Single season single species occupancy from camera trap summary data

[spilo...@gmail.com]

Hello

This question is about applying unmarked, but on a modelling assumption.

I have inherited a camera trap dataset which is summary form; rather than a row for each observation, there is a row for each camera trap location for each species, with columns for the total number of  sampling events (days in this case) and the total number of sampling events where a species was detected. There are no sampling dates, although I have the beginning and end dates for the sampling at each camera trap location.

So,  I could filter the data for one species and then create a matrix of camera trap locations (rows) and sampling days (rows) and populate the rows with 0s and 1s from the summary data; e,g, if the summary was 50 sampling days and detection in 6, i'd have 60 columns, 54 with 0 and 6 with 1.  However, I would have no idea in which order to put the 0s and 1s, so this would be random.

i could then still run the single species occupancy, with added site covariates, but no sampling covariates. I do not know of anything in the modelling that uses the sequence of 0s and 1s, so it  seems that my getting the correct number of these, but in a random order, does not matter. Or am I missing something?   

[Jim Baldwin]

If you don't use sampling covariates (not that you could use them anyway in this situation) AND are able to assume (as opposed to "willing to assume") a constant detection probability at a particular site and that the visits are independent, then it doesn't matter what order you put in the 0's and 1's.  However, I would be more structured in the placement:  0's followed by 1's followed by any NA's to match the counts for each site and the match the maximum number of visits at any one site.

For a theoretically based rationale consider a model with psi (probability of occupancy) being some function of the site covariates and p being the constant probability of a detection at an occupied for a single visit with independent visits with z zeros and o ones.  If o = 0 (i.e., no detections), then the log of the likelihood contribution is

     log(1-psi+psi*(1-p)^z)

If o > 0, then the log of the likelihood contribution is

     log(psi) + o * log(p) + z * log(1-p)

In both cases it is the count of the zero's and one's that tells the whole story and the position is not involved.

Jim

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