Advice on Simulated Encounter History Generation

[murray.efford]

For my own interest I just ran 1000 simulations for N = 100 and p=0.1, 0.2...0.8 in Density comparing the null & Huggins estimators for 2 occasions. As Jim predicted, a substantial fraction of simulations fail when p=0.1 (about 38%) and this leads to negative bias in N-hat at that p; the bias is similar for the two estimators (on the order -20%). However, very few simulations fail at p=0.2 (about 2%) and both estimators at that p are positively biased on the order of +20% - presumably the old small-sample problem with the Lincoln-Peterson estimator, for which the required adjustment is known. The bias drops below +5% for p>=0.4.
Murray

[murray.efford]

I meant Petersen, really
Murray

[mtreglia]

All,

Thank you again for your input- you have clarified many things for me and have given me some more insight into the problems of population estimation with low detectability. I will keep experimenting with different encounter probabilities. It seems that Huggins models do not fail as much at low p (as Jim suggested) but perhaps full-likelihood models give more accurate representations of what one would see in these cases, where you need to incorporate corrections for small sample? Also, Huggins yielded overestimates at high p. I am curious to see what happens as I change number of encounter periods.

I hope that I am done with asking questions for a few days, but it is really great to have such a supportive community in the field.

Cheers,
Mike

[mtreglia]

Hi All,

I was just playing around with this simulation again (first time in a few months) and found something interesting going on that I couldn't explain.

Previously, when running a Huggins closed capture simulation of a 2-encounter situation, with the assumptions of p=c and constant p I set all PIM values as the same (i.e, every box in both PIMs were filled in with 1). When running that simulation with low encounter probability (<0.1) I got a bunch of unestimable Ns because it seemed individuals no 'marked' individuals were not being 'recaptured' in the simulation.

I was just trying the same thing, but had each PIM entry as different (but set the beta values the same, 0.05), and successfully got derived Ns. While the derived Ns were much lower than the population size, which makes sense (often <20 individuals), I was surprised that all simulation runs went without a problem. Was I simply initially doing it wrong? I hope I'm not just missing some obvious big-picture thing, but would like to know if I am

I understand from previous posts on this forum that a 2 encounter Huggins Closed Capture model is the same as the Lincoln-Petersen estimator, though which one? Looking at the Pollock et al 1990 monograph, they list 3 variations of it. Also, is there a reference anybody can direct me to that explains how the Huggins Closed Capture model for 2 occasions is the same as the Lincoln-Petersen method? I am just curious to understand it better.

Thanks a lot!
Mike

[mtreglia]

Sorry,

realized I asked a somewhat stupid question. I didn't have my p2 constrained at all. If I set p2=c, with a simulated population detection probability of 0.05 I get lots of crazy high (unestimable?) derived N estimates . (though if somebody sees that I'm mistaken for some reason, please let me know)

I would still be curious to find out about the derivation of the Petersen method from the Huggins closed capture model if anybody has a reference to suggest.

Thanks,
Mike