Evidence of Absence (EoA) is a USGS-produced statistical estimator that is intended to produce population estimates when the observed number of individuals is very low or zero. EoA is frequently used to estimate impacts to sensitive bird or bat species at wind energy production facilities. Because these sensitive species tend to be rare and fatalities are rarer still, fatality monitoring studies often result in few or no fatalities detected. 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 app calculates Evidence of Absence (EoA) fatality estimates based on carcass counts and detection probabilities over a number of years. It is not intended for the analysis of real data. It is intended to give a basic sense of what to expect from EoA for those who do not care to install the R statistical software or the USGS EoA software on their machines. 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 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.Years when monitoring does not occur can be
indicated by setting the detection probability to 0.001. The
Evidence of Absence estimator is responsive to the average detection
probability over all years.