Evidence of Absence (EoA) is a USGS-produced statistical estimator that is intended to produce fatality estimates when the observed number of fatalities is very low or zero during standardized carcass monitoring. EoA is frequently used to estimate impacts to sensitive bird or bat species at wind energy facilities. Because these sensitive species tend to be rare and fatalities are rarer, fatality monitoring studies often result in few or no fatalities detected during standardized carcass searches. Traditional estimators are unreliable in this case, and Evidence of Absence was developed as an alternative. Software to execute EoA and a user manual with more comprehensive notes on the EoA model is freely available from the USGS.
This application calculates fatality estimates using the Evidence of Absence (EoA) framework using carcass counts and detection probabilities over a number of years. The application can also be used to approximate detection probabilities (g).
This application is not intended for the analysis of real data. It is intended to give a basic sense of what to expect from EoA. The EoA software has the capacity to produce several different kinds of analyses, but the one that is illustrated here estimates total fatality (estimate of dead animals) based on the total count of carcasses from a monitoring study, and the detection probabilities during each year of the study.
The g Approximation tab calculates detection probabilities that can be used in the EoA behavior tab.
The EoA Behavior tab takes detection probabilities, carcass counts, and a desired credibility level and produces three figures.
The g figure shows the distribution of the mean detection probability over all monitoring years.
The take estimate (Mhat) figure gives the posterior distribution of total take. Credible bounds of this distribution are always integer-valued. A credible bound from this distribution is what USGS assumed would be used to evaluate compliance with incidental take permits. For bats, a credibility bound of 0.5 (corresponding to the median) is typically used to assess compliance with incidental take permits. The USFWS is contemplating use of the mean value from this distribution to test compliance for eagle incidental take permits. Note that the mean value is generally not an integer and is never less than the median (i.e. it is a more conservative metric); it can be considerably higher than the median. In general, the discrepancy between the mean and the median is greatest with low carcass counts, low detection probability, and low precision in detection probability.
The annual take rate (lambda) figure gives the posterior distribution of the estimated underlying take rate that may have produced the estimated total mortality. Credible bounds of this distribution take any non-negative value, and both credible bounds and the mean of the distribution for lambda tend to be higher than the median or mean of Mhat divided by the number of monitoring years*. USGS anticipated that hypothesis tests about the estimated annual take rate would be used to drive adaptive management programs for bats.
* This is due to the priors that are currently used to estimate Mhat and lambda.To export your g approximation result and its associated inputs, store the scenario, and then download the report. You can store as many scenarios as you would like to export as one excel file. Please note that these scenarios are saved for your current session only and will disappear if the application is closed or refreshed.