Estimating bird and bat fatality at wind farms: a practical overview of estimators, their assumptions and limitations

Abstract

Over the last few years, great efforts have been made to improve the methodologies used to assess bird and bat fatalities at wind farms. For that purpose, several mortality estimators have been proposed. In general, these estimators account for: 1) partial coverage; 2) carcass removal (e.g. by scavengers or decay); and 3) imperfect detection. Perhaps surprisingly, a universal estimator that ensures good quality estimates under general circumstances is still lacking. Further, the existing estimators include different adjustment approaches and a variety of often implicit and misunderstood assumptions that may not be valid, making it difficult for practitioners to choose between them. Focusing on bird and bat fatality at onshore wind farms, we summarise and discuss implementation aspects and the assumptions involved in seven commonly used estimators. This should provide researchers requiring these methods with a basis to choose the most appropriate estimator under a given set of conditions, and contribute to increased standards in wind farm wildlife fatality estimation.

Keywords:

• wildlife
• fatality estimator
• search area
• carcass removal
• detection probability
• wind power

Introduction

Wind power is widely considered to be an environmentally friendly source of energy with few negative impacts. However, wind energy facilities can be responsible for bird and bat direct mortality resulting from collision and, in the bats' case, barotrauma (Kunz et al. 2007; Baerwald et al. 2008; Drewitt & Langston 2008). Over the years, high fatality rates have been associated with some facilities or regions (e.g. Orloff & Flanerry 1992; Marti & Barrios 1995; Williams 2003), raising concerns about wind energy real impacts on birds and bats. In response, the development of methods to estimate wind farm fatalities and assess impacts on populations has become a priority.

Numerous reports (e.g. Young et al. 2003; Lekuona 2001; Kerlinger 2002; Anderson et al. 2004; Arnett 2005; Brown & Hamilton 2006) and, more recently, peer-reviewed literature (e.g. Osborn et al. 2000; Barrios & Rodríguez 2004; Smallwood 2007; de Lucas et al. 2008; Hull & Muir 2010; Rydell et al. 2010) have been published on the subject. Although methods to assess fatality at onshore facilities vary greatly they all aim to answer the question: ‘How many fatalities have occurred?’. In recent years, several authors have tried to find an answer to this question. However, the conceptual model behind the proposed estimators is still absent or incomplete, resulting in a constrained estimation method in the sense that the available procedures are not applicable under general circumstances (Korner-Nievergelt et al. 2011; Strickland et al. 2011). The most frequent methods used in practice to estimate fatality include the Erickson et al. (2000, 2004), Shoenfeld (2004), Kerns et al. (2005) and Jain et al. (2007) estimators. More recently, two other estimators have been proposed by Huso (2010) and Korner-Nievergelt et al. (2011). Simulations evidenced that these estimators can provide better estimates under specific circumstances. However, given their recent publication and associated complexity, these estimators are still not fully adopted in monitoring studies.

Several factors can influence the quality of bird and bat fatality estimates. Therefore these factors must be taken into account during the definition of the field protocols and the statistical data analysis. Contrary to offshore wind farms, where fatality estimation has to be based on flight activity and collision risk models (Band et al. 2007), at onshore facilities the fatality estimation is based on carcass searches around wind turbines. However, the number of carcasses found during searches does not necessarily correspond to the real number of birds and bats killed at wind farms, mainly because: 1) the study area is only partially covered; 2) carcasses are removed (e.g. by scavengers or decay) from the site; and 3) observers do not detect all the carcasses in the searched area.

In many studies, the search plots have been limited to a radius of 40 to 120 m around the turbines (Strickland et al. 2011), assuming zero fatality beyond that. However, bird and bat carcasses can be thrown by the wind turbine blades beyond this search radius. This means that the search radius could be insufficient and, consequently, will underestimate total fatalities (Smallwood 2007). In some cases, particularly at wind farms with a large number of turbines, only a small percentage of the turbines is generally searched in a systematic way. In this case the adjustment for partial coverage is done based on the fraction of randomly selected wind turbines. Additionally, it is often not possible to perform a complete search of a study area beneath the turbines. In these cases, the adjustment for this partial coverage is done by assuming that the number of dead animals present in the searched area is approximately proportional to the size of that area. Hence, an inclusion probability is defined proportionally to the size of the covered area and the number of observed carcasses is divided by that probability. However, the density of carcasses is known to be not constant, decreasing with the distance to turbines. Therefore scaling-up the observed fatality based on the proportion of the surveyed area may lead to overestimation.

Other key factors that justify the difference between observed fatality and true fatality are carcass removal and imperfect detection by observers, which can, in turn, be influenced by site- and carcass-specific characteristics, such as carcass size, season, type of vegetation cover and orography (Morrison 2002; Labrosse 2008).

All the available estimators account for these factors by including adjustment terms. However, existing estimators include different adjustment approaches and a variety of often implicit and misunderstood assumptions that may not be valid, making it difficult for practitioners to choose between them. In addition, field surveys (e.g. carcass searches, removal and detection trials) are often limited in time and budget, which may also have implications for the estimation of the adjustment terms and, consequently, on the accuracy and precision of the estimators. Another challenge faced by practitioners when adjusting the observed fatality is the fact that in many cases the estimators were developed independently and different notations are used to denote the same quantities. Additionally, although some authors use the same notation to denote the same quantity, this quantity may be calculated in a different way.

Focusing on bird and bat fatality at onshore wind farms, we summarise and discuss from a practical point-of-view the key adjustment terms and the assumptions associated with seven estimators used to estimate bird and bat mortality at wind farms. The objective is to provide a baseline tool for those who need to correct the observed fatality so they can select and properly apply an estimator that better fits their own monitoring programme and data, while acknowledging its assumptions and limitations. Additionally, the notation used across the different estimators has been standardised.

Estimators overview

In recent years, several calculation procedures have been used in monitoring reports or published in peer-reviewed papers to adjust the observed fatalities for the main error sources. In this section, we present the estimators that, as far as we are aware, were published and are most frequently used in practice. All the following methods aim to estimate a dead animal population size (M) within a region for a particular unit of time.

Erickson et al. (2000) defines a fatality estimator as:

1

where n is the total number of turbines, i is the interval between searches in days, C is the total number of carcasses found, n′ is the number of turbines sampled, is the mean carcass removal time and p is the average probability that a carcass is detected by the searchers. According to the authors, the variance of is defined using the variance of a ratio formula (Cochran 1977) as:

2

with the variance of the observed fatalities, var (C), being calculated by standard methods (Ramsey & Schafer 2002) and the variance of the adjustment terms, and p using the variance of a product formula (Goodman 1960).

The same authors defined the mean carcass removal time () as the average time (in days) that a carcass remains at the site before removal given by:

3

with z representing the total number of carcasses placed in a removal carcass trial, z′ the number of carcasses persisting at the end of the trial and t _l being the time of removal of carcass l (l=1,2, … ,z). This formula gives the maximum likelihood estimator for the mean value, assuming that the removal times follow an exponential distribution and that there is right-censoring of data (Erickson et al. 2004).

Shoenfeld (2004) published a report developing two estimators. The first version of the estimator assumes that the number of deaths occurs as a Poisson process and is defined as:

4

The second estimator suggested by the same author is given by:

5

To evaluate precision Shoenfeld suggests the use of confidence intervals and standard errors calculated using Monte Carlo/bootstrapping methods.

Kerns et al. (2005) proposed a different estimator. For weekly searches and three-week removal trials, the authors developed the following expression:

6

Here, the carcass persistence probability is estimated by the empiric cumulative survivor distribution function, represented by the term S _T (t) = 1 − P[T≤t], that corresponds to the observed probability that a carcass persists beyond t days. The equation accounts for the possibility that a carcass overlooked may be found in a subsequent search. The searcher detection probability (p) is calculated by the authors based on a distance sampling approach. Finally, A, that denotes an adjustment for the area not searched within the plot, is defined as:

7

where c _y is the number of fatalities found in the y-th 10 m distance band from the turbine, p _y is the estimated observer detection probability in the y-th 10 m distance band from the turbine, b _y is the proportion of the y-th 10 m distance bands that was sampled across all turbines, and y′ the total number of 10 m distance bands inside the each search plot. Variance and 90% confidence intervals are also calculated by Kerns et al. (2005) using Monte Carlo/bootstrapping methods.

Jain et al. (2007) suggested a simple estimator defined as:

8

where p _r is the probability of carcass persistence, that is defined by the empirical proportion of carcasses persisting approximately half of the search cycle (e.g. approximately after 4 days, assuming weekly searches), based on the assumption that the probability of a collision event is constant over all days of the search cycle. Jain et al (2007) calculated the variance of following the same standard methods used by Erickson et al. (2000).

Pollock (2007) proposed a similar estimation procedure to that suggested by Jain et al. (2007). However, Pollock's estimator defines p _r as:

9

with z _j being the number of carcasses remaining at the end of an interval j (j=1, … ,w) and w the number of time intervals over which a cohort of placed carcasses is followed. Additionally, Pollock seems to admit that the entire study area is covered, as this estimator does not define how to account for partial coverage.

Huso (2010) published the estimator:

10

where π is defined by the authors as the product of the proportion of the actual fatalities that is contained in the searchable area of the plot and the probability of including that plot in the sample. The parameter d=min(), with representing the length of time beyond which the probability of a carcass persisting is ≤ 1% (i.e. is such that ). Hence, assuming an exponential distribution, can be estimated as . The parameter called the ‘effective search interval’ is defined as . Besides point estimates, Huso (2010) calculates confidence intervals using bootstrapping methods.

Korner-Nievergelt et al. (2011) recently developed a new estimator defined as:

11

with p _d representing the daily persistence rate (i.e. the probability of a carcass not being removed during 24 h) and u=0, … , s − 1 where s is the number of searches performed at intervals of i days.

Korner-Nievergelt et al. (2011) also proposed a second estimator that, according to the authors, accounts for decreasing detection probability with the number of searches. Hence, for x (x=1, … ,s) searches:

12

where is the proportion of carcasses that is expected to persist after a time interval of i days, given that a proportion of p _d animals persist daily, and k is the factor by which the searcher detection probability decreases with each search. These authors do not define explicitly a variance estimator.

The notation introduced in this section is listed and available as supplementary material online (see file list prior to Acknowledgements section).

Comparative analysis of the estimators

Table 1 summarises the adjustment terms used in, and the assumptions associated with, each of the seven estimators under analysis. The observed fatality adjustment is done considering three main influencing factors: the searched area; carcass removal; and imperfect detection. Other factors, such as the background fatality (natural fatalities that are not caused by the wind turbines) and crippling (animals injured by the wind turbines that die outside the search area and are undetected), are still not accounted for by the estimators, as they are considered either relatively small or unknown in their magnitudes due to insufficient field research (Smallwood 2007).

Table 1  Comparative analysis of the adjustment terms and assumptions associated with the fatality estimators regarding searched area, search interval, carcass removal and searcher detection probability.

	Potential error sources
Estimator	Search area	Search interval	Carcass removal	Search detection probability
Erickson et al. 2000 (eq. 1/3)	Adjustment term based on the proportion of turbines searched.	No explicit requirements.	Adjustment term based on the mean persistence time (in days). Considers right-censored observations. Assumes that removal times follow an exponential distribution.	Adjustment term based on the empirical proportion of carcasses detected by the searchers. Carcass not found during the first search can be found in a subsequent search.
Shoenfeld 2004 (eq. 4/5)	Adjustment term based on the proportion of turbines searched.	In eq. 4 the number of searches is assumed to follow a Poisson model with a rate 1/λ (with λ being the mean time between searches). Eq. 5 implies regular search intervals.	Adjustment term based on the mean persistence time (in days). Considers right-censored observations. Assumes that removal times follow a Poisson distribution, with a rate (eq. 4), or an exponential distribution (eq. 5).	Adjustment term based on the empirical proportion of carcasses detected by searchers. Carcass not found during the first search can be found in a subsequent search.
Kerns et al. 2005 (eq. 6/7)	Adjustment term (A, see eq. 7) accounts for the area that is not searched.	Implies regular search intervals.	Carcass persistence probability is estimated by the empirical survivor function represented by ST(t) = 1 − P[T≤t].	Detection probability estimated by distance sampling analysis. Carcass not found during the first search can be found in a subsequent search. Assumes constant carcass detectability over time.
Jain et al. 2007 (eq. 8)	Adjustment term based on the proportion of turbines searched.	No explicit requirements.	Adjustment term based on the empirical proportion of persisting carcasses after approximately half of the search interval.	Adjustment term based on the empirical proportion of carcasses detected by searchers. Carcasses overlooked are assumed to have zero probability to be detected in subsequent searches.
Pollock (2007) (eq. 8/9)	Not considered in the original formula.	Implies regular search intervals.	Adjustment term based on the empirical proportion of persisting carcasses (see eq. 10). The author claims to assume that the number of verifications until the first carcass removal occurs follows a geometric model.	Adjustment term based on the empirical proportion of carcasses detected by searchers. Carcasses overlooked are assumed to have zero probability to be detected in subsequent searches.
Huso 2010 (eq. 10)	Adjustment term based on the proportion of animals that die outside the search plot and the probability of including that plot in the sample of the turbines searched.	Considers the ‘effective search interval’ (ν) based on the i (the length of time beyond which the probability of a carcass persisting is ≤ 1%).	Adjustment term based on the mean persistence time (in days). Considers right-censored observations. Assumes that removal times follow an exponential distribution.	Adjustment term based on the empirical proportion of carcasses detected by searchers. Carcasses overlooked are assumed to have zero probability to be detected in subsequent searches.
Korner-Nievergelt et al. 2011 (eq. 11/12)	Not considered in the original formula.	Implies regular search intervals.	Adjustment term based on daily persistence probability. Carcass removal is assumed to be constant over time.	Adjustment term based on the empirical proportion of carcasses detected by searchers. Carcasses not found during the first search can be found in a subsequent search. Assumes constant (eq. 11) or decreasing (eq. 12) carcass detectability over time.

In most cases, the adjustment regarding the search area is made considering the percentage of searched turbines (Table 1). Although not explicitly mentioned by any of the authors, whenever less than 100% of the area beneath the turbines (e.g. 50 m radius) is searched, this search limitation is taken into account when estimating the detection probability (e.g. by using a weighted average method that includes the percentage of area not searched). Kerns et al. (2005) proposed a different approach, and estimated the searcher detection probability exclusively for the actually searched areas. As a result, this estimator includes an additional adjustment term (‘A’, equation 7) that adjusts the estimated fatality by the area that was not searched. Huso (2010) also proposed a specific adjustment term that takes into account this partial coverage of the area beneath the turbines (‘π’, equation 10), although does not explain the method for this correction.

In order to minimise the negative impact on estimates resulting from an insufficient search radius, several studies have tried to determine the ideal search plot size, based on field data or by modelling the fall zone (e.g. Gauthreaux 1996; Osborn et al. 2000; Kerns et al. 2005; Hull & Muir 2010). However, in practice, and regardless of the recommendations, financial constraints take an important role when defining the sampling effort and, in many cases, the search is restricted to a radius of 50–60 m around the turbines. Since searches will always be limited in time and space, the fatality estimation method at wind farm sites has to account for the frequently small search radius and for the partial coverage of the study area.

None of the methods described above account for the fact that within the search plot the density of carcasses decreases with distance from the turbine, and that unsearched areas (e.g. due to dense vegetation) tend to be the ones further away from the turbines. Therefore, a simple adjustment to fatality based on the proportion of the plot not searched could lead to fatality overestimates (Strickland et al. 2011).

All estimators assume that the number of carcasses is zero at the beginning of the survey. However, carcasses can remain for long periods of the study area before being removed, and there is no guarantee that a carcass found during the first search died within the considered survey period (e.g. in the last seven days, assuming weekly searches). Kerlinger et al. (2007) suggest that a ‘clean sweep’ of the search plot should be performed prior to the start of the carcass survey. This would increase the likelihood of all carcasses found during the subsequent searches to be associated with events that occurred during the period of systematic surveys. Nevertheless, it is important to note that some carcasses could still be missed due to imperfect detection and field protocols rarely accommodate extra visits for ‘clean sweeps’. As an alternative, some authors recommend discarding the ‘old’ carcasses found during the first searches (Korner-Nievergelt et al. 2011), which can introduce errors in the estimation process.

The search interval, depending on the monitoring programme, can vary from one to 90 days, although recent guidelines advise the use of shorter search intervals (Rodrigues et al. 2008; Strickland et al. 2011). Increasing the frequency of the searches can, in some cases, improve the estimates (see below). However, in practice, the number of surveys performed over a year is also often limited by financial constraints. In order to reduce costs, irregular search protocols have been adopted using more intensive searches during ‘critical’ periods (e.g. bird and bat migration) and more widely spaced searches through the remaining periods. However, few estimators accommodate this possibility since regular searches are generally mandatory (Table 1). To overcome this constraint, fatality estimates are often produced separately for periods with regular search intervals and only then added to calculate the adjusted fatality for the total survey period. Nonetheless, this ‘split’ of the estimation procedure in several periods may introduce an additional error source for the estimated fatalities. From a realistic point-of-view, some estimators (e.g. Kerns et al. 2005) take into account that carcasses overlooked during the first search can be found in a subsequent search (Table 1). However, this adjustment term becomes useless for situations in which an animal dies at the very end of the search period and is not found during it. Hence, the adjusted fatality will be underestimated for this first period of regular searches. In the same way, estimates of the next search period will include fatalities that may have occurred in the previous one. Consequently, each time there is a ‘split’ of the search period to produce separate fatality estimates there is an additional error in the estimation process due to the conflict at both search interval boundaries.

From all the factors that affect the fatality estimation, carcass removal seems to be one of the more challenging ones. It has been shown that the field trial design is the basis for an accurate estimation of the carcass removal rate (Smallwood et al. 2010; Bernardino et al. 2011). Nevertheless, different approaches have been adopted to address this influence and estimate the associated adjustment term (Table 1). The Jain et al. (2007) and Korner-Nievergelt et al. (2011) estimators include an empirical estimation of carcass removal rate, while the Erickson et al. (2000) and several other estimators calculate the average time (days) that a carcass remains in the study area before it is removed. Typically, the removal adjustment term is estimated based on field trials where carcasses randomly placed under turbines are checked daily for a predetermined period of time. Hence, there are often carcasses that remain until the end of the trial for which the exact time of persistence is unknown. For these carcasses, it is only known that the time of persistence is larger than the trial length. Most of the estimators seem to account for these types of observations, said to be right-censored (Table 1). Nonetheless, given that in the removal trials carcasses are usually checked once a day, some observations are interval-censored in the sense that the exact time of persistence of a carcass is not observed and is only known to lie in a time interval obtained from the sequential visits. Interval-censored observations are not explicitly accounted for by any of the available estimators. Additionally, most of the adjustment terms for removal are based on an exponential distribution of times until removal (Table 1). Implicitly, this means that the removal hazard is constant over time which may not be a realistic assumption.

Given these limitations, Bispo et al. (2010) proposed a new methodology for the statistical analysis of the time of carcass removal using parametric survival models. This method allows to account for right- and interval-censored observations, and enables the application of different lifetime distributions (e.g. exponential, Weibull, log-logistic and log-normal) that might describe the data more appropriately. For instance, the hazard function of the log-logistic and log-normal distribution increases from 0 to reach a maximum and then decreases with time, approaching 0 as t → ∞. This means that the probability of a carcass being removed increases during the first few hours, which seems to be a realistic assumption since it has been observed to fit the observed removal trials data in several wind farms (Bispo et al. 2012). Nevertheless, each study area has its own ecological characteristics and, depending on the carcass size, season and local scavenger community, the ‘time until removal’ distribution may vary greatly (e.g. Wobeser & Wobeser 1992; Strickland et al. 2000; Anderson et al. 2004; Brown & Hamilton 2006). Therefore, it is important to guarantee that for each situation the parametric model that shows the best fit to the data is selected.

Besides carcass removal, all of the described estimators highlight the importance of adjusting the number of observed fatalities for the searcher's imperfect detection ability. This adjustment term is mostly defined by the empiric proportion of carcasses detected by searchers (e.g. Erickson et al. 2000), with Kerns et al. (2005) being the only authors that used the distance sampling framework to estimate the detection probability (Table 1). Almost all estimators assumed that the detection probability is constant over time. However, it should be expected that a carcass overlooked during the first search after the animal died, although available to be detected in subsequent searches, will be harder to find by the observer due to decay or partial scavenging. The only estimator to account for decreasing searcher detection probability is the one proposed by Korner-Nievergelt et al. (2011), in the second version of the estimator (equation 12).

Two studies have compared the performance of different estimators by simulation (Huso 2010; Korner-Nievergelt et al. 2011). Both showed that low searcher detection probabilities can strongly bias estimates, especially when the number of fatalities per year is low (under 10). These results underline the need to increase the chance of finding a carcass as much as possible. This can be accomplished, for example, by reducing the interval between searches and/or improving the detection probability through the use of dogs (Arnett 2006; Paula et al. 2011).

Nevertheless, it should also be taken into consideration that in Shoenfeld (2004) (equation 5), Jain et al. (2007) and Huso (2010) estimators short search intervals and long persistence times tend to bias the fatality estimates. According to Korner-Nievergelt et al. (2011), their estimator also tends to overestimate the number of fatalities when the search interval is short. However, it is robust when examining a decrease of removal probability with time.

Concluding remarks

In recent years several efforts have been made to improve and standardise the methodologies used to estimate bird and bat fatality at wind farms (e.g. Anderson et al. 1999; Rodrigues et al. 2008; Strickland et al. 2011). Hence, field protocols and data analysis tend to become more demanding and complex. However, despite recent research efforts, a universal estimator that ensures good quality estimates under general circumstances is still lacking (Korner-Nievergelt et al. 2011).

Fatality estimates are influenced by different factors, such as search interval, carcass persistence time and searcher detection ability. Insufficient search radius, partial coverage of the study area and cumulative fatalities, are error sources which have not been fully addressed by the available estimators and need further research. Carcass removal and search detection trials experimental designs are also still not properly defined in terms of better cost/benefit relationships (minimising the field effort without seriously compromising the accuracy or precision of the estimates for the fatality adjustment terms). Hence, further work is necessary so that well-planned field procedures are established as a basis for a proper adjustment terms estimation and the methods’ limitations can be overcome on the fatality estimation process. Until then, for each study case the most appropriate methods and estimator should be chosen, bearing in mind its assumptions and limitations when assessing the overall impacts and comparing results from different monitoring programmes.

Supplementary data

Supplementary file: List of standard notation used.

Acknowledgements

This research is part of the R&D project, Wind & Biodiversity, co-financed by the national programme of incentives for the Portuguese businesses and industry QREN (in the scope of its R&D incentive programme), under the operational programme Mais Centro, and with the support of the European Regional Development Fund.

The study was also partially sponsored by national funds through the Fundação Nacional para a Ciência e Tecnologia, Portugal - FCT under the project PEst-OE/MAT/UI0006/2011.

Notes

Supplementary data available online at www.tandfonline.com/10.1080/03014223.2012.758155 Supplementary file: List of the used standard notation.