Calculates the probability that a carcass that has fallen in the search area during n regular or irregular search intervals is found by a searcher.
ettersonEq14(s, f, J)
persistence probability, probability that a carcass persists a specific time interval (normally a day), i.e. daily persistence probability. Note that the same time unit as for the length of the search interval must be used.
searcher efficiency, i.e. the probability that a carcass present in the search area is found during one search.
a vector containing the lengths of the search intervals.
This formula can handle irregular search intervals. It assumes constant persistence time and constant searcher efficiency. Confidence intervals are not yet implemented, but a Monte Carlo confidence intervals will be calculated by the function estimateN with the argument form="etterson".
the probability that a carcass that has fallen into the search area during the study is found by the searcher.
In case of regular search intervals the functions ettersonEq14 and pkorner are equivalent (see first example). A mathematical proof for this equivalence is given in the tutorial to carcass (Korner-Nievergelt et al., re-submitted to Wildlife Biology June 2014). When search intervals are irregular, pkorner overestimates the detecton probability (i.e. underestimates fatality rates) as you see in the second example below.
M. A. Etterson
Etterson, M.A. (2013) Hidden Markov models for estimating animal mortality from antropogenic hazards. Ecological Applications, 23, 1915-1925.
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# in case of regular search intervals, the calculations below give the same results ettersonEq14(s=0.8, f=0.8, J=c(3,3,3,3,3)) pkorner(s=0.8, f=0.8, d=3, n=5) # in case of irregular search intervals the function ettersonEq14 is more appropriate ettersonEq14(s=0.8, f=0.8, J=c(3,5,1,4,2)) pkorner(s=0.8, f=0.8, d=mean(c(3,5,1,4,2)), n=5)
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