Average occupancy across sites within geographic boundaries

[birdman]

I was asked to analyze a dataset consisting of 9 years of point count data from three moderately large conservation areas. I had no input on the design so I’m seeking your collective wisdom. I’m currently focused on a single critically endangered species of primary interest. Later, we may choose to delve into a multispecies analysis, so any feedback at this point has broader implications.

In each management location, a grid of points was placed over the appropriate habitat; point counts were conducted at each point 3x per year during the breeding season of this resident bird. Thus, for each unit, I have many sites that were counted replicate times per season, and when entered into a multiseason occupancy analysis framework, I can generate annual colonization/extinction and derived occupancy estimates for all 330 points. Because the species is rare, and rarely detected, we are considering only those points where at least one detection occurred at some time. Our concern is mainly the decline in occupancy in relation to management actions and thus we feel this is justifiable. Management is mostly in relation to the use of prescribed fire, and has been implemented as burns on sub-units such that some points within an area experience fire each year, but individual points may go for numerous years without fire.

I’ve essentially completed the analysis, have a single, well-supported model, and am working on presentation of the results. I am not really interested in how occupancy changes at each point count location each year, but on how fire drives overall colonization and extinction.

Does anyone have thoughts on how best to generalize such patterns at the conservation area level? That is, what is the most appropriate way to present average rates of colonization or extinction across points at a conservation area, given that PRESENCE returns individual estimates at the point level? I should inject here that we “know” occupancy is declining, and that the trends in the declines are similar across the 3 populations, though temporally separated. One population is functionally extirpated, another is half what it was in the beginning but declining at a similar rate, and the third, most robust population is showing the same early patterns seen in elsewhere.

Secondly, is there a straightforward method for pulling the necessary information from PRESENCE and calculating the necessary estimates and CIs for graphical presentation in R or otherwise?

As noted, I was brought in late and given deadlines and data, and not much else. I appreciate any collective wisdom or thoughts you might have.

[Eurycea]

I have a few initial thoughts for you.

With regard to reporting occupancy for a large area, I think one option is to simply report "baseline" occupancy for each area, without your covariate. In other words, run a model that estimates individual parameters by area. You couldn't interpret this as an "average" but perhaps it would convey the information you or your stakeholders are interested in. For this, I would not exclude any sites.

PRESENCE gives you individual estimates for each point because each point presumably has a different covariate value. You can predict occupancy for an "average site" within your conservation area (assuming probabilistic sampling, which would not be the case if you are cherry-picking sites), for example, using an average covariate value. This is easily accomplished within R unmarked using the backTransform function.

Another approach to calculate the mean of your estimates might be to use a variance components method. Assuming it is appropriate in the first place, I think you'd need to be careful because whatever value you generate is for the specific sites you have sampled, and perhaps not generalizable to the whole conservation area (and it definitely won't be generalizable if you are cherry-picking sites). I would think very carefully about this approach as I'm not 100% certain it's correct. I don't know what options in software there are for implementing this. I think I used something like this once to get a mean for time-varying estimates of detection probability, and did the calculations in Excel using output from MARK.

You say "I am not really interested in how occupancy changes at each point count location each year, but on how fire drives overall colonization and extinction" - but, how occupancy changes at each site is the definition of colonization and extinction. Your inclusion and exclusion of fire effects on those occupancy parameters in the model should answer your question about how fire drives overall colonization and extinction, and so generalizing these patterns with means of parameters is not necessary. Simply report the model selection results. You might find it useful to report odds ratios as well, e.g. burned sites are 30% more likely to be colonized than unburned sites, for example. That's the type of approach I would take to summarizing your data.

Hope this gives you some food for thought.

Nate

[birdman]

Thanks Nate. Just back in the office after some unexpected travel and time away. I'll consider your suggestions and see what I can figure out. If anything else helpful arises, I'll post back here for the benefit of others.

[Eurycea]

Good luck. Thinking about this again, I rescind the recommendation of the variance components approach. Since you are talking about averaging values from a fixed effects model with covariates, I don't think that method would make any sense. Please let us know what you come up with.