DOI: 10.5061/dryad.2rbnzs7jh
title: Evidence of absence regression: a binomial N-mixture model for estimating fatalities at wind power facilities

description: 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.
description: This dataset contains mortalities of Indiana bats (INBA)
 (<em>Myotis sodalis</em>) and little brown bats (LBBA)
 (<em>Myotis lucifugus</em>) 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
 (<em>g</em>) using the functions and interface in the
 <em>GenEst</em> R package (columns
 <em>gAlpha</em> and <em>gBeta</em>).
description: 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 (<i>g</i>). 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 (<i>g</i>). 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 (<i>g</i>).