Negatively biased zero-truncated Poisson log-Normal

[lucac1980]

Dear all,
I’m trying to analyze a mark-resight dataset using the zero-truncated Poisson log-Normal estimator.
The capture history is composed of two primary occasions, one for 2015 and one for 2016.
In 2015 we capture for the first time 39 individuals (no captures had occurred before), and resightings were conducted immediately after captures, so that the number of marks available in 2015 was set to 39.
In 2016, 33 new individuals were captured prior to resightings. During the 2016 resighting sessions, 28 animals captured in 2015 were resighted, so that the minimum number of marks available for 2016 sums up to 61 individuals (33+28).
The capture history is included at the bottom of this message.

When trying to fit the zero-truncated Poisson log-Normal estimator (in MARK or RMark), for the year 2016, I get an estimate of 62 individuals (95% CI 55-77), which is clearly negatively biased, as the minimum number of marks alive is 61.
If I set 61 as the number of known marks for 2016, I get a more realistic estimate of 71 individuals (95% CI 66-76), but this approach is theoretically not quite correct, as up to 11 marked individuals captured in 2015 might still be alive, although they were never resighted in 2016.
Reading the paper of McClintock et al. on the zero-truncated PLNE, I found the negative bias could be due to: high level of heterogeneity in resightings, low rate of resighting, or excess of zeros in the capture history.
Individual heterogeneity is present, as models with sigma fixed to zero are considerably less supported, and the resighting rate is actually not that high. Not sure about the number of zeros.

My question is: what do you think could be the problem causing negative bias in the estimate for 2016, in this case? And how could it be fixed, if possible?

Best,
Luca





/* Poisson Log-Normal Mark-Resight_capture history_2015_16*/
/* Individual marks 1 group */
/* Occasions=1 groups=1 */
/* name - ch - freq - cov1 - cov2 */

/* Begin Input File */

+005 1 1 0
0201 1 1 0
02-0 1 1 0
+0-0 1 1 0
01+0 1 0 1
0203 1 1 0
+0-0 1 1 1
0202 1 1 0
0402 1 0 1
0202 1 0 1
01-0 1 1 0
0204 1 1 0
04+0 1 0 1
01+0 1 1 0
0302 1 1 0
0102 1 1 0
0402 1 1 0
0202 1 0 1
05+0 1 0 1
04-0 1 1 0
0501 1 0 1
0201 1 0 1
01-0 1 1 0
0202 1 1 0
0301 1 1 0
0504 1 1 0
02+0 1 1 0
05-0 1 1 0
+0-0 1 0 1
+0-0 1 1 1
01+0 1 1 0
0201 1 0 1
0201 1 1 1
0101 1 0 1
01-0 1 0 1
+002 1 0 1
+003 1 0 1
+001 1 1 0
01-0 1 1 0
..02 1 1 1
..01 1 1 0
..01 1 1 1
..+0 1 1 1
..04 1 1 1
..01 1 1 1
..+0 1 1 1
..02 1 1 1
..01 1 1 1
..04 1 1 0
..+0 1 1 0
..+0 1 1 0
..+0 1 1 0
..03 1 0 1
..+0 1 0 1
..01 1 1 1
..05 1 1 0
..01 1 0 1
..01 1 1 1
..+0 1 1 1
..+0 1 0 1
..03 1 1 0
..+0 1 1 0
..01 1 0 1
..01 1 0 1
..+0 1 1 0
..04 1 1 1
..+0 1 0 1
..01 1 1 0
..+0 1 0 1
..02 1 1 1
..04 1 1 0
..05 1 1 1

Unmarked Seen Group=1;
65 19;

Marked Unidentified Group=1;
29 21;

Known Marks Group=1;
39 0;

/* End Input File */