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Biological Conservation

journal homepage: www.elsevier.com/locate/biocon

Predicting spatial factors associated with cattle depredations by the Mexicanwolf (Canis lupus baileyi) with recommendations for depredation riskmodeling

Reza Goljani Amirkhiza,1, Jennifer K. Freya,⁎, James W. Cain IIIb, Stewart W. Breckc,David L. Bergmand

a Department of Fish, Wildlife and Conservation Ecology, New Mexico State University, Las Cruces, NM 88003, USAbU.S. Geological Survey, New Mexico Cooperative Fish and Wildlife Research Unit, Department of Fish, Wildlife and Conservation Ecology, New Mexico State University,Las Cruces, NM 88003, USAcUnited States Department of Agriculture, National Wildlife Research Center, Fort Collins, CO 80521, USAdUnited States Department of Agriculture, Animal and Plant Health Inspection Service, Wildlife Services, Phoenix, AZ 85021, USA

A R T I C L E I N F O

Keywords:Canis lupus baileyiCarnivoreDepredationEndangered speciesLivestockMaxentRisk modelSpecies distribution modelMexican wolf

A B S T R A C T

Aim: Predation on livestock is one of the primary concerns for Mexican wolf (Canis lupus baileyi) recoverybecause it causes economic losses and negative attitudes toward wolves. Our objectives were to develop a spatialrisk model of cattle depredation by Mexican wolves in the USA portion of their recovery area to help reduce thepotential for future depredations.Location: Arizona and New Mexico, USA.Methods: We used a presence-only maximum entropy modeling approach (Maxent) to develop a risk modelbased on confirmed depredation incidents on public lands. In addition to landscape and human variables, wedeveloped a model for annual livestock density using linear regression analysis of Animal Unit Month (AUM),and models for abundance of elk (Cervus canadensis), mule deer (Odocoileus hemionus) and white-tailed deer(Odocoileus virginiana) using Maxent, to include them as biotic variables in the risk model. We followed currentrecommendations for controlling model complexity and other sources of bias.Results: The primary factors associated with increased risk of depredation by Mexican wolf were higher canopycover variation and higher relative abundance of elk. Additional factors with increased risk but smaller effectwere gentle and open terrain, and greater distances from roads and developed areas.Main conclusions: The risk map revealed areas with relatively high potential for cattle depredations that caninform future expansion of Mexican wolf distribution (e.g., by avoiding hotspots) and prioritize areas for de-predation risk mitigation including the implementation of active non-lethal methods in depredation hotspots.We suggest that livestock be better protected in or moved from potential hotspots, especially during periodswhen they are vulnerable to depredation (e.g. calving season). Our approach to create natural prey and livestockabundance variables can facilitate the process of spatial risk modeling when limitations in availability ofabundance data are a challenge, especially in large-scale studies.

1. Introduction

Large carnivores can cause conflicts with humans by preying onlivestock, which causes economic losses and, in some cases, negativeattitudes toward carnivores (Treves and Bruskotter, 2014; Dickmanet al., 2013). A variety of non-lethal approaches to reduce human-carnivore conflicts are available. Some studies show that non-lethal

methods were often more effective than lethal methods (Treves et al.,2016; Santiago-Avila et al., 2018), however, other studies report thatthere is high variation, indeterminacy and lack of scientific evidences innon-lethal methods effectiveness (Miller et al., 2016; Eklund et al.,2017; Eeden et al., 2018). Moreover, depredation on livestock bywolves may be a learned behavior and therefore may be difficult to stopif all individuals in a pack are involved (Harper et al., 2005). An

https://doi.org/10.1016/j.biocon.2018.06.013Received 6 January 2018; Received in revised form 18 May 2018; Accepted 12 June 2018

⁎ Corresponding author.

1 Current address: Department of Biology, University of South Dakota, Vermillion, SD 57069, USA.

E-mail addresses: [email protected] (R. Goljani Amirkhiz), [email protected] (J.K. Frey), [email protected] (J.W. Cain), [email protected] (S.W. Breck),[email protected] (D.L. Bergman).

Biological Conservation 224 (2018) 327–335

0006-3207/ © 2018 Elsevier Ltd. All rights reserved.

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alternative approach is to prevent conflicts from occurring, which maybe more efficient and less costly than trying to reduce conflict after ithas occurred. Prevention of conflicts depends on recognizing the con-ditions that promote these conflicts (Linnell et al., 1999). Therefore,predicting future depredations from their past patterns can lead tooptimum interventions for reducing carnivore-livestock conflicts(Treves and Rabenhorst, 2017). Predictive spatial models find re-lationships between ecological variables and spatial processes and arecommonly used tools to plan strategies for wildlife management(Guisan and Zimmermann, 2000). Risk maps, created by spatial models,predict spatial distributions of potential conflicts between humans andcarnivores, and provide an opportunity for early warning (Edge et al.,2011; Treves et al., 2004; Treves et al., 2011; Miller, 2015). Moreover,identifying the role of landscape, natural prey, and livestock char-acteristics in depredation can help inform management of livestock andwildlife to reduce depredations (Miller et al., 2015; Treves andRabenhorst, 2017).

The Mexican wolf (Canis lupus baileyi) is an example of a carnivorethat is being restored to part of its native range, but which can causeconflicts with humans. Historically, the Mexican wolf occurred in por-tions of the American Southwest and south through central Mexico,although there is disagreement about precise historical range limits(Heffelfinger et al., 2017; Hendricks et al., 2016; Parsons, 1998). His-torical efforts to eradicate Mexican wolves due to conflicts with live-stock resulted in their extirpation from the United States by 1970(Bednarz, 1988; Brown and Shaw, 2002). The Mexican wolf was listedas endangered under the US Endangered Species Act in 1976 uponwhich the last individuals were captured from the wild in Mexico toinitiate a captive breeding program (McBride, 1980). The first releasesof captive-bred Mexican wolves occurred in 1998 within a primaryrecovery zone in the Apache National Forest in east-central Arizona.Wolves were allowed to disperse throughout the Blue Range Wolf Re-covery Area (BRWRA), which included additional areas of the Apacheand Gila National Forests in Arizona and west-central New Mexico (seeFig. S1. 1 of Appendix S1 in Supporting information). The smallfounding population and low gene diversity have been a concern inMexican wolf recovery efforts (Harding et al., 2016). In 2015, revisionsto the regulations for the nonessential experimental population of theMexican wolf resulted in a dramatic increase in the area where Mexicanwolves would be allowed to occupy, from the former BRWRA to theMexican Wolf Experimental Population Area (MWEPA), which includesareas of Arizona and New Mexico south of Interstate Highway 40(Appendix S1; U.S. Fish and Wildlife Services [USFWS], 2015). Thisexpansion will increase Mexican wolf-livestock conflicts (USFWS,2015). From 1998 to 2017 the Mexican wolf population in the US hasgenerally increased from an initial 11 wolves in 3 packs to a maximumof 114 wolves within 22 packs during 2017 (USFWS, 2017). Residentsof Arizona and New Mexico that oppose Mexican wolf restoration, do soprimarily because of concerns about livestock and human safety(Schoenecker and Shaw, 1997). Depredation by Mexican wolves on li-vestock occurs throughout the year on private and public lands. Prior to2007 management removal of wolves from the population was nega-tively impacting population growth. Protocols were altered to empha-size non-lethal and proactive strategies and minimize removals(USFWS, 2017).

The overarching goal of this study was to develop a model thatexplains landscape scale spatial factors associated with Mexican wolfdepredation on livestock. Specific objectives included: 1) predict re-lative density of livestock and predict relative abundance of potentialnatural prey, including elk (Cervus canadensis), mule deer (Odocoileushemionus) and white-tailed deer (Odocoileus virginiana), in Arizona andNew Mexico with the aim of using estimates from these models as partof the initial suite of variables that were tested for inclusion within therisk model, 2) develop a risk model of Mexican wolf depredation oncattle to understand factors associated with increased risk and to il-lustrate spatial arrangement of depredation conflict hotspots, and 3)

make recommendations for future wolf recovery and livestock man-agement to reduce potential conflicts. Our study was important inseveral ways. First, the depredation risk model provides informationabout areas with high potential for conflict before the distribution ofMexican wolf has expanded within the revised MWEPA. This providesan opportunity to inform future management actions that can reducepotential conflicts before they occur. Second, fine scale spatial data onabundance of livestock and natural prey are rarely available for largeregional study areas. We developed models for livestock density andnatural prey abundance, which were tested as predictors in the riskmodel. Third, few studies have applied maximum entropy modeling(i.e., Maxent; Phillips et al., 2006) using current recommendations(Morales et al., 2017; Yackulic et al., 2013). We incorporated all cur-rently recommended modeling criteria, including correcting samplingbias, defining background extent based on study goals and assumptions,testing model complexity, and avoiding overestimation in model eva-luation.

2. Methods

2.1. Study area

The study area was the states of Arizona and New Mexico, USA. Therisk model was developed based on depredation incidents that occurredon public lands within and near the former BRWRA and then was ex-trapolated as a risk map to the study area (Appendix S1).

2.2. Occurrence records

We focused our analysis on depredations on cattle by Mexicanwolves because cattle represent the majority of livestock production,both in terms of numbers of animals and economic value, and becausethe majority of depredation incidents attributed to Mexican wolvesinvolve cattle (USFWS, 2017). We analyzed 186 confirmed lethal de-predation incidence locations (yearlings n=2, heifers n=2, calvesn=108, bulls n=3 and cows n=71) verified by Wildlife Services aspart of the Interagency Field Team from 1998 to February 2017. Toreduce the effect of sampling bias, we used spatial filtering to randomlyremove all but one depredation record within each 1 km2 pixel. Afterrarefaction, 162 depredation points remained in the dataset.

2.3. Independent variables

We modeled depredation risk as a function of 6 biotic (relativeabundance of elk, mule deer and white-tailed deer, annual livestockdensity, land cover type, land cover variety, canopy cover, and covervariety), 4 human (distance to and density of roads, distance to anddensity of developed areas) and 6 landscape (elevation, slope, terrainruggedness index [TRI], aspect, distance to and density of water re-sources) variables (see Appendix S2 in Supporting information for hy-potheses, variable sources, and variable calculations).

Spatial data on the abundance of livestock was not available for theentire study area and is probably not obtainable given the large numberof livestock operations and variation in how livestock are managed.Consequently, we developed a spatial layer “annual livestock density”that represents the annual capacity for livestock production as a proxyfor actual livestock abundance. We applied generalized linear modelsand used AICc to model annual livestock capacity on basis of AnimalUnit Month (AUM) data for 3876 allotments (covering 39% of the studyarea) on lands managed by the US Forest Service and Bureau of LandManagement and then interpolated to the 61% remainder of our studyarea (see Appendix S3 in Supporting information for details of methodsand results). Similarly, spatial data on the abundance or density of theprimary natural prey of the Mexican wolf (elk, mule deer and white-tailed deer) were not available for the entire study area. Maxent's rawoutput can be directly interpreted as a model of relative abundance

R. Goljani Amirkhiz et al. Biological Conservation 224 (2018) 327–335

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(Phillips et al., 2017). Consequently, we used available occurrence datafor each prey species in Maxent to generate species distribution modelsthat estimate their relative abundance. Development of the prey re-lative abundance models followed similar procedures as used for therisk model (see Appendix S4 in Supporting information for details ofmethods and results). The original pixel size of all variables was 30m,except annual AUM density, which was 1 km. All variables were scaledto 1 km pixel size.

2.4. Modeling approach

Depredation risk models are usually developed in the same manneras correlative species distribution models, but based on depredationlocations rather than species occurrence locations (Miller, 2015). Thedecision-making framework for such modeling is dependent on thepurpose of the model and is determined by the type of survey dataavailable (either presence-absence or presence-background) and howthe survey data interact with sampling bias and imperfect detection(Guillera-Arroita et al., 2015). Early risk models were usually devel-oped based on presence-absence survey data (Miller, 2015). Indeed,presence-absence survey data can estimate probability of occurrence,which is the highest level of information content possible, but this isonly achievable when detection probability is perfect (Guillera-Arroitaet al., 2015). Detection probability for depredation events by Mexicanwolves is low and it varies primarily by producer (Breck et al., 2011).Our goal was to produce a map of the study area that correctly rankslocations for risk of depredation on cattle by Mexican wolves. Suchranking models have high information content and good ability todiscriminate between depredation and non-depredation sites and thesemodels may be created using either presence-absence or presence-background datasets (Guillera-Arroita et al., 2015). We did not havedata on locations where Mexican wolves and livestock overlapped butdepredation had not occurred, and therefore did not have absence data.Consequently, we used presence-background data in Maxent to modeldepredation risk. In addition to be being consistent with our modelingobjectives, this approach also reduced the risk of including false ab-sence data in the model.

Maxent is a machine-learning program that uses the principle ofmaximum entropy to estimate the distribution of a species (or occur-rences such as depredation events) based on occurrence points (Phillipset al., 2006; Elith et al., 2011). Maxent typically has better performancein comparison with other presence-background methods, it performswell with small samples, and it is robust to spatial errors and biasedsampling (Elith et al., 2006, 2011). In addition, Maxent can use bothcategorical and continuous data and it can incorporate interactionsbetween variables (Phillips and Dudík, 2008). However, Maxent hasbeen criticized because many users have failed to understand and ad-dress model assumptions, control model complexity, and report re-levant results (Yackulic et al., 2013; Morales et al., 2017). Maxent onlyperforms well if its assumptions are met and its settings are tuned (i.e.,to find and use optimal model parameters; Merow et al., 2013; Moraleset al., 2017). Thus, we incorporated all currently recommended mod-eling criteria for our Maxent analyses, including correcting samplingbias, defining background extent based on study goals and assumptions,testing model complexity, and avoiding overestimation in model eva-luation (Merow et al., 2013; Radosavljevic and Anderson, 2014).

2.4.1. Sampling biasA key assumption of species distribution models generated via

Maxent is that all locations on the landscape have equal chance to besampled (Royle et al., 2012). Sampling bias can result in overfitting themodel toward areas with clustered points and, thus, inaccurate models(Phillips et al., 2009). To reduce the effect of sampling bias on thedepredation risk model, we used spatial filtering to randomly decreasethe number of presence points in oversampled regions (Boria et al.,2014; Radosavljevic and Anderson, 2014), and removed all but one

depredation record within each 1 km pixel. In this way, we could retain85% of depredation points in the model.

2.4.2. Background extentMaxent compares conditions at the locations of the dependent

variable to randomly selected locations within a background area. Theextent of the area in which background points are selected should bedetermined according to the objectives of the study and characteristicsof the environmental conditions that are desired to be discriminatedfrom presence points (Merow et al., 2013). To define the backgroundextent, we created a buffer around each depredation point using themean home range size for Mexican wolves (17.6 km radius, USFWS,2017). We chose this buffer based on a tradeoff between needingbackground points that represent a range of variation, while restrictingthe background extent to only areas where wolves occur.

2.4.3. Model complexityMaxent is capable of fitting highly complex models. However, less

complicated models are more interpretable and less sensitive to sam-pling bias (Yackulic et al., 2013). We addressed three sources of modelcomplexity, multicollinearity, β multiplier, number and type of fea-tures, by applying sample size corrected Akaike Information Criteria(AICc; Akaike, 1974; Burnham and Anderson, 2007) in a stepwisefashion. First, we used the R package MaxentVariableSelection(Jueterbock, 2015) to obtain a set of models. Each model includedvariables that were not highly correlated (r≤ 0.7) and that had a modelcontribution>5% individually. We repeated the process of variableselection for a range of β multipliers from 0 to 15 at an increment of0.5. The β multiplier is a penalty coefficient to reduce overfitting(Tibshirani, 2011). MaxentVariableSelection is able to consider multi-collinearity, model contribution and β multiplier, but it is not able toinclude specified feature sets. Thus, we considered the variables of themodel with lowest AICc as the input for the next step. Next we used theR package ENMeval (Muscarella et al., 2014) to find the optimum set offeatures from an a priori set of features and retuned the β multiplier forthe variables selected by MaxentVariableSelection. Maxent calculatesfive models for each independent variable known as features: linear (L),quadratic (Q), product (P), threshold (T) and hinge (H). We tested 9 setsof feature classes: L, H, LQ, LQT, LP, HP, LQP, LQTP. We considered Lbecause one side of the unimodal curve might not be included in thebackground data (Elith et al., 2010). We examined H since avoiding Tmay improve the model performance and lead to a simpler andsmoother model (Phillips et al., 2017). We considered LQ because re-sponses of species to environmental variables are mostly nonlinear andunimodal, as observed in fundamental niches (Austin, 2007). We in-cluded LQT since some environmental conditions may limit speciesdistribution (e.g. highly rugged areas). We added P to L, H, LQ, LQTfeature sets since it may negligibly improve model performance, al-though it makes model interpretation difficult (Phillips et al., 2017).

2.4.4. Model evaluationWe did not use Maxent's default model evaluation, random parti-

tioning k-fold cross-validation, because it leads to overestimation ofperformance (Boria et al., 2014). Instead, we evaluated the accuracy ofmodel predictions by applying spatially independent k-fold cross-vali-dation with R package ENMeval using the ‘block’ method (Muscarellaet al., 2014). The block method was chosen because our aim was pro-jecting models developed for a small region (i.e., depredation in-cidences where Mexican wolves currently occur) to the entire studyarea (i.e., areas where depredations by Mexican wolves could even-tually occur; Wenger and Olden, 2012). The block method partitionedour presence points and background points into four bins of equalnumbers based on latitude and longitude lines.

We assessed the accuracy of predictions of models via threshold-independent and threshold-dependent omission rates. For thethreshold-independent evaluation methods we used Area Under the


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Curve of the Receiver Operating Characteristic plot (AUC) to evaluatethe overall model performance (Phillips et al., 2006). We also measuredoverfitting by calculating AUC difference, which is the difference be-tween AUC calculated on training localities and AUC calculated onevaluation localities (Warren and Seifert, 2011). Threshold-dependentomission rates quantify discriminatory ability and overfitting of models.These rates are based on two threshold criteria: 10% omission rate ofthe training records and lowest presence threshold. The former is avalue that excludes the 10% of localities with the lowest predictedvalues and its expected omission rate is 0.10. The latter is the minimumpredicted value for any pixels, including training points, with an ex-pected value of zero for test presence points. Generally, models withlower omission exhibit better discrimination between suitable and un-suitable areas, while models with higher omission rates indicate over-fitting (Anderson and Gonzalez, 2011). For both threshold-independentand threshold-dependent measures, we used the averaged values acrossthe four geographic bins. Maxent models assume that species are atequilibrium with the environmental variables used to fit the model.Extrapolation outside the range of variation represented by the en-vironmental variables can lead to errors. Thus, we ran a MultivariateEnvironmental Similarity Surface analysis (MESS, Elith et al., 2010)using package Dismo (Hijmans et al., 2017) to find where our model isviolating this assumption. MESS analysis quantifies the degree of si-milarity between the range of variables at occurrence locations andprojection data set. Predictions outside of the similar domain may notbe reliable (Elith et al., 2010).

3. Results

The model with the lowest AICc used a β multiplier= 3.5; linear,quadratic and product features, and it had 6 uncorrelated variables witha contribution>5% including canopy cover variation, elk abundance,land cover, slope, density of roads and density of developed areas(Tables 1 and 2). The most important variables in discriminating highdepredation risk from low depredation risk areas were canopy covervariation and relative abundance of elk (33.1% and 29.3% contribu-tion, respectively), both of which had a positive linear relationship withdepredation risk (Fig. 1). Land cover majority type had 13% contribu-tion to the model, with montane grassland having the highest prob-ability of depredation (90% probability), and pine woodland having thelowest probability of depredation (60% probability). There alsowas>65% chance of depredation in areas with a land cover majorityof mixed conifer forest, basin/playa, chaparral, desert/semi desertscrub, disturbed, pinyon-juniper woodland, riparian, rock and savannagrassland. In contrast, depredation risk was negatively related to slope,density of roads and density of developed areas (9.4%, 9.4% and 5.5%contribution, respectively; Fig. 1).

The mean AUC of the model was 0.81 indicating that the model hadgood overall performance (Araújo et al., 2005) in distinguishing areaswith high depredation risk from areas with low depredation risk(Table 1). The AUC difference was low (0.05) suggesting that the model

was not affected by overfitting toward depredation points and, thus,had a good transferability in space (Warren and Seifert, 2011).Threshold-dependent measures indicated that the model had lowoverfitting and high discriminatory ability at 10% omission rate (0.15)and lowest presence threshold (0.006).

The risk map revealed that most of the depredation hotspots arelocated within public lands managed by the U.S. Forest Service (Fig. 2).Within the MWEPA (i.e., south of I-40), the highest depredation riskhotspots were in portions of the Mogollon Highlands (i.e., vicinity ofthe former BRWRA). A large area with moderate risk was on the Mo-gollon Plateau near Flagstaff, Arizona. Other smaller hotspots of low tomoderate risk are in the Zuni Mountains, Magdalena Mountains, SanMateo Mountains, Manzano Mountains, and parts of the SacramentoMountains in New Mexico, and the Nantanes Pleateau and PinalenoMountains in Arizona (Fig. 2). According to the MESS analysis, areasnear large cities (except Flagstaff) had values for variables most outsidethe range of the depredation points, and hence these areas do notpredict well. Based on an examination of individual variable con-tributions to the MESS analysis, the poor prediction of these areas was aproduct of all of the variables except slope (see Appendix S5 in Sup-porting information).

4. Discussion

4.1. Depredation by Mexican wolves

We found that the primary factors associated with increased risk ofdepredation by Mexican wolves on livestock were higher canopy covervariation and higher relative abundance of elk. The positive relation-ship between risk of livestock depredation and abundance of elk isconsistent with other studies that also found a positive correlation be-tween the abundance of natural prey and depredation risk (Bjorge andGunson, 1985; Bradley and Pletscher, 2005; Karanth et al., 2013; Stahlet al., 2002; Treves et al., 2004). Elk are the primary prey for Mexicanwolves within their currently occupied range in Arizona and NewMexico (Carrera et al., 2008; Reed et al., 2006). Abundance of naturalprey is considered a key factor that determines distribution andmovement patterns of wolves (Fuller et al., 2010). A number of studieshave concluded that depredation on livestock ensues when wolves

Table 1Settings and evaluation metrics for a spatial risk model of cattle depredation by Mexican wolf (Canis lupus baileyi).

Featuresa βb Full AUCc Mean AUCd Mean AUC Differencee Mean omission ratef Mean minimum omission rateg Number of parametersh

LQP 3.5 0.88 0.81 0.05 0.15 0.006 11

a L= linear, Q= quadratic, P= product.b β= β multiplier.c AUC (Area Under the Curve of the Receiver Operating Characteristic plot) based on unpartitioned dataset.d AUC based on the testing data averaged across four bins.e Difference between the training AUC (calculated on training localities) and testing AUC (calculated on evaluation localities).f The 10% omission rate of the training records (a value that excludes the 10% of localities with the lowest predicted values).g The lowest presence threshold (the minimum predicted value for any pixels).h The number of parameters in the full model.

Table 2Percent contribution of variables in the risk model for cattle depredation by theMexican wolf (Canis lupus baileyi).

Variables Percent of contribution

Canopy cover variation 33.1Elk (Cervus canadensis) abundance 29.3Land cover 13.7Slope 9.5Density of roads 9.5Density of developed areas 5.5


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pursue their natural prey and unexpectedly confront livestock and shifttheir pursuit to livestock as an easier prey (Bjorge and Gunson, 1985;Bradley and Pletscher, 2005; Oakleaf et al., 2006; Oakleaf et al., 2003).

Elk, like many other prey species, alter their profitable habitat (opengrasslands) in response to predation risk (Mao et al., 2005). Wolves arepursuit predators that prefer to hunt in flat, open areas (Davie et al.,2014; Treves et al., 2011). Consequently, dense forests may be per-ceived as less dangerous to elk than open grasslands (Mao et al., 2005).In the Greater Yellowstone Ecosystem, Creel et al. (2005) reported thatelk used open grasslands in the absence of wolves, but that elk movedinto forest and more steep terrain when wolves were present. Similarly,

we found higher depredation risk in areas with open land cover(montane grassland) and flatter slopes, and lower depredation risk inforested areas with steeper slopes. Cattle also tend to prefer opengrassland and flatter slopes (Bailey et al., 2001; Bailey, 2005). There-fore, it is possible that cattle become more vulnerable to depredation byMexican wolves when elk vacate open grassland and move into forestsor rugged terrain. These relationships also provide an explanation forthe positive relationship between canopy cover variation and depre-dation risk. Areas with higher canopy cover variation might provideideal conditions for elk, due to comingling of high quality (but highrisk) foraging habitats with poor quality (but safer) foraging habitats,

kcotsevilno

noitaderpedflownaicxe

MfoytilibaborP

Canopy Cover Varia�on Rela�ve Elk Abundance

Land Cover MajorityaSlope

Density of Roads Density of Developed Areas

Fig. 1. Response curves of the Maxent model for Mexican wolf (Canis lupus baileyi) depredation on cattle. For description of variables see Table S2.1. aLand covermajority types: 3, mixed conifer forest; 5, basin/playa; 6, chaparral; 7, desert/semidesert; scrub, 8, arroyo; 9, disturbed; 11, montane grassland; 12, oak woodland;13, open water; 14, pine woodland; 15, pinyon-juniper woodland; 18, riparian wetland; 19, rock; 20, savanna/semidesert grassland.


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resulting in less opportunity for predation on elk by wolves (Mao et al.,2005). This could result in increased risk of livestock depredation. Al-though the abundance of natural prey and land cover have been re-cognized as influencing factors associated with depredation risk bywolves in the Southwestern U.S. (our study), Northern Rockies (Bradleyand Pletscher, 2005) and Midwest (Treves et al., 2004), the differencesin natural prey seasonal movements and livestock husbandry practicesmay influence this relationship. For instance, in the Northern Rockiesdepredations are seasonal in relation to how livestock are managed andmigration of ungulates (Bradley and Pletscher, 2005; Nelson et al.,2012). In the Midwest, white-tailed deer is the primary prey and live-stock are mostly kept in confined pastures on private lands (Treveset al., 2004). In the Southwestern U.S., livestock grazing is mostly year-round on public lands and depredations occur year-round, with an in-crease in the denning season (USFWS, 2015). In our study, annual li-vestock density was not an important variable in the best depredationrisk model (its contribution to the model was 2%). Other studies onwolf (Behdarvand et al., 2014), cougar (Teichman et al., 2013), andlynx (Linnell et al., 1999; Mao et al., 2005), also reported no relation-ship between the density of livestock and depredation events. However,some other studies have demonstrated that livestock density is an im-portant factor influencing depredation in areas with different livestockhusbandry systems (Miller, 2015). It is possible that livestock densitywas underrepresented in our model due to the coarse scale and absenceof data on seasonal abundance of livestock. Future studies that includevariables such as herd size, type of operation, and seasonal grazingpatterns may reveal more information about the relationship betweenlivestock density and depredation risk in the Southwestern U.S. Wefound that depredation risk was higher in areas remote from humandevelopment and with lower road density. Similar results were foundby Treves et al. (2004) and Davie et al. (2014). These patterns are likelyrelated to wolf habitat selection. Higher road and human densities can

decrease habitat suitability for wolves and, therefore, wolves establishterritories in areas with lower road and human densities (Mech et al.,1988; Oakleaf et al., 2006; Wydeven et al., 2001).

The risk map revealed the spatial configuration of depredationhotspots. Depredation hotspots are mostly located within montaneareas that are public lands in National Forests. Because these montaneareas have similar environmental conditions compared with thosesurrounding the depredation locations, the model makes robust pre-dictions about depredation risk in most of these areas. Further, many ofthese montane areas are also considered areas most suitable forMexican wolves by virtue of their forest cover, high native ungulatedensity, low livestock density, and low road and human densities(USFWS, 2017). Consequently, our risk map can help inform futureexpansion of the distribution of Mexican wolves in Arizona and NewMexico in order to minimize potential future conflicts. Moreover, thismap can be used to prioritize areas for depredation risk mitigation in-cluding the implementation of active non-lethal methods in depreda-tion hotspots. Our results indicate that spatial overlap of livestock inareas with abundant elk was associated with the risk of depredation.Thus, spatiotemporal management of livestock grazing to reduce thisoverlap could decrease the risk of depredation. For instance, depreda-tions might be reduced by releasing livestock into pastures withinhotspot areas after elk calving has occurred and elk become more dis-persed. Other strategies for reducing depredation risk include limitingthe exposure of young livestock to open range situations where theymay be more prone to being attacked by wolves (Oakleaf et al., 2003),increasing human presence while simultaneously using non-lethal toolsin an adaptive and proactive fashion (Stone et al., 2017) and preventingMexican wolves from denning around areas of higher depredation risk(USFWS, 2003).

Spatial risk models demonstrate the interactions between predatorsand livestock in a dynamic system (Miller, 2015). Therefore, with the

Fig. 2. Map of predicted depredation on cattle by the Mexican wolf (Canis lupus baileyi) in Arizona and New Mexico, USA. Lines are major highways and stars aremajor cities. Depredation risk is highest in areas in red and is lowest in areas in dark blue. Depredation incidences (black dots) are filtered at 1 km scale. (Forinterpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)


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expansion of Mexican wolves' distribution, the depredation risk mapshould be updated by adding new data and the results of managementfeedback. Mexican wolves may adjust their hunting patterns in responseto alteration in patterns of natural prey and livestock distribution anddensity. In areas where deer are the primary prey, the relationshipbetween depredation risk, natural prey abundance and livestock maychange. Landscape variables are only part of the picture. Complimen-tary studies on the effect of individual and population level aspects(e.g., breed, size, and age of livestock; management of livestock; wolfpack makeup) on depredation risk will be required with an expansion ofMexican wolf distribution.

There are several caveats or limitations to our study. First, our de-predation risk model was developed at a 1 km resolution landscapescale based on GIS layers. Therefore, the model does not consider otherfactors at the individual or population level that can contribute to de-predation risk, such as breed, sex, age, or management of livestock (DeAzevedo and Murray, 2007; Ogada et al., 2003; Teichman et al., 2013)or demographics of wolves (Marucco and McIntire, 2010). Second, ourrisk map assumes Mexican wolves are present throughout the entirestudy area. Obviously, there is no risk of depredation by wolves wherethey are not actually present. Third, the depredation risk model wasbuilt based on environmental conditions around depredation locationsthat occurred from 1998 to 2017, which were primarily within theformer BRWRA. Thus, the accuracy of the model's predictions outside ofthis range depends on the degree of similarity of the environmentalvariables within and outside of this range. The MESS analysis demon-strated that the model predicts well in all areas of the study area exceptaround some (but not all) major cities, where wolves are unlikely tooccur. Finally, the relative abundance of mule deer and white-taileddeer were not important predictors in our model, probably because elkare the primary prey species in vicinity of the former BRWRA. However,deer are the primary prey for Mexican wolves where elk are absent(Bednarz, 1988; Brown and Shaw, 2002). Therefore, we urge caution ininterpreting the model in areas, such as the Sky Island region ofsoutheastern Arizona, where elk are generally absent and deer wouldprovide the primary natural prey for wolves.

4.2. Recommendations for risk modeling

We developed the risk model for Mexican wolf depredation on li-vestock by 1) selecting variables based on a full spectrum of specificwell-rationalized biological hypothesis related to factors that may in-fluence depredation risk, 2) creating important variables that were nototherwise available (e.g., livestock density and prey abundance), 3)developing Maxent models by adhering to all current recommendationsfor reducing biases and overfitting, and 4) using multiple model eva-luation metrics. Our approach can serve as a model for other futuredepredation risk modeling studies.

1. When developing a depredation risk model, it is important to in-clude a predictor variable related to livestock abundance. Our re-sults did not support our assumption that depredation risk was re-lated to livestock abundance. However, because we tested thisrelationship using fine scale data on livestock abundance, it providesstronger support for our key findings that wolf depredation wasprimarily associated with abundance of natural prey rather thanlivestock. This suggests that management to reduce depredationcould preferentially focus on areas with high natural prey abun-dance, rather than areas with high livestock abundance. Detaileddata on livestock abundance are generally not available. This pro-blem may be more challenging for large regional study areas, forareas with free range livestock grazing (such as public lands allot-ment grazing management in western U.S.), or where there is amosaic of various land ownership, in comparison with areas wherelivestock are raised on small farms or in small fenced pastures. Ourmodel of annual livestock density is the first model to rigorously

predict livestock abundance at a large regional scale. We demon-strated that AUM stocking rates can be predicted by environmentalvariables. Stocking rate data, such as AUM, are available in manyareas under managed livestock grazing. Modeling stocking rateusing appropriate methods and predictors can fill the gap of live-stock abundance data in human-wildlife conflict studies.

2. Abundance of natural prey is perhaps the most important variable toincorporate in depredation risk modeling (Miller, 2015). In ourstudy, relative abundance of elk was a primary predictor of depre-dation risk. However, actual data on abundance of natural prey arerarely available, except in small study areas where field studies haveoccurred. Estimates of abundance of natural prey over large studyareas, such as those based on game management units, may be toocrude or have too much uncertainty to fulfill study goals (Pearce andBoyce, 2006). Maxent's raw output can be interpreted as an estimateof relative abundance (Phillips et al., 2017). Therefore, speciesdistribution models created with Maxent can serve as a surrogate forprey abundance in the absence of detailed field data. However, theperformance of Maxent depends on the quality of dependent andindependent variables and proper configuration of its settings(Merow et al., 2013). An advantage of using Maxent is that thedependent variable (species occurrence data) is usually alreadyavailable from a variety of sources (e.g., Global Biodiversity In-formation Facility). However, these data have their own constraints,especially spatial bias, which must be addressed to obtain accurateresults (Beck et al., 2014). Our study showed that Maxent's rawoutput can fill the gap of natural prey abundance in human-wildlifeconflict studies. More research is needed to understand the re-lationships between Maxent output and actual animal abundances.Also, future studies should use independent data to validate ourmodels.

3. In this study, we incorporated all current recommendations forimproving Maxent performance including correcting sampling bias,defining background extent, evaluating model complexity (reducingmulticollinearity, tuning beta parameter, tuning feature classes),and performing unbiased model evaluation (Merow et al., 2013;Radosavljevic and Anderson, 2014). Few studies of any kind (in-cluding to our knowledge no spatial risk modeling studies) haveimplemented all recommendations for producing unbiased and ro-bust Maxent models (Morales et al., 2017). Using Maxent's defaultsettings can lead to overly complex models that reveal odd re-lationships between variables and depredation risk as a result ofoverfitting, and consequently potentially lead to incorrect conclu-sions (Radosavljevic and Anderson, 2014).

4. Based on our prey model results, we suggest that when developingspecies distribution models over large areas it is important to testperformance of models generated based on different backgroundextents and scales of rarification. In addition, our results supportconclusions of others that Maxent models be evaluated using mul-tiple metrics including expert evaluation (Muscarella et al., 2014;Radosavljevic and Anderson, 2014).

5. Conclusions

Negative human-wildlife interactions can reduce the perceivedvalue of a species (Conover, 2001). Therefore, employing creative andless costly approaches such as spatial risk models can help to reversethis process (Treves et al., 2011). We showed that spatial risk modelscan be created using available data. However, the quality of predictionsdepends on the quality of predictor variables and the modeling ap-proach. Our approach to create natural prey and livestock abundancevariables can facilitate the process of spatial risk modeling when lim-itations in availability of prey abundance data are a challenge, espe-cially in large-scale studies.


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Acknowledgements

We thank US Department of Agriculture/Animal and Plant HealthInspection Service/Wildlife Services, US Fish and Wildlife Service,Arizona Game and Fish Department, New Mexico Department of Gameand Fish, United States Forest Service Southwest Region, Bureau ofLand Management, and Mexican Wolf Recovery Program for providingdata and advice. We are grateful to the following people for their as-sistance and support: Dawn VanLeeuwen, Amy Ganguli, Jay Gedir,Fitsum Abadi, Julia Smith, Nicole Quintana, James Pitman, TimothyFrey, Jim Heffelfinger, Rick Langley, John Oakleaf, Alan May and KevinSanchez. Any use of trade, firm, or product names is for descriptivepurposes only and does not imply endorsement by the U.S.Government.

Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.biocon.2018.06.013.

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Appendix S1: Description of the study area.

The study area was the states of Arizona and New Mexico (Figure S1.1). This region is

within the Interior Plains and Intermontane Plateaus physiographic regions, which contain three

physiographic provinces: the Great Plains in the eastern portion, the Colorado Plateau in the

north-central portion, and the Basin and Range in the central and western portion (Wahlberg,

Triepke, & Stringer, 2014). The climate is mostly cold semi-arid, but ranges from desert climate

at the lowest elevations to cool summer humid continental climate in the mountains (Peel,

Finlayson, & McMahon, 2007). Elevations range from 22 m at the Colorado River to 4,013 m at

Wheeler Peak in northeastern New Mexico.

Figure S1. 1. Map of study area and boundaries of the Blue Range Recovery Area and Mexican

Wolf Experimental Population Area.

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Geiger climate classification. Hydrology and Earth System Sciences Discussions, 4, 439–

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Wahlberg, M., Triepke, F. J., & Stringer, S. H. (2014). Ecological Response Units of the

Southwestern United States. US Department of Agriculture, Forest Service, Southwestern

Region.

Appendix S2: Hypotheses, sources, and calculations of predictor variables used for modeling risk of cattle depredations by the Mexican wolf (Canis lupus baileyi).

The influence of natural prey on depredation rates is not always obvious. The rate of wolf depredation on livestock may be greater where the density of natural prey is low (Kaartinen, Luoto, & Kojola, 2009). However, predators may not be attracted by presence of livestock, per se. Rather, predators following their natural prey may fortuitously encounter livestock (Bradley & Pletscher, 2005; Packer, Ikanda, Kissui, & Kushnir, 2005; Treves et al., 2004). Therefore, we hypothesized that high densities of natural prey increases the risk of depredation.

Prior research has documented both linear and nonlinear relationships between cattle density with the risk of depredation by wolves (Bradley and Pletscher 2005; Kaartinen et al. 2009; Treves et al. 2011; Suryawanshi, Bhatnagar & Mishra, 2013; DeCesare, Wilson, Bradley, Inman, Lance, Laudon, Nelson, Ross & Smucker, 2018). Large herds of livestock may serve as a greater attraction to wolves, or have a higher probability that the herd contains highly vulnerable individuals (Bradley & Pletscher, 2005; Edge, Beyer, Belant, Jordan, & Roell, 2011) or increase the encounter rate (Linell et al., 1999, Suryawanshi et al., 2013). Therefore, we hypothesized that there is a positive relationship between livestock abundance and depredation risk.

Different land cover types may encompass different densities of wolves, livestock, natural prey, and/or different rate of wolf attacks on livestock (Bradley & Pletscher, 2005; Kaartinen et al., 2009; Treves et al., 2011). Land cover types may have different levels of attraction for livestock and wolves may find them when they are following their natural prey (Bradley & Pletscher, 2005). Dense vegetation cover can increase the risk of depredation by wolves (Mech, Harper, Meier, & Paul, 2000). In contrast, the probability of cattle depredation by wolves may be higher in open areas (Edge et al., 2011; Treves et al., 2011). In addition, the probability of wolf depredation on livestock may be higher in mosaics of different land cover and canopy cover types (Kaartinen et al., 2009). Our study area is composed of a diversity of land covers ranging from desertscrub to coniferous forests. We tested the hypothesis that such variety could affect the risk of livestock depredation by the Mexican wolf. We included topographic variables in the model because wolves may prefer more rugged terrain and specific aspects because of more concealment opportunity or prey availability (Davie, Murdoch, Lhagvasuren, & Reading, 2014). Conversely, wolves may prefer less structural complexity. It has been suggested that higher elevations may provide safer hunting sites for wolves because of less land use complexity (Suryawanshi et al., 2013).

Wolves may tend to establish territories near water resources (Mladenoff, Haight, Sickley, & Wydeven, 1997). Various densities of water resources can have different attractive levels for wolves (Kaartinen et al., 2009). However, there may be no correlation between depredation risk and amount of open water (Edge et al., 2011). We tested the hypothesis that availability of water resources influences the occurrence of cattle depredation especially because of the arid environments in the southwestern U.S.

It has been suggested that the presence of roads and developed areas may have a negative or positive impact on depredation risk (Kaartinen et al., 2009; Mech et al., 2000). Hence, we included density and distance to roads and developed areas to test these hypotheses.

Table S2. 1 includes variables’ sources and the way they were calculated. The original pixel size of all variables was 30 m, except annual AUM density, which was 1 km. All variables were scaled to 1 km pixel size.

Table S2.1. Descriptions, calculations and sources of variables used in spatial modeling of Mexican wolf (Canis lupus baileyi) depredation on cattle in Arizona and New Mexico, USA. Variable Variable description/calculation Source

BIOTIC VAVRIABLES

Annual livestock density Program R (version 3.2.3; R development core team 2015) to model annual livestock density as a function of different sets of 18 biologically relevant spatial variables (see Appendix S3 for details).

see Appendix S3

Natural prey relative abundance (elk, mule deer and white-tailed deer)

Maxent (version3.3.3a, Phillips et al., 2006) to model occurrence locations of natural prey as a function of 34 biologically relevant spatial variables (see Appendix S4 for details)

see Appendix S4

Land cover majority Arc GIS 10.3 Zonal Statistics tool to identify the major land cover category within each allotment. We reduced the number of land cover categories from 50 to 19 by combining similar land cover types (e.g., Madrean Pine-Oak Forest and Woodland and Southern Rocky Mountain Ponderosa Pine Woodland were considered pine woodland).

Land cover variation Arc GIS 10.3 Focal Statistics tool (Spatial Analysis toolbox) to calculate the number of land cover types within Mexican wolves’ mean home range size

Canopy cover type Arc GIS 10.3 Zonal Statistics tool to identify the major canopy cover category within each allotment.

Canopy cover variation Arc GIS 10.3 Focal Statistics tool (Spatial Analysis toolbox) to calculate the number of canopy cover types within Mexican wolves’ mean home range size

Southwest Regional Gap Analysis land cover map (USGS 2007,)

Southwest Regional Gap Analysis land cover map (USGS 2007, http://swregap.nmsu.edu/) LANDFIRE canopy cover (USGS 2013, http://www.landfire.gov/) LANDFIRE canopy cover (USGS 2013,

HUMAN VARIABLES

Density of roads Arc GIS 10.3 Focal Statistics tool (Spatial Analysis toolbox) to calculate density of major roads in natural prey’s average home range size

TIGER data (United States Census Bureau, https://www.census.gov/)

Distance to roads Arc GIS 10.3 Euclidean Distance tool (Spatial Analysis toolbox) to calculate the minimum distance from each pixel to major roads


Density of developed areas Arc GIS 10.3 Point Density tool (Spatial Analysis toolbox) to calculate density of population of developed areas (city, town and census-designated place) in Mexican wolves’ average home range size

GIS data: TIGER data (United States Census Bureau, https://www.census.gov/); population data (2010): American Fact Finder (United States Census Bureau, https://factfinder.census.gov)

Distance to developed areas

Arc GIS 10.3 Euclidean Distance tool (Spatial Analysis toolbox) to calculate the minimum distance from each pixel to developed areas


LANDSCAPE VARIABLES

Elevation Downloaded elevation data National Elevation Dataset (http://nationalmap.gov/elevation.html)

Slope Arc GIS 10.3 slope tool (Spatial analysis toolbox) National Elevation Dataset (http://nationalmap.gov/elevation.html)

Aspect Arc GIS 10.3 Slope/Aspect transformation tool (Geomorphometry & Gradient Metrics toolbox; Evans et al. 20114) to transform circular aspect to linear aspect in which North and Northeast (typically wettest and coolest slopes) are assigned a value of zero, and a value of one is assigned to South and Southeast (typically hotter and drier slopes; Robert

National Elevation Dataset (http://nationalmap.gov/elevation.html)

and cooper 1989). Other directions are assigned a value between zero and one resulting in a continuous variable.

Terrain ruggedness index Arc GIS 10.3 Raster Calculator tool to calculate the average absolute difference between each pixel elevation value and each of its eight neighbors

National Elevation Dataset (http://nationalmap.gov/elevation.html)

Density of water resources Arc GIS 10.3 Focal Statistics tool (Spatial analysis toolbox) to calculate the density of pixels containing a perennial water resource (spring, artificial water resource, river and lake) within Mexican wolves’ average home range size.

National Hydrologic Dataset, https://nhd.usgs.gov/)

Distance to water resources

Arc GIS 10.3 Euclidean Distance tool (Spatial Analysis toolbox) to calculate the minimum distance from each pixel to perennial water resources.

National Hydrologic Dataset, https://nhd.usgs.gov/)

REFERENCES:

Bradley, E. H., & Pletscher, D. H. (2005). Assessing factors related to wolf depredation of cattle in fenced pastures in Montana and Idaho. Wildlife Society Bulletin, 33, 1256–1265.

Davie, H. S., Murdoch, J. D., Lhagvasuren, A., & Reading, R. P. (2014). Measuring and mapping the influence of landscape factors on livestock predation by wolves in Mongolia. Journal of Arid Environments, 103, 85–91.

DeCesare, N. J., Wilson, S. M., Bradley, E. H., Gude, J. A., Inman, R. M., Lance, N. J., Laudon, K. , Nelson, A. A., Ross, M. S. and Smucker, T. D. (2018), Wolf-livestock conflict and theeffects of wolf management. Journal of Wildlife Management, doi:10.1002/jwmg.21419

Edge, J. L., Beyer, D. E., Belant, J. L., Jordan, M. J., & Roell, B. J. (2011). Adapting a predictive spatial model for wolf Canis spp. predation on livestock in the Upper Peninsula, Michigan, USA. Wildlife Biology, 17, 1–10.

Kaartinen, S., Luoto, M., & Kojola, I. (2009). Carnivore-livestock conflicts: Determinants of wolf (Canis lupus) depredation on sheep farms in Finland. Biodiversity and Conservation, 18, 3503–3517.

Linnell, J. D. C., Odden, J., Smith, M. E., Aanes, R., & Swenson, J. E. (1999). Large carnivores that kill livestock: Do “problem individuals” really exist? Wildlife Society Bulletin, 27, 698–705.

Mech, L. D., Harper, E. K., Meier, T. J., & Paul, W. J. (2000). Assessing Minnesota factors farms to predispose depredations wolf cattle. Wildlife Society Bulletin, 28, 623–629.

Mladenoff, D. J., Haight, R. G., Sickley, T. A., & Wydeven, A. P. (1997). Causes and Implications of Species Restoration in Altered Ecosystems. BioScience, 47, 21–31.

Packer, C., Ikanda, D., Kissui, B., & Kushnir, H. (2005). Conservation biology: Lion attacks on humans in Tanzania. Nature, 436, 927–928.

Suryawanshi, K. R., Bhatnagar, Y. V., Redpath, S., & Mishra, C. (2013). People, predators and perceptions: patterns of livestock depredation by snow leopards and wolves. Journal of Applied Ecology, 50, 550–560.

Treves, A., Martin, K. a., Wydeven, A. P., & Wiedenhoeft, J. E. (2011). Forecasting environmental hazards and the application of risk maps to predator attacks on livestock. BioScience, 61, 451–458.

Treves, A., Naughton-Treves, L., Harper, E. K., Mladenoff, D. J., Rose, R. A., Sickley, T. A., & Wydeven, A. P. (2004). Predicting human-carnivore conflict: A spatial model derived from 25 years of data on wolf predation on livestock. Conservation Biology, 18, 114–125.

Appendix S3: Detailed description of the methods and results for the annual livestock density model, which was used as a predictor variable in the Mexican wolf (Canis lupus baileyi) depredation risk model.

Methods

Annual livestock density was modeled on basis of Animal Unit Month (AUM) data for 3876 allotments on lands managed by the US Forest Service (USFS) and Bureau of Land Management (BLM). Together, these allotments accounted for 39% of the study area (entire Arizona and New Mexico), while the interpolated area accounted for 61%. We used BLM and USFS data because they were most widespread and accurate available data on livestock abundance in the study area. On public lands, livestock stocking rates are based on animal unit month (AUM), which is the amount of forage needed by one “animal unit” for one month, and where the animal unit is defined as one mature 454 kg cow and her nursing calf (Holechek, 1988). Other types of livestock are assigned AUM equivalents. Stocking rates for a type of livestock can be calculated based on the estimated amount of available forage in an area (Sprinkle & Bailey, 2004), although in practice on public lands stocking rates are typically based in reference to historical values that seek to maintain sustainability of forage production and other considerations (i.e., livestock carrying capacity; Holechek, 1988). Therefore, given that AUM is based on forage consumption, the “annual AUM density” (=annual livestock density) is premised on the inference that the carrying capacity for livestock in terms of allowable AUM varies in relation to spatial variables (e.g., elevation, annual precipitation). Because stocking rates may be reduced by mandate or choice during drought periods, we obtained AUM data for 2010 since the Palmer Drought Severity Index (PDSI; Dai, Trenberth, & Qian, 2004) during that year was near zero. We obtained AUM data for 3,876 allotments from the USFS Southwestern Region and the BLM Rangeland Administration System (BLM, 2015). We summed the AUMs of different seasons to obtain annual AUMs and, then, converted them to density on basis of the area of their corresponding allotments.

We used generalized linear models (family = normal, link = identity) in Program R (Version 3.4.0; R core team, 2017) to model annual AUM density as a function of different sets of 37 biologically relevant spatial variables that represent, biotic, landscape, and bioclimatic features (Table S3.1). For the biotic variables, we used land cover type because some types might provide more grazing opportunity than others (Holechek, Pieper, & Herbel, 1998), we used tree canopy cover percentage because the amount of solar radiation reaching understory vegetation (which is available to livestock for grazing) is influence by tree canopy cover (Holechek et al., 1998), and we used Normalized Difference Vegetation Index (NDVI), a greenness index, to describe productivity, which is likely to influence livestock density (Feilhauer, He, & Rocchini, 2012).

For landscape variables, we included elevation as a master covariate because it has a strong influence on other covariates such as climate, productivity and land cover. We included slope (%) and Terrain Ruggedness Index (TRI) because livestock might avoid steep slopes and areas with high topographic ruggedness (Cook, 1966; Gillen, Krueger, & Miller, 1984). Ecological Site Description (ESD) is a classification system that describes ecological potential for different land use including grazing (Butler et al., 2003). We used soil suborder as a surrogate because ESDs were not available for the entire study area and they are ultimately based on soil

types and climate (Butler et al. 2003). We included horizontal distance to water and water availability because in arid environments livestock may limit their activities to areas near water resources (Bailey, Kress, Anderson, Boss, & Miller, 2001; Bailey, 2005). In addition, we used vertical distance to water because the relationship between cattle density and distance to water may differ in areas with rough topography from those with less topographic variation (Bailey, 2005; Gillen et al., 1984).

For the bioclimatic variables, we included mean temperature of warmest quarter and mean temperature of the coldest quarter of the year because they influence plant dormancy and, consequently, the level of available nutrients for livestock during hot and cold seasons (Schmidt, 1975). We included annual precipitation, precipitation of the warmest quarter of the year, and precipitation of the driest quarter of the year because precipitation influences primary production and hence availability of forage in the year, during the growing season, and during the season when precipitation may be limiting (Feilhauer et al., 2012). We included an interaction term between mean temperature of the coldest quarter of the year and precipitation of the coldest quarter of the year on the premise that it represented the type of precipitation (rain versus snow) in the coldest quarter. In addition, we included precipitation and temperature seasonality because they may influence temporal accessibility of livestock to forage (Fynn & Connor, 2000).

The original scale of the predictor variables was 30 m except the bioclimatic variables which was 1 km. All rasters were rescaled to 1 km. For soil suborders, we converted the polygon base map to a raster with 1 km pixel size (Table S3.1). We extracted the mean for each continuous variable for each allotment using zonal statistics in ArcGIS 10.3. For categorial variables, we extracted the category with the largest representation in each allotment.

We conducted exploratory analyses to develop a set of a priori models for testing. First, we removed influential observations using Cook’s distance method based on a preliminary model (Ramsey & Schafer, 2002). Next, we evaluated two parameters, coefficient of variation (CV) and quadratic term, for each continuous independent variable. We considered the CV as ameans to describe variation within allotments, since variables represented means calculatedbased on allotments. We evaluated potential quadratic relationships by examining residual plotsand by considering biological assumptions about the shape of these relationships. We tested ifthe CV or quadratic term, or combinations of these terms, were more informative than the linearform of a variable based on AICc. Due to the large number of possible variables and lack of priorinformation about how AUM is influenced by environmental varaibles, we created a preliminaryset of 500 models that represented an array of simple to complex combinations of variablesrepresenting different classes of environmental variables that might influence annual AUMdensity. To avoid collinearity, we only included variables and terms in the same model that werenot highly correlated (i.e., |r|<0.7). After eliminating models that had weights near zero (<0.00001), our final model set for testing included 108 models.

We checked the assumptions of the linear regression for top ranked models by examining scatter plots of variables and diagnostic plots of standardized residuals versus fitted values, normal quantile plot of residuals and residuals versus each explanatory variable. The normal quantile plot of residuals indicated that the response data are left skewed. Thus, we transformed annual livestock density to the logarithmic form using Box-Cox transformation (λ=0). We followed an information-theoretic approach (Burnham & Anderson, 2007) using AICc and assigning AICc weights to rank candidate models. We considered all models with ΔAICc ≤ 2 to be competitive, except in instances where a more informative model (model with lower AICc) was nested within a less informative model (model with higher AICc; Arnold 2010). We ran ten

repeats of 10-fold cross-validation of the best model to find the average prediction error of the top ranked model. Finally, we used estimated coefficients (β) of the top ranked model to create a livestock capacity prediction map for Arizona and New Mexico. The scale of our model was the allotment (we used average and CV of the variables within each allotment as independent variables to build the model), while we needed to create a prediction map at 1 km pixel size scale, which was the scale of our study. Thus, for each variable, we calculated the mean value for each pixel using a moving-window approach based on the mean allotment size using the Focal Statistic Tool in ArcMap 10.3.

Results

The GLM analysis revealed two models with ΔAICc ≤ 2 (Table S3. 2). However, we selected model 97 as the top model because it had the lowest ΔAICc and it was nested within the second best model (model 98). Model 97 had a 68% likelihood of being the best model in the set of 108 candidate models. The average prediction error for model 97 based on ten repeats of 10-fold cross-validation was 0.3, indicating good performance of the model (Molinaro, Simon, & Pfeiffer, 2005).

Based on the top model, the land cover types with the strongest positive relationship with annual AUM density were plains scrub (β= 0.26) and mountain grassland (β= 0.21), while developed (β= -0.41) and disturbed (β= -0.20) had the strongest negative relationship. The soil suborders with the strongest positive relationship with annual AUM density were Boralls (β= 0.24) and Ustalfs (β= 0.13), while Cambids (β= -0.62) and Gypsids (β= -0.55) had the strongest negative relationship. Annual AUM density had a negative quadratic relationship with canopy cover and TRI, and a positive quadratic relationship with temperature and precipitation seasonality, and precipitation of the driest, warmest, and coldest quarter of the year. Annual AUM density had a negative relationship with CV of vertical distance to water, TRI and precipitation seasonality and a positive relationship with CV of precipitation of the driest quarter (Table S3. 3).

The map of annual AUM density indicates areas with high livestock capacity primarily in the Great Plains region of eastern New Mexico and certain isolated montane regions in northern New Mexico and central and southern Arizona. In contrast, there was generally much lower annual AUM density in low elevation desert regions of both states (Figure S3.1).

Table S3.1. Description of covariates for spatial modeling of annual animal unit month (AUM) density on livestock grazing allotments managed by the Bureau of Land Management and United States Forest Service in Arizona and New Mexico during 2010.

Variable Abbreviation Variable description/calculation Source

BIOTIC VARIABLES

Land cover majority - Arc GIS 10.3 Zonal Statistics tool to identify the majorland cover category within each allotment.We reduced the number of land cover categories from 50to 19 by combining similar land cover types (e.g.,Madrean Pine-Oak Forest and Woodland and SouthernRocky Mountain Ponderosa Pine Woodland wereconsidered pine woodland).

Tree canopy cover (%)

Considering the middle range of tree cover categories toobtain a continuous raster

Average Annual Normalized Difference Vegetation Index of 2010

NDVI Arc GIS 10.3 Raster Dataset tool (Data managementtoolbox) to mosaic annual NDVI raster files to create anintegrated raster for entire study area

Southwest Regional Gap Analysis land cover map (USGS 2007, http://swregap.nmsu.edu/)

LANDFIRE canopy cover (USGS 2013, http://www.landfire.gov/) Web-Enabled Landsat data (USGS 2015, )

LANDSCAPE VARIABLES

Elevation - Downloaded data National Elevation Dataset (USGS 2009, http://nationalmap.gov/elevation.html)

Slope (%) - Arc GIS 10.3 slope tool (Spatial analysis toolbox) National Elevation Dataset (USGS 2009, http://nationalmap.gov/elevation.html)

Terrain Ruggedness Index

TRI Arc GIS 10.3 Raster Calculator tool to calculate the average absolute difference between each pixel elevation value and each of its eight neighbors (Riley et al. 1999)

Soil Suborder Majority

- Arc GIS 10.3 Zonal Statistics tool to identify the majorsoil suborder of the Integrated soil suborder maps

Horizontal Distance to Water Resources

HDW Arc GIS 10.3 Euclidean Distance tool (Spatial Analysis toolbox) to calculate the minimum distance from each pixel to perennial water resources including springs, artificial water resources, rivers and lakes

Coefficient of Variation of HDW

HDW (CV) Arc GIS 10.3 Raster Calculator to calculate CV of HDW by calculating the ratio of its standard deviation (SD) to its mean

Vertical Distance to Water Resources

VDW ArcGIS 10.3 Cost Path tool by using the variation of slope as a cost layer.

Coefficient of Variation of VDW

HDW (CV) Arc GIS 10.3 Raster Calculator to calculate CV of VDW by calculating the ratio of its standard deviation (SD) to its mean

Water availability - Arc GIS 10.3 Zonal Statistics and Raster Calculator Tocalculate the percentage of pixels containing perennialwater to the total numbers of pixels within a buffer with3.2 km radius (Holechek 1988).

National Elevation Dataset (USGS 2009, http://nationalmap.gov/eleva tion.html) Soil Survey Geographic (SSURGO, USDA 2015, ) and General Terrestrial Ecological Units (GTES, USFS 1998, https://www.fs.usda.gov/deta il/r3/landmanagement/gis/?ci d=stelprdb5201889) datasets National Hydrologic Dataset (USGS 2015, https://nhd.usgs.gov/)

National Hydrologic Dataset (USGS 2015, https://nhd.usgs.gov/) National Hydrologic Dataset (USGS 2015, https://nhd.usgs.gov/) National Hydrologic Dataset (USGS 2015, https://nhd.usgs.gov/) National Hydrologic Dataset (USGS 2015, https://nhd.usgs.gov/)

BIOCLIMATIC VARIABLES

Temperature seasonality

BIO4 Standard deviation of the 12 mean monthly temperature values multiplied by 100

(Hijmans, Cameron, Parra, Jones, & Jarvis, 2005; http://www.worldclim.org/)

Coefficient of Variation of BIO4

BIO4(CV) Arc GIS 10.3 Raster Calculator to calculate CV of BIO4 by calculating the ratio of its standard deviation (SD) to its mean

(Hijmans et al. 2005; http://www.worldclim.org/)

Mean temperature of warmest quarter

BIO10 Mean temperature of three consecutive months with highest mean maximum monthly temperature


Quadratic term of BIO10

BIO102 Arc GIS 10.3 Raster Calculator to calculate the quadratic term of BIO10





Mean temperature of coldest quarter

BIO11 Mean temperature of three consecutive months with lowest mean maximum monthly temperature








Annual precipitation BIO12 Mean annual precipitation (Hijmans et al. 2005; http://www.worldclim.org/)







Precipitation Seasonality

BIO15 Standard deviation of the means of monthly precipitation (Hijmans et al. 2005; http://www.worldclim.org/)







Precipitation of driest quarter

BIO17 Sum of mean precipitation for three consecutive months with lowest mean precipitation








Precipitation of warmest quarter

BIO18 Sum of mean precipitation for three consecutive months with highest mean precipitation









BIO19 Sum of mean precipitation for three consecutive months with lowest mean monthly temperature








The interaction of BIO11 and BIO19

BIO11*BIO19 Arc GIS 10.3 Raster Calculator. (Hijmans et al. 2005; http://www.worldclim.org/)

Table S3.2. The top four modelsa explaining the logarithmic transformation of annual animal unit month (AUM) density on 3,876 livestock grazing allotments managed by the Bureau of Land Management and United States Forest Service in Arizona and New Mexico during 2010 based on Akaike’s Information Criterion with a correction for finite sample sizes (AICc).

Model numberb Variablesc Kd ΔAICce Akaike weightf

97

Land Cover Majority + Canopy cover + Canopy cover2 + TRI + TRI2 + TRI -(CV) + Soil Suborder Majority + VDW (CV) + BIO18 + BIO182 + BIO19 + BIO192 + BIO4 + BIO42 + BIO15+ BIO152 + BIO15 (CV) + BIO17 + BIO172 + BIO17 (CV)

49 0.00000 0.68000

98

Land Cover Majority + Soil Suborder Majority + Canopy cover + Canopy -cover2 + VDW + VDW (CV) + TRI + TRI2 + TRI (CV) +BIO18 + BIO182 + BIO19 + BIO192 + BIO4 + BIO42 +BIO15+ BIO152 + BIO15 (CV) + BIO17 + BIO172 + BIO17 (CV)

50 1.49300 0.31000

101

Land Cover Majority + Soil Suborder Majority + BIO18 + BIO182 + BIO19 + BIO192 + BIO4 + BIO42 + DW (CV) + TRI + TRI2 + TRI (CV) + BIO15+ BIO152 + BIO15 (CV) + BIO17 +BIO172 + BIO17 (CV)

47 15.66900 0.00020

80

Land Cover Majority + Soil Suborder Majority + Canopy cover + Canopy -cover2+ BIO18 + BIO182 + BIO19 + BIO192 + BIO4 + BIO42 + DW (CV) + TRI + TRI2 + TRI (CV) + BIO15 (CV) + BIO17 + BIO172 + BIO17 (CV)

47 24.32200 0.00003

a The remaining104 models had close to zero Akaike weight (< 0.00001); b Model number in the set of a priori models; c Variables within each model; d The number of estimated parameters; e The difference between the model and the best model (ΔAICc); f Akaike weight (ranging from 0 to 1). For descriptions of variables, see Table S3.1.

10

Table S3.3. Estimated coefficients (β) and standard errors (SE) for variables in the top model (model 97) of annual animal unit month (AUM) density on livestock grazing allotments managed by the Bureau of Land Management and United States Forest Service in Arizona and New Mexico during 2010.

Parameter β SE Intercept 4.10300 1.56800 Land cover type Conifer forest -0.03501 0.10200 Chaparral and montane shrub -0.03487 0.05775 Desert and semidesert scrub 0.02738 0.03172 Developed -0.41590 0.13760 Disturbed -0.20080 0.02578 Dune 0.17910 0.18240 Montane grassland 0.21070 0.14000 Oak woodland 0.15340 0.05983 Pine woodland 0.04558 0.04437 Pinyon-juniper woodland referent referent Plains grassland -0.13290 0.04874 Plains scrub 0.26040 0.12960 Rock -0.09765 0.13030 Savanna and semidesert grassland 0.02198 0.02908 Canopy cover 0.00407 0.00345 Canopy cover2 -0.00028 0.00009TRI 0.00289 0.00051 TRI2 -0.00012 0.00000TRI (CV) -0.00194 0.00051Soil suborder Argids -0.26960 0.02782 Boralfs 0.02946 0.04843 Borolls 0.23760 0.07220 Calcids -0.32970 0.12740 Cambids -0.62800 0.13630 Durids -0.26040 0.31250 Fluvents 0.07452 0.07011 Gypsids -0.55230 0.25430 Mollisols referent referent Ochrepts 0.08711 0.03643

Orthents -0.13310 0.03252 Orthids -0.12230 0.02949 Psamments -0.09221 0.07298 Torrerts -0.21190 0.43670 Ustalfs 0.12980 0.03095 Ustepts -0.44380 0.13460 Usterts 0.11240 0.25320 VDW (CV) -0.00310 0.00057BIO18 0.00476 0.00163 BIO182 0.00017 0.00050 BIO19 -0.01021 0.00129BIO192 0.00005 0.00001 BIO4 -0.00051 0.00043BIO42 0.00418 0.00028 BIO15 -0.02653 0.00586BIO152 0.00143 0.00004 BIO15 (CV) -0.03728 0.00730BIO17 -0.02087 0.00292BIO172 0.00114 0.00002 BIO17 (CV) 0.00469 0.00227

Figure S3.1. Map of annual AUM (animal unit month) density (number of animal unit months per 1 km2 grid) in Arizona and New Mexico, USA, predicted by generalized linear model.

REFERENCES:

Arnold, T. W. (2010). Uninformative parameters and model selection using Akaike’s information criterion. The Journal of Wildlife Management, 74, 1175–1178.

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Bailey, D. W., Kress, D. D., Anderson, D. C., Boss, D. L., & Miller, E. T. (2001). Relationships between terrain use and performance of beef cows grazing foothill rangeland. Journal of Animal Science, 79, 1883–1891.

BLM. (2015). Rangeland Administration System (RAS). Accessed April 2015. Retrieved from

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Appendix S4: Detailed description of the methods and results for models of the relative abundance of elk (Cervus elaphus), mule deer (Odocoileus hemionus) and white-tailed deer (Odocoileus virginiana), which were used as predictor variables in the Mexican wolf depredation risk model.

Methods

The primary prey for the Mexican wolf (Canis lupus baileyi) are elk (Cervus elaphus), mule deer (Odocoileus hemionus) and white-tailed deer (Odocoileus virginiana; Reed et al., 2006). Data on density or abundance of these species is not available for the study area. However, several authors have found a correlation between species distribution models (SDMs) and local abundance estimated through independent studies (Bradley, 2016; Nielsen, Johnson, Heard, & Boyce, 2005; Tôrres et al., 2012; VanDerWal et al., 2009; Weber, Stevens, Diniz-Filho, & Grelle, 2017) and it has been concluded that Maxent’s raw output can be directly interpreted as a model of relative abundance (Phillips, Anderson, Dudík, Schapire, & Blair, 2017). Consequently, we develop species distribution models for the Mexican wolf’s primary prey species using Maxent (Phillips, Aneja, Kang, & Arya, 2006) and used the raw outputs of the model prediction maps as biotic variables in the depredation risk model.

We obtained spatially unique presence points for each species (elk n = 1,775; mule deer n = 1,120; white-tailed deer n = 367) from the Global Biodiversity Information Facility database (GBIF, www.gbif.org, accessed May 2015), New Mexico Department of Game and Fish, and Arizona Game and Fish Department. We modeled the relative abundance of natural prey as functions of an initial suite of 19 bioclimatic, 7 biotic, and 8 landscape and human variables (see Table S4.1 for the list of variables, sources and calculation details). The original scale of variables was 30 m except the bioclimatic variables which were 1 km. All rasters were rescaled to 1 km. For the soil suborders, we converted the polygon base map to a raster with 1 km pixel size. We followed the same modeling approach that was used for the depredation risk model with some modifications in components and justifications.

Sampling bias

Sampling bias is common in data from open access databases like GBIF (Beck, Böller, Erhardt, & Schwanghart, 2014; Hortal, Jiménez-Valverde, Gómez, J., Lobo, & Baselga, 2008). In addition, presence points obtained from Game and Fish agencies are derived from census survey data that are mostly gathered from areas with high natural prey abundance. Hence, our natural prey presence points database was suspected to be affected by sampling bias. Therefore, we used spatial filtering, which functions to decrease randomly the number of presence points in oversampled regions, to reduce the effect of sampling bias (Boria, Olson, Goodman, & Anderson, 2014; Kramer-Schadt et al., 2013; Radosavljevic & Anderson, 2014). To find the optimum filtering scale for each prey species, we randomly removed all but one presence point within three scales: 1 km (covariates’ pixel size); the radius of the species’ average home range size; and the radius of the species’ maximum home range size. We tested these two home range sizes because there was wide variation in reported home range sizes of these species in the western states (Heffelfinger, 2006). We did not use the minimum reported home range sizes because they were smaller than 1 km square for deer. We calculated the average home range sizes by averaging the radius of minimum and maximum reported home range sizes. The minimum and maximum reported home range radii for western populations of the prey species

were: 5.7 - 14.2 km2 for elk; 2.7 - 6.6 km2 for mule deer; and 1.2 - 3.2 km2 for white-tailed deer (DeYoung & Miller, 2011; Mackie, Kie, Pac, & Hamlin, 2003; Wallace, 1991).

Background extent

We used three different scales for defining the background extent in the natural prey species models. We restricted the background extent to the maximum reported dispersal distance for each species (Anderson & Raza, 2010). For mule deer and white-tailed deer, the maximum reported dispersal distance in western states were 113 km and 224 km, respectively (Hygnstrom et al., 2008). For elk, the maximum reported dispersal distance was 2,800 km (O’Gara, 2002). Because the longest dispersal distance for elk was larger than the dimensions of our study area we did not apply this limitation for it. However, it also has been argued that including inaccessible areas in background might not affect the accuracy of the model because Maxent still can recognize whether these points are similar or dissimilar to presence points (Merow, Smith, & Silander, 2013). Thus, we also made models without background extent limitation. In addition, we considered a smaller scale by limiting the background extent in maximum reported home range size of the species allowing Maxent to model the effects of environmental variables on relative abundance within home range scale. Thus, for each species we created 3 sets of filtered presence points that rarified at different scales and 3 sets of background points based on 3 different scales (Table S4.2). To identify the best combination of presence and background points, we ran Maxent using each combination of filtered presence points and background data. We then compared the accuracy of their predictions to find the best combination by applying spatially independent k-fold cross-validation (see the model evaluation section).

Model evaluation

Although the threshold-dependent and independent metrics are the most common metrics in evaluating the accuracy of Maxent models, there is no convention on which metric performs better than others (Muscarella et al., 2014). Moreover, there is no certain threshold applicable for all situations to distinguish a good model from a bad model (Muscarella et al., 2014; Yackulic et al., 2013). Thus, to find the most accurate model for each species of natural prey, we also evaluated the accuracy of models’ predictions based on expert knowledge on the distribution and abundance of species across the study area. Moreover, SDMs predict potential distribution of species (Guisan & Zimmermann, 2000), while we needed the relative abundance of natural prey in their actual distribution range as the predictors in the depredation risk model. Thus, we compared the prediction maps with reported natural prey occurrence in Arizona and New Mexico’s game management units to modify predictions (changed to zero) in those game management units without species occurrence (for Arizona we used AZGF 2017a, b and for New Mexico we used expert knowledge).

Results

Evaluation metrics could not distinguish the best models predicting natural prey abundance in their current distribution range and, therefore, we relied on expert’s evaluations. For elk, the experts selected the model made with 14 km filtered presence points and without background limitation as best (Tables S4.2 –S4.3). However, this model overestimated the relative abundance of elk in some isolated mountains in southern game management units where no elk populations currently exist (since the model predicted potential not actual relative abundance). Therefore, we changed the predicted relative abundance values in these areas to

zero. The prediction map of this model indicated that areas with highest relative abundance of elk (most suitable habitats) existed in major mountain ranges and high plateaus (Figure S4. 1).

For mule deer, the experts selected four models as best, but each had its own strengths and weaknesses (Tables S4.2 –S4.3). Since an average prediction map can enhance the accuracy of predictions, we made an average prediction map based on these selected models (Marmion et al 2009). We did not use weighted averaging because none of the metrics could rank models well. The average prediction map showed that the mule deer was the most widespread species among the natural prey. Areas with highest mule deer relative abundance were mostly located in mountainous and rugged areas at moderate and high elevations, whereas areas of lowest relative abundance were mostly in flat and low elevation areas (Figure S4.2).

For white-tailed deer, the experts selected two models as best (Tables S4.2 –S4.3). Prediction maps of these models were averaged to produce the prediction maps. According to this map, areas with higher relative white-tailed deer abundance were mostly located in the central and southeastern Arizona and major mountain areas of southern New Mexico (Figure S4. 3).

Table S4.1. Description of covariates for spatial modeling of natural prey abundance in Arizona and New Mexico Variables Abbreviation Variable description/calculation Source

BIOTIC VAVRIABLES

Land Cover Majority

LCM Arc GIS 10.3 Focal Statistics tool to identify the major landcover category within each species’ mean home range size. We reduced the number of landcover categories from 50 to 19 by combining similar landcover types (e.g., Madrean Pine-Oak Forest and Woodland and Southern Rocky Mountain Ponderosa Pine Woodland were considered pine woodland).

Land Cover Majority Variation

LCMV Arc GIS 10.3 Focal Statistics tool (Spatial Analysis toolbox) to calculate the number of landcover types within each species’ mean home range size.

Average annual Normalized Difference Vegetation Index of 2010

NDVI Arc GIS 10.3 Raster Dataset tool (Data management toolbox) to mosaic annual NDVI raster files to create an integrated raster for entire study area

Canopy Cover Majority (categorical)

CCM Arc GIS 10.3 Focal Statistics tool to identify the major landcover category within each species’ mean home range size.

Southwest Regional Gap Analysis land cover map (USGS National Gap Analysis Program 2007; ) Southwest Regional Gap Analysis land cover map (USGS National Gap Analysis Program 2007; ) Web-Enabled Landsat data (USGS 2015;) LANDFIRE canopy cover (USGS 2013; )

Tree Canopy Cover (continuous)

TCC Considering the middle range of tree cover categories.

Vegetation Height VH Arc GIS 10.3 Focal Statistics tool to identify the major vegetation height category within each species’ mean home range size.

Vegetation Height Variation

VHV Arc GIS 10.3 Focal Statistics tool (Spatial Analysis toolbox) to calculate the number of vegetation height categories within each species’ mean home range size.

Soil Suborder Majority

SSM Arc GIS 10.3 Zonal Statistics tool to identify the major soil suborder of the Integrated soil suborder maps within each species’ mean home range size.

LANDFIRE canopy cover (USGS 2013;)LANDFIRE canopy cover (USGS 2013; ) LANDFIRE canopy cover (USGS 2013; ) Soil Survey Geographic (SSURGO,USDA 2015; and General Terrestrial Ecological Units (GTES, USFS 1998; datasets

LANDSCAPE AND HUMAN FEATURES

Elevation - National Elevation Dataset National Elevation Dataset

Slope - Arc GIS 10.3 slope tool (Spatial analysis toolbox)

Heat Load Index HLI Arc GIS 10.3 Heat Load Index tool (Geomorphometry & Gradient Metrics toolbox; Evans et al. 20114)

Terrain Ruggedness Index

TRI Arc GIS 10.3 Raster Calculator tool to calculate the average absolute difference between each pixel elevation value and each of its eight neighbors (Riley et al. 1999)

Density of Roads DenR Arc GIS 10.3 Focal Statistics tool (Spatial Analysis toolbox) to calculate density of major roads in natural prey’s average home range size

Distance to Roads DisR Arc GIS 10.3 Euclidean Distance tool (Spatial Analysis toolbox) to calculate the minimum distance from each pixel to major roads

Distance to Water Resources

DW Arc GIS 10.3 Euclidean Distance tool (Spatial Analysis toolbox) to calculate the minimum distance from each pixel to perennial water resources including springs, artificial water resources, rivers and lakes

National Elevation Dataset (USGS 2009; )

National Elevation Dataset (USGS 2009; https://lta.cr.usgs.gov /NED)

National Elevation Dataset (USGS 2009; https://lta.cr.usgs.gov /NED)

TIGER data (https://www.census. gov/) TIGER data (https://www.census. gov/) National Hydrologic Dataset (USGS 2015b; https://nhd.usgs.gov/)

BIOCLIMATIC VARIABLES

Annual mean temperature

BIO1 Mean of the monthly mean temperature WorldClim (Hijmans, Cameron, Parra, Jones, & Jarvis, 2005

Mean diurnal range

BIO2 Mean of difference between mean monthly maximum and mean monthly temperature

Isothermality BIO3 (BIO2/BIO7) *100

Temperature seasonality

BIO4 Standard deviation of the 12 mean monthly temperature values multiplied by 100

Maximum temperature of warmest month

BIO5 Mean maximum temperature of the warmest month

Minimum Temperature of coldest month

BIO6 Mean minimum temperature of the coldest month

Temperature annual range

BIO7 (BIO5 – BIO6)

Mean temperature of wettest quarter

BIO8 Mean temperature of three consecutive months with highest average monthly precipitation

Mean temperature of driest quarter

BIO9 Mean temperature of three consecutive months with lowest average monthly precipitation

WorldClim (Hijmans et al. 2005; http://www.worldclim.org/)

Mean temperature of warmest quarter

BIO10 Mean temperature of three consecutive months with highest mean maximum monthly temperature


Mean temperature of coldest quarter

BIO11 Mean temperature of three consecutive months with lowest mean maximum monthly temperature


Annual precipitation

BIO12 Mean annual precipitation WorldClim (Hijmans et al. 2005; http://www.worldclim.org/)

Precipitation of wettest month

BIO13 Mean monthly precipitation of wettest month WorldClim (Hijmans et al. 2005; http://www.worldclim.org/)

Precipitation of driest month

BIO14 Mean monthly precipitation of driest month WorldClim (Hijmans et al. 2005; http://www.worldclim.org/)

Precipitation seasonality

BIO15 Standard deviation of the means of monthly precipitation WorldClim (Hijmans et al. 2005; http://www.worldclim.org/)

Precipitation of wettest quarter


WorldClim (Hijmans et al. 2005;

http://www.worldclim.org/)

Precipitation of driest quarter

BIO17 Sum of mean precipitation for three consecutive months with lowest mean precipitation





Precipitation of coldest quarter

BIO19 Sum of mean precipitation for three consecutive months with lowest mean monthly temperature


Table S4.2. Combinations of background extent and presence points filtering scale used for modeling relative abundance of natural prey for the Mexican wolf (Canis lupus baileyi): elk (Cervus elaphus), mule deer (Odocoileus hemionus), and white-tailed deer (O. virginiana).

Species Background extenta Presence points filtering scaleb Elk No 1 km

AHRS (10 km) MHRS (14 km)

Elk MHRS (14 km) 1 km AHRS (10 km) MHRS (14 km)

Mule deer No 1 km AHRS (4.7 km) MHRS (6.6 km)

Mule deer MDD (113 km) 1 km AHRS (4.7 km) MHRS (6.6 km)

Mule deer MHRS (6.6 km) 1 km AHRS (4.7 km) MHRS (6.6 km)

White-tailed deer No 1 km AHRS (2.2 km) MHRS (3.1 km)

White-tailed deer MDD (224 km) 1 km AHRS (2.2 km) MHRS (3.1 km)

White-tailed deer MHRS (3.1 km) 1 km AHRS (2.2 km) MHRS (3.1 km)

aExtent in which random background points were selected: No = No background limitation, MDD = maximum dispersal distance, MHRS = maximum home range size. bScale in which all presence points but one are randomly removed: AHRS = average home range size, MHRS = maximum home range size.

Table S4.3. Settings and evaluation metrics for species distribution models of natural prey for the Mexican wolf (Canis lupus baileyi): elk (Cervus elaphus), mule deer (Odocoileus hemionus), and white-tailed deer (O. virginiana). The spatial models highlighted in gray were selected as best by the experts and used to create species distribution maps.

Spec

ies

Pres

ence

poi

nts

filte

ring

scal

ea

Bac

kgro

und

ex

tent

a

Feat

ures

b

β c

Full.

AU

Cd

Mea

n.A

UC

e

Mea

n.

AU

C.D

IFFf

Mea

n.O

R10

g

Mea

n.O

Rm

inh

Num

ber o

f pa

ram

eter

s

Elk

1 km No LQTHP 1.5 0.930 0.884 0.056 0.272 0.000 39 1 km 14 km HP 0.5 0.714 0.643 0.144 0.258 0.002 61 10 km No LQT 2 0.906 0.888 0.028 0.200 0.006 12 10 km 14 km LQ 3.5 0.613 0.582 0.069 0.139 0.000 14 14 km No LQTHP 2.5 0.898 0.882 0.038 0.242 0.008 7 14 km 14 km LQ 2 0.631 0.560 0.108 0.194 0.056 25

Mule Deer

1 km No LQTP 1 0.823 0.678 0.154 0.287 0.020 112 1 km 113 km LQTP 1 0.811 0.670 0.167 0.310 0.040 28 1 km 6.6 km LQT 1 0.607 0.548 0.073 0.166 0.010 31 4.7 km No LQTP 1.5 0.791 0.684 0.121 0.237 0.010 51 4.7 km 113 km LQT 1 0.791 0.653 0.149 0.309 0.028 87 4.7 km 6.6 km LQT 1 0.627 0.540 0.107 0.261 0.006 53 6.6 km No LQTP 1 0.782 0.688 0.106 0.257 0.022 62 6.6 km 113 km LQTP 1.5 0.787 0.683 0.114 0.240 0.002 45 6.6 km 6.6 km LQT 1.5 0.621 0.527 0.102 0.227 0.005 38

White- tailed deer

1 km No LQTP 3.5 0.908 0.889 0.047 0.134 0.013 18 1 km 224 km LQT 2.5 0.910 0.901 0.036 0.128 0.020 17 1 km 3.1 km LQTHP 2 0.629 0.602 0.039 0.152 0.000 15 2.2 km No LP 4 0.909 0.901 0.028 0.140 0.008 13 2.2 km 224 km LQ 1.5 0.900 0.886 0.050 0.140 0.031 17 2.2 km 3.1 km H 4 0.600 0.521 0.098 0.164 0.016 7

3.1 km No LQP 4.5 0.896 0.898 0.019 0.085 0.008 6 3.1 km 224 km LP 6.5 0.895 0.888 0.039 0.162 0.000 8 3.1 km 3.1 km LQ 5.5 0.560 0.569 0.030 0.076 0.008 2

aSee the description in Table S4.2. bL = linear, Q = quadratic, P = product, T = Threshold and H = Hinge. cβ multipliers. dAUC based on unpartitioned dataset. eAUC based on the testing data (i.e., AUCtest), averaged across four bins. fDifference between AUCtrain and AUCtest. gThe 10 % omission rate of the training records. hThe lowest presence threshold.

Table S4.4. Uncorrelated variables with more than 5 % contribution in the best species distribution models for natural prey of the Mexican wolf (Canis lupus baileyi): elk (Cervus elaphus), mule deer (Odocoileus hemionus), and white-tailed deer (O. virginiana).

Species Background

extenta Presence points filtering scaleb Uncorrelated variables with more than 5% contributionc

Elk No MHRS (14 km) BIO10 (59%), BIO19 (24%), BIO3 (17%)

Mule deer

No MHRS (6.6 km) BIO7 (34%), Slope (28%), BIO4 (17%), BIO19 (7%), VH (8), CCM (6%)

MHRS (6.6 km) 1 km Slope (60%), CCM (40%)

MHRS (6.6 km) AHRS (4.7km) VH (35%), Slope (18%), LCM (17%), CC (14%), DR (10%), HLI (6%)

MHRS (6.6 km) MHRS (6.6 km) CCM (26%), Slope (23%), SSM (14%), TCC (13%), HLI (13%), DW (11%)

White-tailed deer

MDD (224 km) 1 km BIO12 (31%), BIO13 (19%), BIO4 (17%), BIO6 (12%), SSM (11%), LCV (5%), BIO19 (5%)

MHRS (3.1 km) AHRS (2.2 km) SSM (35%), VH (33%), CCM (32%) aExtent in which random background points are selected: No = no background limitation, MDD = maximum dispersal distance, MHRS = maximum home range size. bScale in which all presence points but one are randomly removed: AHRS = average home range size, MHRS = maximum home range size. cSee Table S4.1 for description of variables.

Figure S4.1. Map of relative abundance of elk (Cervus elaphus) in Arizona and New Mexico, USA. Blue represents areas with lower relative abundance and red represents areas with higher relative abundance. Presence points (black dots) are filtered in 14 km scale (maximum home range size).

Figure S4.2. Map of relative abundance of mule deer (Odocoileus hemionus) in Arizona and New Mexico. This map is the average of prediction maps of four selected models (See Table S4.3). Blue represents areas with lower relative abundance and red represents areas with higher relative abundance. Presence points (black dots) are filtered in 1 km scale.

Figure S4.3. Map of relative abundance of white-tailed deer (Odocoileus virginiana) in Arizona and New Mexico based on Maxent modeling results. This map is the average of two selected models (see Table S4.3). Presence points (black dots) are filtered at 1 km scale.

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Appendix S5: Results of multivariate environmental similarity surface (MESS) analysis for variables in the spatial risk model of cattle depredation by the mexican wolf (Canis lupus baileyi).

Figure S5.1. Results of Multivariate Environmental Similarity Surface (MESS) analysis for canopy cover variation in the spatial risk model for cattle depredation by the Mexican wolf (Canis lupus baileyi). Smaller values (darker colors) indicate higher dissimilarity of the environmental variable with locations of depredation incidences, while higher values (lighter colors) indicate higher similarity of the environmental variable with locations of depredation incidences.

Figure S5.2. Results of Multivariate Environmental Similarity Surface (MESS) analysis for relative elk abundance in the spatial risk model for cattle depredation by the Mexican wolf (Canis lupus baileyi). Smaller values (darker colors) indicate higher dissimilarity of the environmental variable with locations of depredation incidences, while higher values (lighter colors) indicate higher similarity of the environmental variable with locations of depredation incidences.

Figure S5.3. Results of Multivariate Environmental Similarity Surface (MESS) analysis for landcover majority in the spatial risk model for cattle depredation by the Mexican wolf (Canis lupus baileyi). Smaller values (darker colors) indicate higher dissimilarity of the environmental variable with locations of depredation incidences, while higher values (lighter colors) indicate higher similarity of the environmental variable with locations of depredation incidences.

Figure S5.4. Results of Multivariate Environmental Similarity Surface (MESS) analysis for slope in the spatial risk model for cattle depredation by the Mexican wolf (Canis lupus baileyi). Smaller values (darker colors) indicate higher dissimilarity of the environmental variable with locations of depredation incidences, while higher values (lighter colors) indicate higher similarity of the environmental variable with locations of depredation incidences.

Figure S5.5. Results of Multivariate Environmental Similarity Surface (MESS) analysis for density of roads in the spatial risk model for cattle depredation by the Mexican wolf (Canis lupus baileyi). Smaller values (darker colors) indicate higher dissimilarity of the environmental variable with locations of depredation incidences, while higher values (lighter colors) indicate higher similarity of the environmental variable with locations of depredation incidences.

Figure S5.6. Results of Multivariate Environmental Similarity Surface (MESS) analysis for density of developed areas in the spatial risk model for cattle depredation by the Mexican wolf (Canis lupus baileyi). Smaller values (darker colors) indicate higher dissimilarity of the environmental variable with locations of depredation incidences, while higher values (lighter colors) indicate higher similarity of the environmental variable with locations of depredation incidences.

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