RD pradel huggins p&c issue with derived abundance estimates

[matthewklein]

Hello all,

I am attempting to use a robust design pradel huggins p and c model to estimate survival and recruitment rates and derive estimates of lambda and abundance in eastern massasauga rattlesnakes. The capture history data has a total of 217 secondary occasions with 15 primary occasions. There is an unequal number of secondary occasions per primary occasion. The first 5 primaries encompass two consecutive months of nearly continuous secondary capture occasions, and the remaining primary occasions include between 3 and 5 secondary occasions. I used dot notation to specify when sampling did not occur or when a snake was censored as not available for capture (being held in captivity for some time). Additionally, sampling did not occur in 2020, so I included 2 secondary occasions coded with dot notation.

When attempting to fit any model, the results output realistic estimates survival, recruitment, capture, recapture, and lambda, however, it fails to provide estimates of abundance. Abundance estimates are all zeros, with upper and lower confidence intervals that are identical. Below are the derived results for abundance as an example of the issue:

Estimates of Derived Parameters
Population Estimates of {Phi(ASL + AvgSVL + AvgSVL^2) f(AvgSVL 4yr prior) p(b + effort)}
95% Confidence Interval
Grp. Sess. N-hat Standard Error Lower Upper
---- ----- -------------- -------------- -------------- --------------
1 1 0.0000000 0.0000000 29.000000 29.000000
1 2 0.0000000 0.0000000 37.000000 37.000000
1 3 0.0000000 0.0000000 47.000000 47.000000
1 4 0.0000000 0.0000000 30.000000 30.000000
1 5 0.0000000 0.0000000 28.000000 28.000000
1 6 0.0000000 0.0000000 30.000000 30.000000
1 7 0.0000000 0.0000000 23.000000 23.000000
1 8 0.0000000 0.0000000 15.000000 15.000000
1 9 0.0000000 0.0000000 39.000000 39.000000
1 10 0.0000000 0.0000000 0.2225074E-307 0.2225074E-307
1 11 0.0000000 0.0000000 17.000000 17.000000
1 12 0.0000000 0.0000000 20.000000 20.000000
1 13 0.0000000 0.0000000 19.000000 19.000000
1 14 0.0000000 0.0000000 29.000000 29.000000
1 15 0.0000000 0.0000000 28.000000 28.000000

To troubleshoot the issue, I have checked my capture history data, and it looks fine. If I fit reduced versions of my global model, I still get the same issue. I then attempted to use one of MARKS example robust design datasets to see if I could produce realistic estimates of abundance. I used the rd_simple1 example data and successfully fit a robust design pradel huggins p and c with realistic estimates of abundance. For this test, I used 4 primary occasions with 4, 4, 4, and 3 secondary occasions. Here are the abundance results using the rd_simple1 data, showing no issue in deriving abundance estimates:

Population Estimates of {phi(.) f(.) p(b+time)}
95% Confidence Interval
Grp. Sess. N-hat Standard Error Lower Upper
---- ----- -------------- -------------- -------------- --------------
1 1 251.63530 6.7681073 241.31305 268.48905
1 2 246.33621 6.7010507 236.11963 263.02803
1 3 230.26532 9.4666589 215.31801 253.10238
1 4 182.45749 7.7589819 171.62838 203.37135

I then decided to include dot notation into the rd_simple1 dataset to replicate the dot notation included in my capture data. I replaced a single capture event with a period for a single individual, so now the rd_simple1 dataset has only 1 period in the entire capture history. Here are just the first 4 lines of the capture history showing the dot on the 4th line on the 3rd capture occasion:

111000000000000 146;
010101000000000 11;
110110000000000 8;
10.001110001001 1;

When replicating the models that I successfully fit with the original rd_simple1 dataset, it produced the same problem with abundance estimates that my dataset produced, seen here:

Population Estimates of {phi(.) f(.) p(b+time)}
95% Confidence Interval
Grp. Sess. N-hat Standard Error Lower Upper
---- ----- -------------- -------------- -------------- --------------
1 1 0.0000000 0.0000000 2756.0000 2756.0000
1 2 0.0000000 0.0000000 1736.0000 1736.0000
1 3 0.0000000 0.0000000 1178.0000 1178.0000
1 4 0.0000000 0.0000000 898.00000 898.00000

I can’t figure out why the inclusion of dots into capture histories is creating this problem, I felt confident that the robust design pradel huggins p and c model allowed for dot notation. Hoping someone may be able to provide some helpful insight, thanks!

Matthew

[murray.efford]

Hello Matthew
I cannot help with your immediate problem (perhaps RMark-specific?), but I was interested to reproduce your example. Where should I find rd_simple1? In RMark I find a dataset of that name but only 12 secondary sessions in total, whereas rd_complex1 has 15 secondary sessions and many more individuals than your population estimates indicate (I think).
Murray

[cooch]

All of the example data sets referenced/used in 'the Book' can be found here:

http://www.phidot.org/software/mark/doc ... rkdata.zip

The link to this .zip archive is found at the bottom of the pull down menu for the individual chapters (LHS) of the main page for 'the Book'.

[murray.efford]

Thanks Evan. 'rd_simple1.inp' distributed in RMark is different. And it seems that Matthew clipped out some data from rd_simple1 rather than using the whole thing. But this doesn't help with his problem.

[matthewklein]

Hey Murray,

I should clarify that I am working in MARK directly, not Rmark. The rd_simple1 provided with MARK does have 15 occasions, but as you say, it wouldn't necessarily change anything regarding this issue. And regarding "And it seems that Matthew clipped out some data from rd_simple1 rather than using the whole thing," I did use the entire dataset, I simply clipped the first 4 lines in my post to show exactly where the single dot was added to the rd_simple1 dataset, but my analysis includes the entire dataset.

As for as I can tell, you can build any RD pradel huggins p and c model and add as many or as few dots as you want to a dataset and it consistently fails to generate estimates of abundance.

[cooch]

Gary has been alerted to the issue - stay tuned. Kudos on a very complete presentation of the problem, and working through the details. And, thanks to Murray Efford for stepping up also.

[cooch]

Gary confirmed the bug, and has just posted a fixed version of MARK to his website (mirrored on PhiDot).

He is also going to make a few other minor tweaks that won't impact this particular problem.

[matthewklein]

Wonderful, thank you all for the help!

[cooch]

No problem. Your original description of the issue(s) you were having was a model for 'how to ask that sort of question'. Congratulations.