Evidence of Absence Regression: A Binomial N-Mixture Model for Estimating Fatalities at Wind Energy Facilities

Abstract

Estimating bird and bat fatalities caused by wind-turbine facilities is challenging when fatalities are rare and the number of observed carcasses is either exactly zero or very near zero. The rarity of found carcasses is exacerbated when particular species are rare, when carcasses degrade quickly, when they are removed by scavengers, or when they are not detected by observers. With few observed fatalities, common statistical methods like logistic, Poisson, or negative binomial regression are biased and prone to fail due to complete or quasi-complete separation. Here, we propose a binomial N-mixture model to estimate fatality rates and totals that incorporates study covariates and separate information on probability of detection. Our model extends the 'evidence of absence' model by relating carcass deposition rates to study covariates and by incorporating the number of turbines. Our model, which we call Evidence of Absence Regression (EoAR), can retrospectively and prospectively estimate the total number of birds or bats killed at a single wind-power facility or a fleet of wind-power facilities given covariates in the relation. Furthermore, with accurate prior distributions the model's results are extremely robust to complete or quasi-complete separation. In this paper, we describe the model, show its low bias and high precision via computer simulation, and apply it to bat fatalities observed on 21 wind power facilities in Iowa.

Evidence of absence regression: a binomial N‐mixture model for estimating fatalities at wind energy facilities

“…1; McDonald et al. 2021). We choose INBA and LBBA for these examples, but species has no bearing on the analysis because EoAR can be run on counts from a single species, collection of species, or event counts in general.…”

“…Data and R scripts (McDonald et al. 2021) necessary to carry out the simulations are available on the Dryad digital repository: https://doi.org/10.5061/dryad.2rbnzs7jh. The EoAR R package (EoAR 2021) is available on Zenodo: https://doi.org/10.5281/zenodo.5086908.…”

Binomial Mixture Model With U-shape Constraint

“…Royle (2004), Kéry (2008), O'Donnell, Thompson III, and Semlitsch (2015), and Wu et al (2015) estimate absolute abundance while accounting for imperfect detection using binomial detection models. The binomial mixture model was also used to estimate bird and bat fatalities at wind power facilities (McDonald et al, 2020).…”

“…where Q(•, •) is a bivariate measure of the binomial size m and the success probability s on N × [0, 1]. In the field of population survey in ecology, m can be modeled as Poisson or negative binomial random variable while s can be modeled as a beta random variable, linked to a linear combination of additional covariates by a logistic function (Royle, 2004;Kéry, 2008;O'Donnell, Thompson III, and Semlitsch, 2015;Wu et al, 2015;McDonald et al, 2020). Such models are always identifiable thanks to the parametric assumptions.…”