Introduction

The information needed to support effective conservation planning includes an understanding of how a species’ distribution, abundance, and demography vary with spatial heterogeneity in natural and anthropogenic features of its environment. At one end of the information spectrum, the distinction between a species’ area of occupancy (where it actually occurs within its geographic range) and its extent of occurrence (its geographic range; [1]) could identify areas where conservation efforts should be focused. Toward the other extreme, understanding how a species’ demography varies with habitat heterogeneity greatly aids in the identification of important areas and habitats for conservation, and enables modeling of the consequences of conservation actions (or inaction; e.g., [2, 3]). For many species of concern, however, demographic information (e.g., birth and survival rates) is not available and conservation planning must rely on indirect proxies of fitness including occurrence and abundance. Habitat selection theory suggests that territorial species should conform to the ideal despotic distribution (IDD; [4]), under which individuals select the highest suitability area that is currently unoccupied, and that the resulting distribution of territorial individuals is one where the highest suitability areas have higher densities of individuals and lower suitability areas have lower densities. Experimental and empirical evidence have generally supported the IDD theory [5, 6], including studies on raptors that have found an inverse relationship between territory size and prey abundance [7–10]. Thus, in the absence of data on how fitness varies with habitat for territorial species, variation in the density of territorial individuals can be interpreted as a proxy for spatial variation in habitat quality.

Using density as a proxy for habitat quality may be especially valuable in conservation planning for species with broad geographic ranges encompassing heterogeneous environments. For such species, it is unusual to have demographic information from multiple populations occupying different ecological settings (see [11] for an exception). This circumstance necessitates analyses and modeling with more readily available data on species occurrence and the relationships between location data and environmental covariates. To be useful for management and conservation, the resulting models must explicitly incorporate regional variation in habitat suitability.

These challenges are exemplified by conservation planning efforts for golden eagles (Aquila chrysaetos) whose breeding populations in western North America span diverse ecosystems from coastal woodlands and temperate forests to sagebrush steppe and southwestern deserts [12]. Golden eagles are large-bodied apex predators that occupy large but variable breeding home ranges (10s - >3,000 km²; [13]), and territories tend to be sparsely distributed at landscape scales. However, territory density can be relatively high (>6 territories/100 km² [14]) in localized areas with abundant nest substrates and prey populations. Breeding territories typically contain multiple nests and support long-term occupancy across multiple generations of golden eagles [15].

In contrast to the relative stability of breeding distributions, golden eagles exhibit a wide variety of intra- and inter-annual movement patterns throughout the annual cycle. For example, populations occupying northern latitudes migrate 1,000s of km between breeding and wintering areas [16, 17], while more southerly populations tend to be resident [12]. Even within resident populations, sub-adult golden eagles (2–4 years of age) may exhibit wide variation in dispersal distances ranging from 10s - >1,000 km [18]. The combination of resident, migratory and dispersing individuals may result in high seasonal variation in the density and composition of golden eagles occupying a given landscape.

As a consequence of their protected status under the Bald and Golden Eagle Protection Act (Eagle Act; 16 U.S.C 668-668d) and potential and actual threats to their populations, golden eagles have received substantial attention from both regulatory agencies [19] and researchers [20]. Golden eagle populations in the western U.S. are stable or slightly decreasing [19, 20], but there is growing concern that increased energy development and land-use change may result in significant future population declines. Threats such as lead poisoning, electrocution, habitat modification/loss, energy development (especially wind energy), and outdoor recreation have long been known or suspected to impact golden eagle populations [19, 21–26]. However, the extent to which these factors, individually or in concert, influence overall golden eagle populations is uncertain. Strategies for managing or reducing such threats require both spatial data on the distribution of hazards (e.g., electrocution risk or lead poisoning) as well as spatial data on the distribution and abundance of golden eagles [27].

Due to the extensive areas required for persistence of golden eagle populations, and myriad threats to their populations, conservation planning for eagles requires planning at broad spatial scales. Population management objectives codified in regulations implementing the Eagle Act require management actions to be “consistent with the goals of maintaining stable or increasing breeding populations in all golden eagle management units and the persistence of local populations throughout the geographic range of each species” (Eagle Permits; Revisions to Regulations for Eagle Incidental Take and Take of Eagle Nests, 81 C.F.R Sect. 91494). A key feature of maintaining or increasing any population is protection of breeding areas. Thus, motivated by the Eagle Act’s requirement to maintain local and regional populations, we modeled the relative density of golden eagle nest sites (hereafter, relative nest site density [RND]) at the scale of large ecological regions (range = 87,288–711,384 km²) to account for broad-scale spatial heterogeneity in habitat relationships in the western U.S.

Data describing golden eagle breeding sites in the western U.S. are routinely collected by land management agencies, researchers, and energy developers during the course of project planning. These data are often collected opportunistically (i.e., without a formal sampling design; but see [28, 29]), limiting their application in presence-absence analysis designs. Presence-only (or presence-available) species distribution models (SDMs), however, have become powerful and popular tools for evaluating species-environment relationships (e.g., [30]). Presence-only models allow for analyses of opportunistically collected data such as museum records, citizen science observations, and monitoring data collected by land management agencies. Importantly, absence data are generally not recorded during these surveys. Conservation planning entails making decisions in the context of incomplete information [31], and presence-only models can provide insights into species-environment relationships that are more informative than location data alone [32–34]. However, the utility of a model based on uncertain or incomplete data depends on its validity and an understanding of its limitations.

MaxEnt [35] is one of the most popular software packages for modeling presence-only data, having been cited >10,000 times (Google Scholar, https://scholar.google.com, accessed 23 Aug 2019). The MaxEnt model algorithm, based on presence-available data, performs identically to fitting an inhomogeneous Poisson point process model [36–39]. As a result, model output can be interpreted as a measure of relative density [40] of the modeled events (e.g., individuals, den sites, rest sites, nest sites), and estimates provided from such models are proportional to event density [41]. Because it is referenced to area, relative density is a more accurate description of the modeled events. Using some simple transformations developed by Boyce et al. [42], we show how MaxEnt output can be used to estimate the magnitude of differences in density of modeled events among areas even when absolute density is unknown. These transformations provide a clear ecological interpretation of MaxEnt’s output, and improve the utility of predictions for conservation and management applications.

SDMs are often used to identify locations within the modeled landscape that have particularly high suitability or likelihood of occurrence values. Such areas may be subsequently prioritized for protection or other conservation action [3, 43, 44]. Similarly, SDMs can also be used to identify landscape locations that have low values where conservation is not prioritized and where development may be incentivized [45]. For species of conservation concern, often a relatively small percentage of the landscape within the species’ range contains the majority of the individuals/nests/dens in that landscape [3, 46, 47]. In such cases, relatively modest conservation actions (e.g., restrictions on allowable land uses) targeted to these areas may result in very large conservation benefits (e.g., [27]).

We developed and evaluated RND models to serve as a foundation for golden eagle conservation planning in the western U.S. Our findings have a number of direct applications relevant to golden eagle conservation including land management planning by federal, state and tribal agencies, evaluation of land-use proposals by regulatory agencies, and decision support for energy developers. Model results can support quantitative risk assessments for a variety of potential risks, including energy development (both renewable and conventional; [45]), electrocution [27], wildland fire, lead poisoning, andvarious land management decisions. Our research goals were to develop models that: 1) could accurately predict the relative density of golden eagle nest sites; 2) were well-calibrated (i.e., the prediction of RND is accurately scaled to observed nest density rather than “simply” discriminating nest sites from non-nest sites); 3) were scaled to reflect the spatial scale at which golden eagles respond to variation in habitat features; 4) could assess habitat use patterns at spatial scales relevant to both potential threats and management actions; 5) were robust (i.e., not over- or under-fit to the data that are used to train the models) and generalizable to the extent of the modeled landscape; and 6) could be used to inform a wide variety of management/conservation actions.

Materials and methods

Study area

Our study area corresponds to the extent of the golden eagle’s breeding range within the conterminous U.S., roughly west of the 100^th meridian (Fig 1). We initiated data collection based on the breeding range provided by Kochert et al. [12], and subsequently modified the eastern boundary based on the distribution of nest records and associated habitat features. The study area consists of multiple distinct ecological regions, ranging from southwestern deserts and sagebrush-dominated interior basins to the Rocky Mountains and Great Plains.

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Fig 1. Geographic extent of study area with boundaries of modeling regions (1–12) shown in colored fill and projection regions (13–15) with crosshatch.

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Regional models: Partitioning the golden eagle’s range

We incorporated regional variation in environmental attributes into our modeling process by partitioning the golden eagle’s range in the western coterminous U.S. into 12 discrete modeling regions (Fig 1) and developing models separately for each region (see [37, 45]). We based our modeling regions on Level III Ecoregions established by the North American Commission for Environmental Cooperation (CEC) [48]. Ecoregions differ broadly in terms of vegetation composition, edaphic conditions, landform, and climate. Given the wide range of habitat types throughout our study area, we expected patterns of golden eagle habitat use to be more similar within than among Ecoregions. For example, the majority of golden eagles in the California Coastal Sage, Chaparral and Oak Woodlands Ecoregion nest in oak woodlands and forage predominantly for California ground squirrels (Otospermophilus beechyi) in annual grassland habitats [14]. In contrast, golden eagles nesting in the Central Basin and Range Ecoregion rely on hares and rabbits (Family Leporidae) in sagebrush habitats and typically build nests on cliffs and rocky outcrops [12, 49]. Fitting a single SDM across such heterogeneous regions would likely result in an overly general model that would fail to identify region-specific environmental relations and have poor predictive ability in any given region.

We adjusted CEC Ecoregion boundaries, and in some cases combined Ecoregions or portions of Ecoregions, to improve the alignment of modeling region boundaries with habitat gradients (e.g., sagebrush cover) important to golden eagles and their prey. We also masked the modeling regions to exclude areas with features that were not suitable golden eagle habitat (e.g., large bodies of water and playas). Overall we developed and evaluated models within 12 modeling regions (Table 1; Fig 1).

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Table 1. Characteristics of sample size of golden eagle nest sites and modeling regions used for developing golden eagle nesting area models in the western U.S. Initial number of nests is the full sample of nests we had available to us and that passed our quality control process.

Number of thinned nest sites is the sample of nest sites used for model development, after we thinned the initial sample to reduce the chance of pseudoreplication. Modeling region size is total size of modeling region, whereas modeling area size is the union of 20-km radius circles around the thinned nest sites. Modeling area percentage of modeling region is the result of dividing the modeling area by modeling region sizes (x 100). Number of sub-regions is the number of discrete sub-regions within each modeling region.

https://doi.org/10.1371/journal.pone.0223143.t001

Modeling procedure

Each modeling region was analyzed independently. Within each region, we compiled a list of candidate variables known or hypothesized to be related to golden eagle nest site selection. Since we were uncertain about the spatial scale(s) at which variables most influenced site selection, we calculated the focal means and standard deviation of each variable at six spatial scales (circular neighborhoods with radii of 120 m, 0.5, 1.0, 2.0, 3.2, and 6.4 km). This range of scales was chosen to represent variation in environmental features hypothesized to be relevant to golden eagle nest site selection. For example, at finer scales we could estimate local topographic relief associated with nest substrates on cliffs, whereas at coarser scales we could estimate land cover, terrain features and climate variation at scales likely meaningful to nesting golden eagles through foraging habitats and prey resources.

Variable identification; variable reduction.

Variables estimated for inclusion in our models included environmental attributes such as topographic indices and landform, land cover, climate indices, wind/uplift, vegetation productivity indices, and anthropogenic features (e.g., agricultural and developed areas) hypothesized to affect nest site selection across ecoregions. To span the possible domain of environmental factors likely to affect golden eagle nest site selection, candidate variables were initially classified into discrete categories based on what aspect of the environment they measured (climate indices, land cover, topographic indices, topographic landforms, vegetation indices, wind and uplift indices, development). We followed a two-step process to identify key variables and to reduce the number of redundant variables for each region based on: 1) estimates of their degree of difference between background and nest locations, and 2) measures of multicollinearity. At step 1, candidate variables at all spatial scales were compared by computing the ratio of the mean nest site value to the mean random site value (1,000 random-site locations). For a given variable, we retained the scale with the largest ratio that had <20% of the locations with non-zero values. At step 2, we computed variance inflation factors (VIF), within variable categories, for the subset of “best”-scale variables from step one. We removed variables with VIF ≥4. Within any variable category, the final set of covariates available for selection in the MaxEnt model fitting process generally had pairwise correlations ρ such that -0.5 ≤ ρ ≤ 0.5.

Creating the MaxEnt relative nest site density model.

All MaxEnt models were fitted using 100,000 background locations, and by evaluating linear, hinge, and quadratic functional relationships for all covariates (referred to as features in MaxEnt). Many surveys for golden eagle nest sites were not based on a probabilistic sampling design. As a result, many nest site locations arose from opportunistic detections and there were extensive areas within each region without knownnest site locations. To address this source of sampling bias, we restricted the selection of background locations to a polygon defined by the union of all 20-km radius circles centered on the thinned presence locations (hereafter referred to as the modeled area, which is distinct from, and smaller than, the modeling region; see S1 Fig). Circle size was based on the assumption that nesting golden eagles could easily access an area within a 20-km radius area centered on the nest site. We believe that restricting the selection of background locations in this way partially addressed potential sampling biases in the nest location data (see discussion in [54]).

For each region, the initial fitted model included the complete subset of scale-dependent covariates remaining after the variable reduction process. After evaluating this model, all covariates with percent contributions to the model <1.0 were removed, resulting in a reduced model. The percent contribution of each covariate was measured in MaxEnt by the increase in gain of the model by modifying the coefficient for that covariate [35]. This process of reducing model complexity resulted in models that performed nearly identical to the initial models but with many fewer covariates.

Optimizing the regularization multiplier.

The default MaxEnt algorithm includes a regularization penalty parameter to reduce model over-fitting by forcing some covariate coefficients to be zero. The regularization multiplier is user-defined with a default value of 1.0. Lower values of the regularization multiplier predispose areas with high RND to have covariate values very similar to presence locations, whereas higher values produce a more general model [55, 56]. Given the potential influence of this multiplier on covariate selection, we evaluated eight different regularization multiplier values (0.1, 0.5, 0.75, 1, 2, 3, 4, and 5) and optimized each reduced model’s regularization multiplier based on cross-validation results. We conducted cross-validation, whereby each of 10 times we randomly withheld 25% of the nest sites (with replacement) and trained the model with the remaining 75% of nest sites. In all cases, a random sample of 100,000 background locations was used. We then evaluated the distribution of the 25% withheld nest sites predicted to occur among 10 equal-sized RND bins (e.g., 0.0–0.1, 0.1–0.2, 0.2–0.3 …, 0.9–1.0) based on the model fitted to the (75%) training data (see below). We estimated the mean squared prediction error (MSE) between the predicted number of test nest sites occurring within each of the 10 bins relative to the observed number of test nest sites occurring within each bin. Predicted number of nest sites within each bin was calculated as: (1)

Where:

N_p(i) = Number of predicted nest sites in bin i

N_t = total number of nest sites in the test sample,

p_A(i) = proportion of the area in bin i (see below), and

AAF_i = area-adjusted frequency (AAF) for bin i (see below, following Boyce et al. [42]).

AAF_i was computed with the training data using the following steps:

1. Compute the size (area) of the modeled area (A),
2. Partition relative habitat suitability scores (from MaxEnt output) from each cell into K, equal-interval bins.
3. Compute the area (a_i) within each bin i = 1, 2, 3, …, K.
4. Count the number of nest sites (n_i) within each bin i.
5. Calculate AAF_i as:

(2)

Where:

n_i = number of nests in bin i,i = 1,2,…,K

a_i = area within bin i

N = total number of nests =

A = total area of study region =

p_A(i) = proportion of area in bin i =

p_N(i) = proportion of nests in bin i =

Assuming nest sites to be randomly distributed across the modeled area—the null hypothesis of no relationship with measured environmental covariates—the predicted number of nest sites within each bin is proportional to the modeled area within a given RND bin (i.e., AAF = 1). Area-adjusted frequencies (AAF) were initially proposed by Boyce et al. [42] as a method of evaluating resource selection functions. Evaluating the rank correlation of bin rank and AAF rank (referred to as the Boyce Index by Hirzel et al. [57]) provides an assessment of the extent to which an estimated model diverges from expectations under a null hypothesis of a random distribution of breeding locations [42].

For each regularization multiplier value, cross-validation resulted in 100 predicted and 100 observed values (10 replicates by 10 bins), and the MSE was calculated as the average squared difference between N_p(i) and n_i. We used the regularization multiplier value with the smallest MSE to fit our final models.

Assuming a sample of N nest sites within a given region, the fitted model predicts how those N nest sites are distributed among 10 RND bins. The difference between observed and predicted frequencies across bins is a measure of model fit. Note that in contrast to the more commonly reported MaxEnt output metrics (raw or logistic estimates of relative habitat suitability), our estimates are interpreted as relative density. In addition, comparing AAF values among bins can be used to estimate the extent to which nest density differs among bins.

Model evaluation with independent data.

For nine regions (all except the Chihuahuan Desert, Intermontane Basins and Valleys, and Southwestern Plateau regions), additional nest location data became available to us after final models had been fit. This provided an opportunity for model evaluation based on independent data not used in model fitting. For those modeling regions with independent data, we evaluated the final model’s ability to accurately predict the distribution of test nest sites among RND bins (using Eq 1) after thinning the new nest locations so that they were ≥ 3 km from each other and from training locations. The predicted number of nest sites in each bin requires an estimate of the proportion of area within each of the 10 RND bins. Therefore, we centered 20-km radius circles on each of the thinned independent nest sites and estimated the proportion of area (union of circles) in each RND bin. We then compared the number of nest sites predicted to be in each RND bin to the actual number occurring in each bin.

Geographic evaluation.

To evaluate geographic variation in model performance, we subdivided each region into two to eight sub-regions (Figs in S2 Fig) based on U.S. Forest Service Ecological Sections [58]. For each sub-region, we applied our final model to the entire modeled area and estimated the number of nest sites predicted to occur within each of 10 RND bins and compared those predictions to the observed number of nest sites within each bin. Estimated number of nest sites within each RND bin within each sub-region was based on an adjustment to Eq (1) as follows: (3)

Where:

N_p(i)SR(j) = Number of predicted nest sites in bin i of sub-region j,

p_SR(j) = proportion of the modeled area in sub-region j, j = 1, 2, 3,…, K.

The geographic evaluation of model performance within sub-regions provided insights into the spatial variation in model performance within a modeling region. If the model performed poorly in a particular sub-region, it would suggest that it might be reasonable to consider: 1) developing a sub-region specific model; 2) focusing future field survey efforts in that sub-region to increase the sample size of nest sites; or, 3) utilizing more nuanced considerations of risk assessment/conservation opportunities in those areas.

Projecting models.

Each model was developed and evaluated within the modeling area and subsequently projected to the remaining area of its modeling region (Figs in S1 Fig). We provide descriptive statistics on the proportion of the modeling region that the modeling area represented, and the amount of modeling areas and modeling regions in each of 10 RND bins.

Projecting models outside of modeling regions.

In three cases we projected models to portions of ecoregions outside of the focal modeling region that had similar environmental conditions (Figs in S1 Fig). This allowed us to project models to nearly all of the western U.S. study area, including areas for which data were lacking. We projected the California Foothills model to the California Central Valley due to the near absence of available training data, and limited extent of potentially suitable habitat in that region. The Madrean Archipelago also had a small sample of nest sites, and was included by projecting the Southwestern Deserts model. Although the Uinta Basin and North Park areas likely had an adequate sample of nest sites to generate a new model, they contained highly similar environmental conditions to those in the adjacent Wyoming Basin region for which we had a model. We therefore projected the Wyoming Basin model to the Uinta Basin and North Park. Performance of the projected models was evaluated by comparing the number of observed nest sites to the number of predicted (using Eq 1) nest sites in each of 10 RND bins, where observed nest sites were independent nest locations thinned by the same criteria as the training data.

Results

We compiled 160,510 golden eagle nest records and identified 33,118 that met our criteria for discreteness, occupancy status and spatial accuracy. After the thinning process, the presence sample included 6,561 nest sites, ranging from 118–1,050 (( = 547) among modeling regions (Table 1).

Among regions we considered 276–578 variables. After selecting the “best” scale for each variable and conducting VIF analyses, the number of covariates evaluated in initial models ranged from 18–34 (Table 2) among regions. Final models included from six—14 covariates (Table 2). The most influential covariate in each region’s final model was related to terrain steepness (mean or variation) at local spatial scales (120 m for 11 regions and 1 km for one region; Table 3, Figs in S3 Fig). Overall, individual topographic indices covariates contributed 37.2–94.2% to fitting each full model (Table 3, Figs in S3 Fig). Additional covariates across modeling region’s models included landcover, climate indices, wind and uplift indices, and developed areas. Although terrain covariates weren’t identical across all modeling regions’ final models, the functional forms of the terrain covariates in each region were generally quite similar. RND increased with increasing steepness, generally in a threshold shape with the positive influence of steepness on RND declining above moderate steepness values. Final models for the California Foothills, Forested Montane, Intermontane Basins and Valleys, and Wyoming Basin included sagebrush or grassland habitat covariates, at 0.5–6.4 km scales, as influential covariates (Table 3, Figs in S3 Fig), and in each case showed a strongly positive relationship (linear or threshold) between RND and amount of, or variation in amount of, grassland or sagebrush habitat. In contrast, for the Northwestern Plains’ final model, SD of cultivated cropland was an influential covariate (Table 3, Figs in S3 Fig), and showed an inverse and linear relationship with RND.

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Table 2. Number of initial variables considered, number of covariates in the initial model, and number of covariates in each modeling region’s final model.

https://doi.org/10.1371/journal.pone.0223143.t002

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Table 3. List of covariates that contributed ≥5% to each modeling region’s final model.

Values beneath each modeling region are the covariate’s percentage contribution to fitting each final model.

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The optimal regularization multiplier value varied from 0.75–6 across modeling regions (Table 4). Because the lowest MSE for the Southwestern Plains, Southwestern Deserts, and California Foothills was found at the highest regularization value initially assessed (5), we evaluated those regions at multiplier values of 6 and 7. We found that the MSE increased at higher values for the Southwestern Plains and Southwestern Deserts, but decreased for the California Foothills (Table 4). After models were re-estimated using the optimized regularization multiplier, the contribution of a small number of covariates dropped to below 1% but were retained in the models.

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Table 4. Mean squared prediction error (MSE) among regularization multiplier values for each modeling regions’ final golden eagle nesting area model.

The lowest MSE value is italicized and has gray shading. For the Southwestern Plains, Southwestern Deserts, and California Foothills modeling regions, the lowest MSE was found at regularization values of 5 (the largest value we initially evaluated), so we evaluated two larger regularization multiplier values (6 and 7) to determine whether MSE continued to decline with increasing regularization.

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Model performance

Predicted versus observed densities: Cross-validation.

Cross-validation revealed that for each of the 12 modeling regions, model predictions were consistent with the distribution of presence data in the evaluation data set (Fig 2). Deviations between predictions and withheld data were greatest for the Columbia Plateau, Southwestern Plains, Intermontane Basins and Valleys, California Foothills, and Chihuahuan Desert modeling regions, which had some of the smallest sample sizes of nest sites coupled with modeling areas being a smaller percentage of their respective regions (Table 1).

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Fig 2. Bar graphs of mean (±2SE) predicted and observed number of golden eagle nest sites in each of 10 relative nest density (RND) bins within each modeling region.

Both predicted and observed numbers were from the 25% withheld data from 10 cross-validations of each region’s model.

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Predicted versus observed densities in sub-regions.

Overall, regional models predicted nest site densities of golden eagles within sub-regions very well (Fig 3). Coefficients of determination between estimated number of nest sites within RND bins within sub-regions and observed number of golden eagle nest sites within RND bins ranged from 0.36 (Southwestern Plains) to 0.92 (Northwestern Plains; and nine of 12 r² values were >0.75; Fig 3). In no cases did models predict extremely small or large numbers of nest sites when the opposite reality existed.

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Fig 3. Scatterplots of predicted versus observed number of golden eagle nest sites among 10 RND bins within each modeling region’s sub-regions.

Numbers in each region’s plot refer to sub-regions. Sub-region names can be found in S2 Fig.

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Independent test data.

We obtained 553 independent nest site locations within nine modeling regions. The number of independent nest sites by region ranged from 13 (California Foothills) to 114 (Northern Great Basin). We compared the number of predicted to number of observed nest sites occurring within each RND bin within each region, and generally found only minor differences between predicted and observed nest sites within RND bins. Among all independent nest sites, 40% of the differences, between predicted and observed, were less than 1, 71% were less than 2.5, and 91% were less than 5; the largest difference was 9.5 (Fig 4).

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Fig 4. Bar chart of distribution of observed and predicted nests sites (observed–predicted) within RND bins for 553 independent nest sites within nine modeling regions.

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Projecting models outside of modeling regions.

Three regional models were projected to large areas with similar conditions. We had independent nest site data for the Madrean Archipelago (n = 48 nest sites) and the Uinta Basin and North Park (n = 132 nest sites), and used those to evaluate how well the projected models predicted the distribution of independent nest sites among RND bins. The Southwestern Deserts Model was projected to the Madrean Archipelago, and in general the model under-predicted the distribution of nest sites within higher RND (>0.5) bins (Fig 5) and over-predicted the distribution of nest sites with lower RND (<0.5) values. The Wyoming Basin model was projected to the Uinta Basin and North Park, and it quite accurately predicted the distribution of nest sites among RND bins (Fig 5). Due to the small number of nest sites in the California Central Valley, we were unable to meaningfully evaluate the projection of the California Foothills model.

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Fig 5. Bar plots of the distribution of predicted and observed nest sites among RND bins in the Madrean Archipelago, and Uinta Basin and North Park.

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Area-adjusted frequencies

The rank correlation between bin and AAF ranks was > 0.96 for all regions (it was 1.0 for 10 regions) indicating a highly non-random distribution of nest sites among RND bins (Table 5). In low RND bins the magnitude of difference from random expectation was not as pronounced as it was for high RND bins (Table 5). For example, among all modeling regions, the highest RND bins (0.9–1.0) had between 21.0–166.2 times more nest sites than expected based on area within that bin, whereas the lowest RND bin (0–0.1) had from 4.2–16 times fewer nest sites than expected (Table 5). Within modeling regions, variation in AAF values among bins revealed extremely large differences in relative densities of nest sites. For example, the factor by which the highest bin’s relative nest site density exceeded the lowest bin’s ranged from 132–2,660 among regions (Table 6).

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Table 5. Area Adjusted Frequencies of each modeling regions’ final model among RND bins.

The Columbia Plateau modeling region had too few observations in bin 0.9–1 to be meaningfully estimated.

https://doi.org/10.1371/journal.pone.0223143.t005

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Table 6. Factor by which golden eagle nest density varies from the lowest bin for each modeling regions’ final model.

https://doi.org/10.1371/journal.pone.0223143.t006

Nest site distribution among RND bins in modeling areas

All modeling areas and regions were primarily composed of low RND areas, while high RND areas had limited spatial extent (Figs 6 and 7, S4 Fig, and S2 Table). Hence, a disproportionately large number of nest sites were predicted to occur on a relatively small percentage of the landscape. For example, we estimated that areas with RND values <0.3 represented from 62.8–97.8% ( = 82.5%) of each modeling area, and those areas contained from 14.7–30.0% ( = 22.1%) of the nest sites. In contrast, areas with RND values >0.5 represented from 1.0–12.8% (= 6.3%) of modeling areas, and those areas contained from 47.7–66.9% ( = 57.3%) of the nest sites.

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Fig 6. Percent area within ten equal-sized relative nest site density (RND) bins in modeling areas (gray bars) and modeling regions (white bars).

https://doi.org/10.1371/journal.pone.0223143.g006

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Fig 7. Maps of the distribution of RND in all regions.

https://doi.org/10.1371/journal.pone.0223143.g007

Discussion

We developed relative nest site density models for golden eagles for use in large-scale conservation prioritization efforts. Within all modeling regions only a small proportion of each region’s area was predicted to have high RND values, and large areas had relatively low RND values. The highest RND bin intervals were estimated to have 132–2,660 times greater nesting densities than the lowest bin interval (Table 6). Thus, prioritization of conservation actions on a small portion of each region could have a disproportionately large benefit to breeding golden eagles.

Given the large geographic extent of the golden eagle’s range in the western U.S., our subdivision of this area into discrete modeling regions was warranted, and resulted in good to excellent models. Explicit consideration of unique local and regional scale habitat associations, population characteristics and constraints is essential for effective conservation planning for broadly distributed species such as greater sage-grouse (Centrocercus urophasianus)[59], northern spotted owls (Strix occidentalis caurina)[3], and golden eagles [60, 61]. A consequence of developing multiple regional models, however, is that relative nest density values (RND and AAF) from individual regions are not directly comparable among regions. For example, an RND value of 0.8 in one region may correspond to a different observed density than RND of 0.8 in another region (Fig 8).

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Fig 8. Observed densities of golden eagle nest sites used in model training within ten equal-sized relative nest site density (RND) bins, for each of twelve modeling regions.

https://doi.org/10.1371/journal.pone.0223143.g008

We sought models that would provide reliable predictions of relative density of golden eagle nest sites, as opposed to describing and quantifying the species’ niche. Nonetheless, it is important that model predictions are interpretable if they are to be incorporated into management and conservation planning. Our models reflected well-known patterns of habitat selection exhibited by golden eagles across the western U.S. and corresponded well to previously published descriptions and models of breeding habitat [62, 45]. Topographic features corresponding to nest substrates on cliffs and steep terrain at finer scales (120 m– 1.0 km) were important predictors in all model regions (Table 3). This finding is consistent with empirical studies and regional models of breeding habitat selection in areas where golden eagles nest predominantly on cliffs and rock outcrops [62, 45]. Field studies have consistently identified variable terrain and gentle slopes, along with wind and orographic uplift variables, as important predictors of golden eagle space-use within home ranges [52, 62–64]; in our study these variables were moderately important covariates in 8 of 12 modeling regions (Figs in S3 Fig). Our models also incorporated land cover variables thought to influence prey availability positively, such as sagebrush and grassland cover, and riparian habitat; or negatively, including barren areas, cropland, and introduced annual grasses (e.g. cheatgrass, Bromus tectorum) [52, 64, 65]. At coarser scales (1.0–6.4 km) surrounding nest sites, model predictions were influenced by regionally specific suites of covariates related to foraging and prey habitats. In the California Foothills modeling region, where most golden eagles nest in woodlands, our model predictions were strongly influenced by the combination of rugged terrain, grass cover and woodland cover covariates (Figs in S3 Fig). These variables were found to be correlated with spatial variation in occupancy and reproduction of golden eagle territories studied by Wiens et al. [2] in the Diablo Range portion of our California Foothills modeling region.

Cross-validation showed that all models accurately predicted numbers of golden eagle nest sites within RND bins, and geographic evaluation showed consistently good predictive success among sub-regions for nine regions. We believe model results for the Central Basin and Range, Northwestern Plains, Northern Great Basin, Wyoming Basin, Southwestern Plateaus, Southwestern Deserts, Forested Montane, and Chihuahuan Desert were strongly validated. Models for the Columbia Plateau, Southwestern Plains, Intermontane Basins and Valleys, and California Foothills were less robust, but still performed quite well. For these four regions, models could likely be improved by increasing samples of nest sites from larger portions of each region. Variation in model quality among regions was related to variation in sample size and dispersion patterns of thinned nest sites, as well as the degree of contrast between high and low RND in regions. In general, as sample size increased and as modeling areas represented larger portions of modeling regions, model predictive power increased, and models were more robust. The Chihuahuan Desert, for example, had by far the largest percentage (95%) of its area in the lowest RND bin. Although we had a small sample of thinned nest sites in the Chihuahuan Desert, the model performed well, we suspect owing to so much of the region being of poor nesting suitability (i.e., high contrast).

When projecting the Southwestern Deserts, and Wyoming Basin models to the Madrean Archipelago, and Uinta Basin and North Park, respectively, we found that only the model projected to the Uinta Basin and North Park resulted in accurate predictions of the distribution of independent nest sites (Fig 5). Although the projected models may be the best current estimates of the distribution of RND in the projected to areas, we would recommend development of RND models specifically within the Madrean Archipelago.

Converting SDM continuous outputs into binary classifications results in the loss of information [66], especially considering that we can estimate the magnitude of differences in nest-site density among RND bins within a modeling region by calculating AAF values. A binary classification of our RND output within each region would have combined areas with large differences in densities of golden eagle nest sites in both the “suitable” and “unsuitable” or “present” and “absent” categories. For example, for all regions, the AAF values in the highest bin (0.9–1.0) were from 21–166 times greater than would be expected based on a random distribution of nesting sites (Table 5). Furthermore, in seven modeling regions, the highest RND bin was estimated to have more than twice the density of nest sites as the next lower bin (Table 5). A binary classification of the results would have resulted in a complete loss of this understanding of differences, which could have large consequences for conservation and management.

In the absence of designed, probabilistic nest surveys, the actual number of golden eagle nest sites within each region could not be estimated. Observed densities of golden eagle nest sites within RND bins in all modeling regions were consistent with nesting densities reported in the literature (e.g., [64, 28, 2]). Two important points need to be made about our observed golden eagle nest site densities within RND bins. First, they are based on a sample of thinned nest sites, and it is certain that those underestimate the actual number of independent golden eagle nest sites in modeling areas. Second, our density calculations assume contiguous areas of each RND bin, whereas the reality is that nearly all breeding sites contain mixtures of varying RND values. Few golden eagle pairs have uniformly contiguous territory-sized areas of high-value RND habitat available to them. Nonetheless, we believe the variation we estimated in AAF values among bins represents real variation, and the steep gradient between low and high RND bin values represents differences with real biological relevance.

We interpreted model results based on MaxEnt output as measures of relative nest site density. Royle et al. [67] criticized the interpretation of MaxEnt output as a habitat suitability index, in part because “it is not suitable for making explicit predictions of an actual state variable.” We believe our approach, based on modifying MaxEnt output by computing an AAF, transformed MaxEnt output into a biologically relevant state variable (relative density) that has a clear biological interpretation. Although AAF is proportional to density, it is more than a simple ranking of densities among RND bins because the magnitude of differences in density among bins can be explicitly estimated. Our modeling results provide direct measures of spatial variation in golden eagle nest site density and how this variation relates to spatial variation in environmental covariates. We believe our modeling approach is broadly applicable to other species and circumstances, including the modeling of presence-only data collected opportunistically.

The golden eagle nest data we compiled came from a broad range of survey efforts, including systematic statewide aerial surveys, local research projects, and landscape-scale surveys by land management agencies. However, we recognize several potential sources of bias in the data. For example, state and federally required surveys of public land targeted for oil, gas and coal extraction, as well as wind and solar energy development areas, often resulted in relatively high densities of golden eagle breeding sites recorded in those landscapes. Conversely, large expanses of privately owned ranch and farmland receive few surveys, as do remote wilderness areas. Even in surveyed areas, negative survey results are not always recorded into agency databases. To address potential spatial bias in the distribution of presence locations, Phillips et al. [54] recommended restricting the selection of available locations to a small neighborhood surrounding the presence locations. In our analyses, we sampled available locations within the union of a 20-km radius buffer (the modeling area) around all thinned golden eagle nest sites. Because golden eagle home ranges can be very large, and individuals often make periodic excursions <75 km outside of their home ranges in relatively short periods [52, 13], we assumed that each nesting pair could assess the 20-km radius area surrounding their breeding site.

Halvorsen [68] identified three motivations for fitting SDMs to presence-only data: 1) to estimate an ecological response, 2) for spatial predictions to unsampled locations, and 3) projective prediction modeling (i.e., projecting the model outside of the fitted area). Our models addressed all three goals, with an emphasis on spatial prediction. We chose to fit models using covariates supported by previous studies and current understanding of golden eagle nest site selection. This approach supported our primary focus on spatial prediction of golden eagle nesting density, while resulting in biologically interpretable models for use in conservation planning.

Supporting information

Acknowledgments

Disclaimer: The findings and conclusions presented in this paper are those of the authors and do not necessarily reflect the views of the U.S. Fish and Wildlife Service. Jeffrey R. Dunk accepts responsibility for the integrity and validity of the data collected and analyzed.

We are indebted to many researchers, biologists, and citizen scientists who contributed golden eagle nest data, participated in expert reviews and field tests of draft models, and conducted targeted surveys in support of our modeling effort. Without their dedication and interest in these birds, this project would not have been possible. In particular, we would like to thank USFWS Western Golden Eagle Team members Greg Beatty, Jim Dick, Thomas Dietsch, Gjon Hazard, David Leal, Katie Powell, Matt Stuber, David Topolewski, Hillary White, and Gary Williams who lead our outreach effort for eagle data. Bryan Bedrosian, Ross Crandall, Kenneth Jacobson, Michael Kochert, Robert Murphy, Chuck Preston, Steve Slater, Chad Smith and Jim Watson played important roles in data acquisition and model review. Clint Boal, Frank Isaacs, Mike Lockhart, Rob Spaul, Dale Stahlecker and Zach Wallace provided expertise and conducted targeted surveys in support of modeling. Trent McDonald provided input that improved our modeling procedures. We extend our gratitude to many additional individuals and institutions, listed in Table in S3 Table, who contributed data and valuable input to our modeling effort. Jason Carlisle and Brian Millsap provided helpful comments that improved earlier drafts of this manuscript. We would also like to thank an anonymous reviewer and academic editor Lyi Mingyang for recommendations that improved the manuscript.