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I set up a study using a BACI design testing for the impacts of a restoration treatment on several species of wildlife. I conducted mark-recapture on small mammals in trapping grids. I had planned to analyze these data using closed capture models to estimate abundance on each grid by year, then use those abundance estimates as response variables in the BACI model. Then I became aware of random effects and zero-inflated models and planned to incorporate those.

This is what I imagine is a common problem in our world. Does anyone have thoughts integrating closed capture abundance estimates with generalized linear mixed models?

A more fundamental question: can you articulate what you mean by 'abundance' and justify the assumptions involved? There is no particular true 'abundance' associated with a trapping grid unless that samples an entire habitat island.
Murray

Hmmm. Interesting questions. I guess by abundance I mean, density at the time of sampling. I recognize this is a "snapshot" approach.

The assumptions of the closed capture framework (closed population, no births, deaths, immigration, or emigration) are definitely violated. I've had females give birth in traps, euthanized injured individuals, and had individuals move between trapping grids. I don't think there is anything I can do about these violations except make the case that they are minor. Trapping is done in as narrow a time frame as possible and for the most part the assumptions seem valid, even though I know they are not. How's that for hand waving?

Besides the closed capture assumptions, there are the assumptions of the larger BACI study design.

1. Abundance of the sampled population is representative of the larger population.
2. Changes in abundance of the sampled population can be attributed to the habitat manipulation. In other word there is a causal relationship between changes in abundance and the habitat manipulation. This assumption is strengthened through the use of reference sites.
3. A linear trend exists between temporal changes in abundance.
4. the system was in equilibrium before the manipulation. I'm not sure small mammals are ever in equilibrium.
5. All the statistical assumptions of the generalized mixed model apply.

Lots of assumptions here. Some testable, some not.

You really rose to the challenge, but not in quite the way I was meaning!

I guess by abundance I mean, density at the time of sampling.

I like this because (i) it shows that you and I share an understanding of 'abundance' as a fuzzy umbrella term for density and population size; others also use 'abundance' as a jargon term for 'population size' (ii) if you want to model density then you probably should be using spatially explicit capture-recapture methods, not methods in which population size is the parameter of interest. Historically these issues have been fudged, but there is no longer any need to do that.

You seem to be on top of the other assumptions, but some off-the-cuff comments:

1. Abundance of the sampled population is representative of the larger population.

This needn't be an assumption - it can be a matter of experimental design.

3. A linear trend exists between temporal changes in abundance.

It's easy to test for non-linear trend

4. the system was in equilibrium before the manipulation. I'm not sure small mammals are ever in equilibrium.

Small small mammals (absolutely) never...
Murray

Will 'secr' be a good framework for a BACI design? Will I be able to test for treatment effects or at least get grid specific estimates of density that I can use in a mixed model.

Rereading your reply above Murray, I saw that it is an appropriate, likely even most appropriate method.

Will I be able to test for treatment effects...

To the extent of comparing models by AIC, anyway

at least get grid specific estimates of density that I can use in a mixed model.

Yes, that is possible.