival and recovery

Postby tlyons4 » Tue Feb 13, 2018 3:56 pm

I'm working on band-recovery using the Seber model. Birds are banded as HY and AHY, I have ~100-300 per each age class per year, for 15 years. When I try to fit the same age-structure to S and r that includes a difference between HY birds and others, the recovery estimate for HY birds always gets pinned at 1. I just wanted to clarify if this was a structural issue vs. some artifact of my data?
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Re: Seber recovery age-dependent survival and recovery

Postby cooch » Tue Feb 13, 2018 5:40 pm

tlyons4 wrote:I'm working on band-recovery using the Seber model. Birds are banded as HY and AHY, I have ~100-300 per each age class per year, for 15 years. When I try to fit the same age-structure to S and r that includes a difference between HY birds and others, the recovery estimate for HY birds always gets pinned at 1. I just wanted to clarify if this was a structural issue vs. some artifact of my data?


You'll need to provide more informatin than that -- specifically, what -- exactly -- is the PIM structure you're using for the two groups, for both parameters? That will help clarify vague language like 'includes a difference betwen HY birds and others' (which I could interpret in any number of ways).
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Re: Seber recovery age-dependent survival and recovery

Postby tlyons4 » Tue Feb 13, 2018 7:10 pm

Sorry. should have said HY vs. all others...It'd look something like this....

Code: Select all
    INPUT --- model={ S(~is.hy)r(~is.hy) };

  INPUT ---    group=1 S    rows=15 cols=15 Triang ;
  INPUT ---        1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ;
  INPUT ---        1 1 1 1 1 1 1 1 1 1 1 1 1 1 ;
  INPUT ---        1 1 1 1 1 1 1 1 1 1 1 1 1 ;
  INPUT ---        1 1 1 1 1 1 1 1 1 1 1 1 ;
  INPUT ---        1 1 1 1 1 1 1 1 1 1 1 ;
  INPUT ---        1 1 1 1 1 1 1 1 1 1 ;
  INPUT ---        1 1 1 1 1 1 1 1 1 ;
  INPUT ---        1 1 1 1 1 1 1 1 ;
  INPUT ---        1 1 1 1 1 1 1 ;
  INPUT ---        1 1 1 1 1 1 ;
  INPUT ---        1 1 1 1 1 ;
  INPUT ---        1 1 1 1 ;
  INPUT ---        1 1 1 ;
  INPUT ---        1 1 ;
  INPUT ---        1 ;


  INPUT ---    group=2 S    rows=15 cols=15 Triang ;
  INPUT ---        2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ;
  INPUT ---        2 1 1 1 1 1 1 1 1 1 1 1 1 1 ;
  INPUT ---        2 1 1 1 1 1 1 1 1 1 1 1 1 ;
  INPUT ---        2 1 1 1 1 1 1 1 1 1 1 1 ;
  INPUT ---        2 1 1 1 1 1 1 1 1 1 1 ;
  INPUT ---        2 1 1 1 1 1 1 1 1 1 ;
  INPUT ---        2 1 1 1 1 1 1 1 1 ;
  INPUT ---        2 1 1 1 1 1 1 1 ;
  INPUT ---        2 1 1 1 1 1 1 ;
  INPUT ---        2 1 1 1 1 1 ;
  INPUT ---        2 1 1 1 1 ;
  INPUT ---        2 1 1 1 ;
  INPUT ---        2 1 1 ;
  INPUT ---        2 1 ;
  INPUT ---        2 ;

  INPUT ---    group=1 r    rows=15 cols=15 Triang ;
  INPUT ---        3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 ;
  INPUT ---        3 3 3 3 3 3 3 3 3 3 3 3 3 3 ;
  INPUT ---        3 3 3 3 3 3 3 3 3 3 3 3 3 ;
  INPUT ---        3 3 3 3 3 3 3 3 3 3 3 3 ;
  INPUT ---        3 3 3 3 3 3 3 3 3 3 3 ;
  INPUT ---        3 3 3 3 3 3 3 3 3 3 ;
  INPUT ---        3 3 3 3 3 3 3 3 3 ;
  INPUT ---        3 3 3 3 3 3 3 3 ;
  INPUT ---        3 3 3 3 3 3 3 ;
  INPUT ---        3 3 3 3 3 3 ;
  INPUT ---        3 3 3 3 3 ;
  INPUT ---        3 3 3 3 ;
  INPUT ---        3 3 3 ;
  INPUT ---        3 3 ;
  INPUT ---        3 ;

  INPUT ---    group=2 r    rows=15 cols=15 Triang ;
  INPUT ---        4 3 3 3 3 3 3 3 3 3 3 3 3 3 3 ;
  INPUT ---        4 3 3 3 3 3 3 3 3 3 3 3 3 3 ;
  INPUT ---        4 3 3 3 3 3 3 3 3 3 3 3 3 ;
  INPUT ---        4 3 3 3 3 3 3 3 3 3 3 3 ;
  INPUT ---        4 3 3 3 3 3 3 3 3 3 3 ;
  INPUT ---        4 3 3 3 3 3 3 3 3 3 ;
  INPUT ---        4 3 3 3 3 3 3 3 3 ;
  INPUT ---        4 3 3 3 3 3 3 3 ;
  INPUT ---        4 3 3 3 3 3 3 ;
  INPUT ---        4 3 3 3 3 3 ;
  INPUT ---        4 3 3 3 3 ;
  INPUT ---        4 3 3 3 ;
  INPUT ---        4 3 3 ;
  INPUT ---        4 3 ;
  INPUT ---        4 ;


4 always come back as estimated as 1.
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Re: Seber recovery age-dependent survival and recovery

Postby cooch » Tue Feb 13, 2018 8:16 pm

Based on that design, and using the Seber parameterization, then you'll have trouble estimating the first-year diagonal for both parameters (S and r). Because you are using separate parameters between the groups for adult survival and recovery rates, you don't have any information needed to estimate first-year values. This is analogous to trying to estimate using a mark-as-young only data set. For live-encounter 9CJS) data, this isn't a problem, but with dead recovery data, it is. Your preferred strategy is to assume that 'adult survival is adult survival' (regardless of the age of marking) -- and that 'adult recovery rate is adult recovery rate' (ibid).

To prove this for yourself, try simulating data under the design you propose, and then see how well you can regenerate the true parameter values. YThis is easy to do in MARK (Appendix A), and you'll see quickly the problem.
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Re: Seber recovery age-dependent survival and recovery

Postby ganghis » Tue Feb 13, 2018 8:37 pm

I'm probably not thinking clearly, but I'm having trouble seeing why you wouldn't be able to estimate all 4 parameters. Clearly the adult (AHY) parameters are estimable, and then it seems like the HY would be through e.g. the number of recoveries of HY birds that survive their first year but are subsequently recovered (the expectation is R_hy * S_hy * (1-S_ahy) * r_ahy which only depends on 1 unknown; R_hy being the number of HY releases). Do you have many of these types of recoveries? It could be that the parameters are structurally identifiable but not estimable due to data sparseness.

Paul
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Re: Seber recovery age-dependent survival and recovery

Postby cooch » Tue Feb 13, 2018 9:21 pm

ganghis wrote:I'm probably not thinking clearly, but I'm having trouble seeing why you wouldn't be able to estimate all 4 parameters. Clearly the adult (AHY) parameters are estimable, and then it seems like the HY would be through e.g. the number of recoveries of HY birds that survive their first year but are subsequently recovered (the expectation is R_hy * S_hy * (1-S_ahy) * r_ahy which only depends on 1 unknown; R_hy being the number of HY releases). Do you have many of these types of recoveries? It could be that the parameters are structurally identifiable but not estimable due to data sparseness.

Paul


Considering the following analysis of data siumulated under a true generating model that follows the PIMs as originally posted, with the following parmaeter values: for HY individuals, S=0.5 on the diagonal, 0.85 off the diagonal (for adults). For marked as adult, S=0.7. For the recovery parameter, r=0.3 for the diagonal, 0.65 off the diagonal. For marked as adults, 0.55.

Based on 5000 individuals release per occasions, 7 total occasions, and 1000 simulated data sets, here are the summary results. I don't know about you NOAA types, but I don't see a mean of 0.41 being particularly close to 0.5, and 0.838 is not even ballpark to 0.65. Some estimates are spot on (specifically, the stuff from marked as AHY), some terrible (juv survival for HY marked individuals, both juv and adult recovery for HY marked individuals). Given the size of the simulated data, if things were estimable, they should be spot on. The whole thing is twitchy, which is why I made the initial observation. [Summary shown as mean and SE of same.]

Code: Select all
     REAL1           0.410          0.1337       
     REAL2           0.849          0.0150         
     REAL3           0.700          0.0067         
     REAL4           0.287          0.1476         
     REAL5           0.838          0.1398     
     REAL6           0.550          0.0082       


Further, Paul, if your logic is correct (and if I'm interpreting correctly in the first place) then you'd be able to estimate juvenile survival for individuals marked only as you, which you can't.
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Re: Seber recovery age-dependent survival and recovery

Postby gwhite » Tue Feb 13, 2018 10:28 pm

Evan:
You're not thinking correctly. The model is just the {S(age) r(age)} model in the NPMALES example distributed with MARK. Further, this is one of the models in Program BROWNIE and described in the Brownie et al. band recovery books.

Gary
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Re: Seber recovery age-dependent survival and recovery

Postby cooch » Tue Feb 13, 2018 11:20 pm

gwhite wrote:Evan:
You're not thinking correctly. The model is just the {S(age) r(age)} model in the NPMALES example distributed with MARK. Further, this is one of the models in Program BROWNIE and described in the Brownie et al. band recovery books.

Gary


In the Northpark example, the adult survival is set equal for both marking groups, which is why it works.

In other words, if you use something like

Code: Select all
1 2 2 2 2
  1 2 2 2
    1 2 2
      1 2
        1


for marked as young, and something like the following for marked as adults (where adult survival is indexed by parameter 2)

Code: Select all
2 2 2 2 2
  2 2 2 2
    2 2 2
      2 2
        2


then, no problem (this is analogous to the general structure use in the NP example).

But, if you use

Code: Select all
1 2 2 2 2
  1 2 2 2
    1 2 2
      1 2
        1


for marked as young, and something like the following for marked as adult, where you allow adult survival to differ as a function of ago of marking

Code: Select all
3 3 3 3 3
  3 3 3 3
    3 3 3
      3 3
        3


doesn't work so well. Because the extra information from the marked as adults does not inform juv estimates for marked as young, since they don't share the parameter.

It is this second structure that was described in the original post.

This is the basis of the simulation results I posted in response to Paul's post.
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Re: Seber recovery age-dependent survival and recovery

Postby cooch » Tue Feb 13, 2018 11:34 pm

Try the following data set - 7 occasions, 2 groups (HY and AHY, say) -- simulated under S=0.4 and 0.8 for the 2 age classes for HY individuals, S=0.7 for AHY adults. For r, r=0.2 and 0.4 for the 2 age-classes for HY individuals, and r=0. for the adults marked AHY.

Code: Select all
11000000000000 1194 851;
10000000000000 7589 7290;
10000001000000 196 315;
10010000000000 345 660;
10000100000000 241 430;
10000000000001 121 92;
10000000010000 171 200;
10000000000100 143 162;
00100000000000 7809 7416;
00110000000000 1161 872;
00100100000000 271 608;
00100000010000 207 316;
00100001000000 257 411;
00100000000001 136 147;
00100000000100 159 230;
00001000000000 7921 7464;
00001100000000 1149 894;
00001001000000 329 655;
00001000000100 201 311;
00001000010000 238 431;
00001000000001 162 245;
00000010000000 8023 7736;
00000011000000 1197 919;
00000010010000 318 618;
00000010000100 259 446;
00000010000001 203 281;
00000000110000 1157 887;
00000000100000 8279 8046;
00000000100001 252 385;
00000000100100 312 682;
00000000001000 8556 8488;
00000000001100 1135 913;
00000000001001 309 599;
00000000000010 8875 9141;
00000000000011 1125 859;


If I fit the try generating model to these data, I get the following real estimates:


Real Function Parameters of {S(HY - dot/dot, AHY - dot)r(HY - dot/dot AHY - dot)}
95% Confidence Interval
Parameter Estimate Standard Error Lower Upper
-------------------------- -------------- -------------- -------------- --------------
1:S 0.6808783 18.597501 0.2968076E-072 1.0000000
2:S 0.8146861 0.0087082 0.7970079 0.8311509
3:S 0.7009760 0.0042597 0.6925608 0.7092576
4:r 0.3634081 21.178386 0.6782752E-078 1.0000000
5:r 0.2458439 6.7149868 0.4828466E-031 1.0000000
6:r 0.2973238 0.0030336 0.2914124 0.3033038


As per my comments on Paul's note, the 'adult' estimates are OK for survival, but juvenile for HY is way off (0.680 vs true value of 0.4), as are both the recovery parameter estimates for HY individuals.

And, as indicated by the SE and CI, real 1 and real 4 and 5 are garbage anyone, which is why they're 'off'.
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Re: Seber recovery age-dependent survival and recovery

Postby tlyons4 » Tue Feb 13, 2018 11:42 pm

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.
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