closed capture Huggins models

[Bryan Hamilton]

I'm working on some closed capture Huggins models for mice with mass as a covariate.

one model Mtb - {p(t), c(t)} returns a riduculous standard error around the derived estimate N (370-153,000) with the standard errors around p as essentially from 0-1. The estimates of c are realistic. M t+1 = 13.

The other 7 candidate models (M0, Mt, Mb, Mh, Mth, Mbh, Mtbh) return realistic estimates of p, c, and N.

Has anyone else had similar experiences with closed capture models?

[ganghis]

Hi Bryan,

Huggins type models have the potential to be unstable when capture probability for one or more individuals are estimated near 0. I imagine this may be the case for the model that is causing you problems. You might check to see if this the issue by plotting capture probability (p) as a function of mass for the offending model's parameter estimates and see if any of your mice have a mass giving a value close to zero. If this is the case, two options make sense: 1) discretize the mass covariate into 2 or more categories, or 2) throw out the offending model. If you decide on option 1), you'll need to rerun each of your models in order to make valid comparisons.

Shameless plug related to this issue:
Conn, P. B., A. D. Arthur, L. L. Bailey, and G. R. Singleton. 2006. Estimating the abundance of mouse populations of known size: promises and pitfalls of new methods. Ec Apps 16:829-837

Cheers, Paul Conn

[Bryan Hamilton]

Thanks Paul,

I'll try plotting mass as a function of capture probabilty and then move on from there. Do you think the low M t+b (13) may be contributing as well?

I read your "shameless plug"(Conn, P. B., A. D. Arthur, L. L. Bailey, and G. R. Singleton. 2006. Estimating the abundance of mouse populations of known size: promises and pitfalls of new methods. Ec Apps 16:829-837)

Its why I moved on to Huggins models from full likelihood models. It also relieved a lot of stress because most of my standard errors in estimating N included 0 when I was using mixtures. The use of mass as a covariate has generally stabilized my estimates of abundance.

[ganghis]

Bryan,

Sorry, your M_{t+1} figure didn't fully register when I first read your post. Yes, the problem may also be data sparseness... in fact, M_{t+1} is small enough that I would have very low confidence in any model-based point estimate generated from these data. Nevertheless, I think the best approach is to consider simple models for p, such as logit(p)=beta0+beta1*mass. At the very least, limit yourself to models where there are only a few effects on capture probability. For instance, mass + behavior or mass + time would be the farthest I'd go here, and even then you probably don't have enough data to estimate these effects reliably.

Hope this helps... it's definitely tough when sample sizes are small!

-Paul

[Bryan Hamilton]

Paul,

In one of my habitat types I have M (t+1) = 85 and in the other
M (t+1)=13.

For both habitats AIC supports the mixtures models (more so with the higher abundances) but with poor estimates of p and c (and sometimes N). Without the mixtures estimates of p, c, and N are more precise. I guess I'll have to accept that there is likely heterogeneity in the data but because of sparseness I'll be unable to model it.

Bryan