by **jhines** » Sun Aug 21, 2022 11:07 am

To determine how many times you need to visit a site to allow detection of a species, you need to compute "p*", which is the probability that the species is detected at least once, given the species occupies the site. The formula for p* is:

p* = 1 - (1-p1)(1-p2)(1-p3)...(1-pk)

where p1-pk are the survey-specific detection probabilities, and k is the number of surveys. If all detection probabilities are the same then,

p* = 1 - (1-p)^k

Unless p = 1, p* will be less than 1, so it would require an infinite number of surveys to confirm that a species present or absent. Otherwise, you have to decide how close to 1.0 is acceptable for you. For example, if p is constant at 0.5, and k=4, then p* = .9375. If k=5, the p*=0.96875 and you would be >95% certain that you would detect the species if it was there with 5 surveys.

The 95% level in that example might seem extreme. The way the question is worded, you might want to know how many surveys are needed to get a reasonable chance of detecting the species. So, you might be satisfied with 50%. If the species is difficult to detect, you might even be satisfied with 10 or 20%. The lower the probability of detection, the more sites will be needed to get accurate estimates of occupancy.