I'm working with some colleagues who have a large dataset with dead recoveries that are summarized in recovery matrices. The direct recoveries in the year following marking were not recorded and recovery matrices only include indirect recoveries in the years after the year of marking. Thus, the first diagonal of the recovery matrices is zero. I expected this would be problematic but wanted to confirm with an exploratory analysis.
I used the data for mallards that is an example dataset with Mark, and fit the age-structured model on page 8-14 to 8-15 of the manual:
- Code: Select all
/* San Luis Valley Mallards: Page 92, Brownie et al. 1985
encounter occasions=9, groups=2
glabel(1)=Adults
glabel(2)=Young */
recovery matrix group=1;
10 13 06 01 01 03 01 02 00;
58 21 16 15 13 06 01 01;
54 39 23 18 11 10 06;
44 21 22 09 09 03;
55 39 23 11 12;
66 46 29 18;
101 59 30;
97 22;
21;
231 649 885 550 943 1077 1250 938 312;
recovery matrix group=2;
83 35 18 16 06 08 05 03 01;
103 21 13 11 08 06 06 00;
82 36 26 24 15 18 04;
153 39 22 21 16 08;
109 38 31 15 01;
113 64 29 22;
124 45 22;
95 25;
38;
962 702 1132 1201 1199 1155 1131 906 353;
The parameter estimates from the age-structured model (J= green, A=adult) perform nicely for survival (S, top panel) and recovery (f, bottom panel):
What if the direct recoveries are not available? I recoded the matrices with zeros for the direct recoveries:
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/* San Luis Valley Mallards: Page 92, Brownie et al. 1985
encounter occasions=9, groups=2
direct recoveries set to zero
glabel(1)=Adults
glabel(2)=Young */
recovery matrix group=1;
0 13 06 01 01 03 01 02 00;
0 21 16 15 13 06 01 01;
0 39 23 18 11 10 06;
0 21 22 09 09 03;
0 39 23 11 12;
0 46 29 18;
0 59 30;
0 22;
0;
231 649 885 550 943 1077 1250 938 312;
recovery matrix group=2;
0 35 18 16 06 08 05 03 01;
0 21 13 11 08 06 06 00;
0 36 26 24 15 18 04;
0 39 22 21 16 08;
0 38 31 15 01;
0 64 29 22;
0 45 22;
0 25;
0;
962 702 1132 1201 1199 1155 1131 906 353;
If the direct recoveries are missing, the model rankings and parameter estimates are quite different. Here are the estimates for the same model:
The difference in results might be expected from looking at the table of probability expressions on page 8-13 of the manual. The same recovery rates are on both the diagonal and offdiagonal, so missing data in the year after release should lead to negative bias in f for adults, and f*=0 for the juveniles. I haven't worked with dead recovery models much before, so perhaps this result is obvious to folks with more experience.
Posting this note as a caution if anybody else encounters the same situation. I expect that I cannot use the Brownie or Seber models without direct recoveries, but wondered if I have overlooked some clever way to code the PIMs, or a way to recode the recovery matrix or discount the number of releases. Looks like the BTO model might be an option if I drop both the direct recoveries and the number of releases, and assume a constant recovery rate. Chapter 8 was helpful in working through these steps.
Thanks, Brett.
B.K. Sandercock
Senior Research Scientist
Norwegian Institute for Nature Research