Closed Capture vs. Huggins -Very Different Results

[cheryl]

Hello,
I have a fairly simple capture/recapture dataset with 44 individuals at a maximum of 8 time intervals (some missing data: individuals trapped from 4-8 timeperiods each). I have been trying to run some models to estimate capture/recapture probabilities and abundance. For all of the models, I am getting hugely different results using Huggins vs. standard closed capture models. I would really appreciate any help in why this is happening and if I can trust abundance estimates for either type of model. Thanks!

For instance: Here are results from a simple model {p(.),c(.)}

Huggins:
c= 0.331e-4 (se.0027)
p=0.662
N-hat=283920 (se 23048234)
c-hat=5.8
(all models have high c-hat, very low cap. prob estimates & high N-hats)

Closed Capture {p(.),c(.), N(.)}
p=0.262
c=0.662
N=47.7 (se 3.54)
c-hat=0.53
(Most CC models have c-hats<1, and singular values for N (se=0)- even though I constrain last c and p values. In all models, I have at least constrained p5=p6=p7=p8 and likewise for c.

I am testing models with and without groups (sex)- or with Huggins, I use sex as a single covariate. I am running simple models to look at- if p is lower for first few trapping events, if p=c, varies by sex, & also tried to test for 2 groups in Huggins heterogenous model.

Dataset with sex as covariate:
00001110 1 1;
01111111 1 1;
00000001 1 0;
010100.. 1 1;
001100.. 1 0;
1110.... 1 1;
0001.... 1 1;
001100.. 1 1;
0010.... 1 0;
0001.... 1 1;
0001.... 1 1;
0100.... 1 1;
0100.... 1 1;
1010.... 1 1;
0101.... 1 1;
0111.... 1 0;
1111.... 1 1;
0001.... 1 1;
1111.... 1 1;
0111.... 1 0;
1111.... 1 0;
0101.... 1 1;
0001.... 1 1;
0001.... 1 1;
0001.... 1 1;
0011.... 1 1;
0111.... 1 1;
0010.... 1 1;
0101.... 1 1;
00.00010 1 0;
00.01111 1 1;
0011.... 1 0;
0011.... 1 0;
0001.... 1 0;
0011.... 1 1;
001110.. 1 1;
010110.. 1 1;
000001.. 1 0;
010001.. 1 0;
000111.. 1 0;
000011.. 1 0;
000011.. 1 0;
001111.. 1 1;
000111.. 1 1;

[Paul Lukacs]

What are the '.' (missing data) representing in the encounter histories? In the open population models they would be unsampled individuals, but that doesn't cross over to the closed models well. For the closed models you would have to know whether each individual is available for trapping whether you caught them or not.

[cheryl]

The data represents individuals pooled among multiple sites of a sparse population. Some sites we were only able to sample 4 times & others up to 8 times.

[gwhite]

Cheryl:
For whatever reason, the Huggins estimator is unstable with this set of data. When I simulate the Huggins estimator with a low p value, I get lots of failures. Such behavior is to be expected -- see the Otis et al. 1978 Wildlife Monograph, or the White et al. Los Alamos report for explanations of how the Zippin estimator has a failure criterion, and what is happening with your data is that the Huggins estimator is hitting that failure.

Gary

[cheryl]

Gary,
Thank you so much for your follow up on this issue!
Cheryl