Data type selection and small sample size

questions concerning analysis/theory using program MARK

Data type selection and small sample size

Postby Ataucher » Thu Aug 10, 2017 11:14 am

Hi there,
I am trying to run models in the closed capture type. We collected capture-mark-recapture data on hedgehogs in four parts of the city. As the data collection took part over relatively short time, I think I am fine with using a "closed" system and I will be estimating abundances in different areas individually.
As I simply want to estimate abundance (not taking individual covariates into account), is it right, that I am best of using a "Full likelihood p and c" data type? I then calculated the pre-defined models and took the weighted average for the abundance estimate.
Additionally, two of my areas has so few hedgehogs (4 individuals found on 8 capture occasions) that I don't get reliable estimates. Is there a way to calculate some kind of estimate, as we invested the same search effort in all four areas?
Thank you very much for any help.
Best wishes,
Anouk
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Re: Data type selection and small sample size

Postby ehileman » Fri Sep 01, 2017 3:53 pm

Hi Anouk,

As I simply want to estimate abundance (not taking individual covariates into account), is it right, that I am best of using a "Full likelihood p and c" data type? I then calculated the pre-defined models and took the weighted average for the abundance estimate.

Using full likelihood closed models and model averaging in the scenario you described seems reasonable to me. However, it sounds like you may have very sparse data, at least for two of your populations. In my experience, Huggins closed models (conditional likelihood) tend to perform better than full likelihood models when data are sparse. Another benefit of using conditional likelihood (i.e., the Huggins model) is that you can estimate overdispersion using the Fletcher c-hat method. See chapter 5 of Evan and Gary’s manual and Fletcher (2012) for details.

Abundance estimators are notoriously sensitive to latent heterogeneity. Given that you have eight sampling occasions, you might consider using Huggins Closed models with Pledger (discrete) mixtures (2 mixtures are usually adequate) or random (continuous) effects if your encounter probabilities are decent (>20%, White and Cooch 2017).

Additionally, two of my areas has so few hedgehogs (4 individuals found on 8 capture occasions) that I don't get reliable estimates. Is there a way to calculate some kind of estimate, as we invested the same search effort in all four areas?

Regarding the two areas with few captures, there is the risk of introducing bias, but you could consider combining these two datasets, or even additional datasets with similarly low encounter probabilities, to generate more precise estimates of encounter probabilities, which in turn would improve the precision for your derived estimates of abundance for the two sites with very low detection (See White 2005 for details). I hope this helps!

Eric

    Fletcher, D.J. 2012 Estimating overdispersion when fitting a generalized linear model to sparse data. Biometrika 99:230-237.
    White, G.C. 2005. Correcting wildlife counts using detection probabilities. Wildlife Research 32:211-216.
    White, G.C. & Cooch, E.G. 2017. Population abundance estimation with heterogeneous encounter probabilities using numerical integration. Journal of Wildlife Management 81:322-336.
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