Occupancy: Defining visits in sites of varying sizes

[cnagy]

I have wrestled with an issue re: occupancy modeling for a while in numerous studies and figured I’d ask you folks here.

We are studying the distributions of a number of species in urban parks. Often this involves occupancy/detection modeling, where we sample systematically or randomly in many different parks. I’ll explain my question using a camera trapping situation, but it could apply to point counts or other methods.

Cameras within individual parks are likely not independent, closed sites, and thus we use whole parks as our separate sites. However we are not sure how to then define visits. The first option would be to make visits be the cameras in each park.
e.g., say I deployed cameras in 4 parks for 1 month (4 weeks). My data could be arranged as:

Code: Select all

   
       Cam1   Cam2   Cam3
Park1  0       1       1
Park2  1       1       1
Park3  0       0       0


Where a 1 would mean I detected the species at least once at that camera over the month, and a 0 would mean I didn’t detect the species at that camera ever.

The problem arises because these parks are different sizes and thus to adequately sample them, big parks get more cameras. Some of our parks get 2 cameras and some get 12 – 15 keeping a steady camera density. It seems that if I had a park with just, say, 2 cameras and did not get any detections, it could come out that the estimates for that park would be less precise since I “only sampled it twice”, even though in truth I sampled it equally – proportional to its size – as the larger parks with more visits. We would ideally like to be able to account for differences in detection rate across cameras, so I would like to go with the visits = cameras setup where I can enter sampling covariates on p if possible.

Alternately, we could define a visit as some time period (say, a trap-night or –week) in which the whole park was sampled, where a 1 or 0 would mean I either detected or didn’t detect the species anywhere in the park within a particular week. I have done analyses using visits=trap nights, but we are less interested in detection changes over time. It also would not reflect legitimate differences in sampling effort or camera density when cameras fail or are stolen.

It seems like these issues would arise in many occupancy studies where sites vary in total size (and thus in the amount of sampling effort needed). I’d appreciate anyone's thoughts or advice.

Thanks
chris

[bacollier]

Alternately, we could define a visit as some time period (say, a trap-night or –week) in which the whole park was sampled, where a 1 or 0 would mean I either detected or didn’t detect the species anywhere in the park within a particular week. I have done analyses using visits=trap nights, but we are less interested in detection changes over time. It also would not reflect legitimate differences in sampling effort or camera density when cameras fail or are stolen.

hanks
chris

Are you interested in estimating a RSF based on some covariates collected at the camera point locations? If so, then you would want to use temporal measures of your cameras (e.g., weekly samples) to estimate the occurrence process (MacKenzie 2006 I think) relative to conditions at the sample point.

If you are not interested in estimating some sort of a RSF for where species are likely to be distributed within the park, but rather for occurrence rates at the 'park' scale (e.g., park level estimates of occupancy), then I think the above is the appropriate option. The 'less cameras on small sites' issue falls away if you don't treat cameras as reps in your enc history to try and get a park-scale estimates.

It seems like these issues would arise in many occupancy studies where sites vary in total size (and thus in the amount of sampling effort needed). I’d appreciate anyone's thoughts or advice.

Its because the issue you are dealing with is not actually a occupancy modeling issue, but a sampling design issue. If you are doing park-level occupancy, then you sample on some temporal schedule and build your histories at the park level, if you are building a RSF for all parks or a specific park, then you sample repeatedly at locations within the park and have within-park locations as the rows in your capture history, you seem to be considering both, which makes this a 'what is your question' question.

You might have a look at MacKenzie and Royle (2005)-J. Applied Ecology and Efford and Dawson (2012)-Ecosphere as they discuss some of these issues.

Bret

[cnagy]

Hi Bret,
Thanks for the advice. We are interested in park-level questions so it looks like we'll go with the temporal repeats.

I wonder though if this problem would arise if you were using (or forced to use) spatial replicates. Sampling a larger area systematically would lead to more reps for that site than for a smaller site. Some minimum number of trap locations/point counts/etc would be needed i guess.

Thx
chris