I am designing an occupancy study of small terrestrial rodents in a forest that is difficult to access (rugged with high elevation and rainfall). Besides, resources are limited.
The problem with single occasion occupancy studies is that it becomes difficult to disentangle whether you missed the species at a given site because it was really not there (area not occupied, a true 0) or because it was there but you missed it (a false 0, a detectability issue). There are possible ways of doing so, namely for example that described by
Ferreira, M.; Filipe, A. F.; Bardos, D. C.; Magalhaes, M. F. & Beja, P. Modeling stream fish distributions using interval-censored detection times Ecology and Evolution, 2016, 6, 5530-5541 - I believe that paper is actually available on RG here (Article Modeling stream fish distributions using interval-censored d...
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In the proposed framework, you can use the time spent surveying until you detect the species at each site to tell you something about the probability of the species being present when you do not detect it. It has underlying assumptions, but all methods to deal with occupancy under imperfect detection do. SO you just have to consider whether the assumptions are valid under your setting.
I believe Tiago has covered the issue well. I would only add that, if possible, try to enhance you sampling effort (e.g. 2-4 times your normal number of Sherman live traps per site) as to reduce the chance of imperfect detection.