Estimating bird and bat fatalities caused by wind-turbine facilities is challenging when carcass counts are rare and produce counts that are either exactly zero or very near zero. The rarity of found carcasses is exacerbated when live members of a particular species are rare and when carcasses degrade quickly, are removed by scavengers, or are not detected by observers. With few observed carcass counts, common statistical methods like logistic, Poisson, or negative binomial regression are unreliable (statistically biased) and often fail to provide answers (i.e., fail to converge). Here, we propose a binomial N-mixture model that estimates fatality rates as well as the total number of carcass counts when these rates are expanded. Our model extends the ‘evidence of absence' model (Huso et al., 2015; Dalthorp, Huso, and Dail, 2017) by relating carcass deposition rates to study covariates and by incorporating terms that naturally scale counts from facilities of different sizes. Our model, which we call Evidence of Absence Regression (EoAR), can estimate the total number of birds or bats killed at a single wind energy facility or a fleet of wind energy facilities based on covariate values. Furthermore, with accurate prior distributions, the model's results are extremely robust to sparse data and unobserved combinations of covariate values. In this paper, we describe the model, show its low bias and high precision via computer simulation, and apply it to bat carcass counts observed at 21 wind energy facilities in Iowa.

This dataset contains mortalities of Indiana bats (INBA) (Myotis sodalis) and little brown bats (LBBA) (Myotis lucifugus) collected during 2015, 2016, and 2017 at twenty-one operating wind power facilities located in Iowa. We conducted these studies in part because INBA are listed as endangered under the Endangered Species Act and LBBA are considered rare and of concern. LBBA are considered to occur statewide in Iowa, while INBA officially occur only in its range that encompasses the southeast quarter (approximately) of the state.

During data collection, field personnel regularly searched for bat carcasses beneath turbines on plots of varying size and shape. In 2015 and 2017, personnel walked the perimeter of each turbine's pad and along the access road to a distance of 100m from the turbine. In 2016, technicians mowed square plots centered on the turbine at a random sample of 20% of the turbines. The size of mowed plots were 60m X 60m, 100m X 100m, or 200m X 200m. We call the mowed plots 'full' plots and technicians searched them by walking straight transects placed 10m apart. At the other 80% of turbines in 2016, technicians walked the perimeter of the turbine pad and along the access road out to a distance of 100m from the turbine. Data collection occurred at nine facilities in 2015, thirteen facilities in 2016, and two facilities in 2017. Three facilities received survey effort in both 2015 and 2016.

The covariates we include are ecological sub-region of the facility, an east-west grouping of facilities we termed 'stratum', and distance to the nearest river greater than class 4. Based on visit timing, visit frequency, searcher efficiency, carcass persistence, and the proportion of the carcass distribution searched, we computed facility and year-specific probabilities of detection (g) using the functions and interface in the GenEst R package (columns gAlpha and gBeta).

Metadata for the data set is included in the spreadsheet. 

Metadata for the R code files: 

The simulations require the EoAR R package. The EoAR R package can be obtained at https://github.com/tmcd82070/EoAR.

EoARSimulation1.R - R code to carry out simulations associated with Figure 2 of the main text which assessed the bias of EoAR for unimodal λ distribution over different numbers of sites and different distributions for probability of detection (g). Unmodified, the code also performs simulations for higher values of lambda than those plotted in Figure 2. Plots of simulations for higher values of lambda (i.e., lambda = 10, 25, and 50) show similar results.

EoARSimulation2.R - R code to carry out simulations associated with Figure 3 of the main text which assessed the bias of EoAR for two λ values over different numbers of sites and different distributions for probability of detection (g). Unmodified, the code also performs simulations for higher values of lambda than those plotted in Figure 3. Plots of simulations for higher values of lambda (i.e., lambda = 10 and 20) show similar results.

EoARSimulation3.R - R code to carry out simulations associated with Table 5 of the main text which assessed the bias and confidence interval coverage of EoAR for two λ values over different numbers of sites, different site sizes, and different distributions for probability of detection (g).