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Received: 15 January 2021
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Revised: 16 September 2021
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Accepted: 22 September 2021
DOI: 10.1002/jwmg.22173
RESEARCH ARTICLE
Desert bighorn sheep habitat selection,
group size, and mountain lion predation risk
Andrew S. Jones |Esther S. Rubin |Matthew J. Clement |
Larisa E. Harding |Jacob I. Mesler
Arizona Game and Fish Department, 5000 W.
Carefree Highway, Phoenix, AZ 85086, USA
Correspondence
Andrews S. Jones, Arizona Game and Fish
Department, 5000 W. Carefree Highway,
Phoenix, AZ 85086, USA.
Email: AJones@azgfd.gov
Present address
U.S. Fish and Wildlife Service, 5275 Leesburg
Pike, Falls Church, VA 22041, USA.
Funding information
Safari Club International Foundation;
Pittman‐Robertson Federal Aid in Wildlife
Restoration Grant; Arizona Desert Bighorn
Sheep Society
Abstract
Bighorn sheep (Ovis canadensis) evolved for thousands of years
in the presence of numerous predators, including mountain
lions (Puma concolor). Bighorn sheep have presumably devel-
oped predator avoidance strategies; however, the effective-
ness of these strategies in reducing risk of mountain lion
predation is not well understood. These strategies are of in-
creasing interest because mountain lion predation on bighorn
sheep has been identified as a leading cause of mortality in
some sheep populations. Therefore, we investigated how
mountain lions affect both bighorn sheep habitat selection and
risk of mortality in Arizona, USA. We used 2 approaches to
investigate the predator‐prey relationship between mountain
lions and bighorn sheep. We fit 103 bighorn sheep (81 females
and 22 males) with global positioning system radio‐collars in
2 Arizona populations from 2013 to 2017, and used a negative
binomial resource selection probability function to evaluate
whether bighorn sheep selected for habitat features in ac-
cordance with presumed predator avoidance strategies, in-
cluding terrain ruggedness, slope, topographic position, and
horizontal obstruction, in 2 seasons (winter and summer). We
then estimated how habitat features such as terrain rugged-
ness, slope, horizontal obstruction, and group size, influence
the risk of mortality due to mountain lion predation using an
Andersen‐Gill proportional hazards model. Generally, both
sexes selected areas with lower horizontal obstruction and
intermediate ruggedness and slope, but selection patterns
differed between seasons and sexes. The use of more rugged
J Wildl Manag. 2022;1–28. wileyonlinelibrary.com/journal/jwmg © 2022 The Wildlife Society
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areas and steeper slopes decreased the risk of mortality due to
mountain lion predation, consistent with presumed predator
avoidance strategies. Increased group size decreased risk of
bighorn sheep mortality due to mountain lion predation but this
effect became marginal at approximately 10 individuals/group.
We did not identify a relationship between horizontal obstruc-
tion and bighorn sheep mortality risk. Our findings can be used
in habitat and population management decisions such as the
prioritization of habitat restoration sites or selection of trans-
location sites. In addition, we suggest that augmentation of low‐
density bighorn sheep populations may reduce mountain lion
predation risk by increasing group size, and that releasing large
groups of bighorn sheep in population augmentation and re-
introduction efforts may help to reduce mountain lion predation.
KEYWORDS
Arizona, bighorn sheep, mortality, mountain lion, Ovis canadensis,
predation, Puma concolor, Sonoran Desert
Mountain lions (Puma concolor) and bighorn sheep (Ovis canadensis)haveco‐occurred in the American Southwest for
the last 8,000–11,000 years (Geist 1971, Logan and Sweanor 2001). Deer (Odocoileus spp.) are typically recognized as
the primary prey of mountain lions, but bighorn sheep are also key prey items (Buechner 1960,Kelly1980). During their
long association with mountain lions and other predators, bighorn sheep likely evolved habitat use patterns and
gregarious behavior as predator avoidance strategies. These presumed predator avoidance strategies include use of
steep and rugged terrain that impedes predator movements, use of open habitat where predators can be visually
detected, and increased vigilance through group living (Geist 1971,Berger1978,Hansen1980a,RisenhooverandBailey
1985, Mooring et al. 2004). The effectiveness of these presumed predator avoidance strategies is not well understood,
yet they may be important because mountain lion predation is a leading cause of mortality in some sheep populations,
and several studies suggest that mountain lions may limit bighorn sheep population growth or drive small populations to
extirpation (Wehausen 1996, Hayes et al. 2000,Kamleretal.2002,Romingeretal.2004,Wakelingetal.2009).
Growing concern about mountain lion predation on bighorn sheep has resulted in several hypotheses regarding
human‐induced changes to bighorn sheep habitat that may increase their risk of mountain lion predation. These
include the hypotheses that long‐term fire suppression has resulted in dense vegetation that increases risk of
mountain lion predation (Krausman et al. 1996, Holl et al. 2004), and that the addition of artificial water sources has
increased bighorn sheep predation risk by facilitating shifts in the distributions of mountain lions or alternate prey
species such as deer (Broyles 1995). Other hypotheses focus on additional human‐induced changes, such as the
cessation of long‐term intensive predator control programs and extirpation of other dominant carnivores, both of
which may have increased mountain lion abundance and distribution (Young and Goldman 1944, Brown 1985,
Rominger 2017). Likewise, range expansion of mule deer (O. hemionus) into portions of bighorn sheep range may
also have led to changes in mountain lion distribution (Berger and Wehausen 1991, Rominger 2017).
Studies of mountain lion predation on bighorn sheep have typically focused on documenting sources of
mortality for marked individuals to evaluate demographic effects (Cunningham and deVos 1992, Hayes et al. 2000).
Other studies have explored the potential influence of mountain lion predation on bighorn sheep population
viability with computer simulations using empirical data (Ernest et al. 2002, Rubin et al. 2002, Harris et al. 2009)or
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assessed the effectiveness of mountain lion removal on bighorn sheep population recovery (Logan and Sweanor
2001). The question remains as to why some bighorn sheep populations are threatened by mountain lion predation
when they have evolved with an array of predators, including mountain lions.
Our understanding of this predator‐prey relationship can benefit from testing predictions about bighorn sheep
predator avoidance strategies, including habitat selection and grouping behavior. Bighorn sheep are believed to
exhibit habitat selection patterns that minimize predation risk, including selection for rugged terrain that impedes
predator movements (Buechner 1960,Hansen1980b), selection for areas with high visibility where they may be
better able to detect predators (Risenhoover and Bailey 1985,Krausmanetal.1999), and increased vigilance through
gregarious behavior (Risenhoover and Bailey 1985, Mooring et al. 2004). The effectiveness of these strategies in
reducing mountain lion predation has not, to our knowledge, been empirically investigated, but this information could
be used in conservation strategies for bighorn sheep populations. Specifically, determining how habitat characteristics
and bighorn sheep grouping behavior influence predation risk is relevant to management decisions related to fire,
habitat restoration, predator control, and translocation strategies. Our objectives in this study were to evaluate
bighorn sheep habitat selection patterns as they relate to presumed predator avoidance strategies, and assess the
environmental and behavioral variables influencing bighorn sheep risk of mortality due to mountain lion predation.
We hypothesized (hypothesis 1) that bighorn sheep would select habitat in concordance with presumed
predator avoidance strategies, and predicted (prediction 1) that bighorn sheep would select for areas with greater
topographic complexity, steeper slopes, and less horizontal obstruction. We also hypothesized (hypothesis 2) that
bighorn sheep habitat selection patterns would differ between male and female bighorn sheep because of dif-
ferences in predation risk tolerance and forage exploitation (Festa‐Bianchet 1988, Bleich et al. 1997, Mooring et al.
2003). Specifically, we predicted (prediction 2) that during periods of sexual segregation, males would trade‐off
increased forage resources at a cost of decreased security cover (less topographic complexity, less steep slopes, and
greater horizontal obstruction), while females would sacrifice increased forage resources for increased security
cover. In assessing environmental and behavioral variables influencing bighorn sheep risk of mortality due to
mountain lion predation, we hypothesized (hypothesis 3) that bighorn sheep mortality risk would be explained
primarily by either bighorn sheep predator avoidance strategies, mountain lion presence, or bighorn sheep trans-
location history. Under the bighorn sheep predator avoidance framework, we predicted (prediction 3) that greater
topographic complexity, steeper slopes, less horizontal obstruction, and larger group size would decrease bighorn
sheep risk of mortality due to mountain lion predation. Under the mountain lion presence framework, we predicted
(prediction 4) that bighorn sheep would be at higher risk of predation in vegetation associations and landforms
preferentially used by mountain lions, including woodland, chaparral, and riparian areas, and areas of gentle slopes
and canyon bottoms. Under the bighorn sheep translocation history framework, we predicted (prediction 5) that
bighorn sheep released into vacant habitat, translocated from populations without previous exposure to mountain
lion predation, and from the first translocated cohorts would be at higher risk of mountain lion predation. While
several aspects of our hypotheses have been addressed by previous research on bighorn sheep habitat selection
(Festa‐Bianchet 1988, Etchberger et al. 1989), causes of mortality (Cunningham and deVos 1992, Hayes et al.
2000), or via presumed risk based on bighorn sheep behavior (Berger 1978, Mooring et al. 2004), we used empirical
data to develop hazard ratios associated with specific habitat use patterns and grouping behavior. As such, our
approach is unique because it allowed us to estimate the effectiveness of presumed predator avoidance strategies
and to better understand the influence of habitat use patterns and grouping behavior on actual predation risk.
STUDY AREA
We conducted this study at 2 sites in the Sonoran Desert of Arizona, USA (Figure 1). The first study area was the
Arrastra Mountains Wilderness area (Arrastra), located primarily in Mohave County in west‐central Arizona, and
encompassing 1,195 km
2
. Elevations ranged from 600 m to 1,400 m and topography varied from low hills to deep,
MOUNTAIN LIONS AND BIGHORN SHEEP
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wide canyons and steep, rugged mountainous terrain. The majority of the area was managed by the Bureau of Land
Management, interspersed with Arizona State Trust and private lands. The vegetation community was primarily a
Sonoran Desert scrub assemblage of the Arizona upland subdivision with limited areas of interior chaparral, semi‐
desert grassland, and Great Basin conifer woodland (http://azconservation.org, accessed 1 Sep 2017). Predators
included mountain lion, bobcat (Lynx rufus), coyote (Canis latrans), gray fox (Urocyon cinereoargenteus), black bear
(Ursus americanus), and golden eagle (Aquila chrysaetos). The Arrastra site supported a low‐density population of
desert bighorn sheep (O. c. nelsoni), javelina (Pecari tajacu), mule deer, domestic cattle, and feral burro (Equus asinus).
Climate in the Arrastra area was characterized by a bimodal precipitation pattern with rains occurring in winter and
during summer monsoons, and mean annual precipitation was 18.4 cm. Yearly mean maximum monthly tempera-
tures ranged from 17.8°C in January to 40.3°C in July. Yearly mean minimum monthly temperatures ranged from
0.5°C in December to 20.5°C in July (Western Regional Climate Center 2018a).
The second study site was in the Santa Catalina Mountains (Catalina) located in Pima County in southeastern
Arizona, bordering the Tucson metropolitan area, and bighorn primarily occupied the Pusch Ridge Wilderness area
within the mountain range. The Catalina study area encompassed 472 km
2
and elevations ranged from 850 m to
2,800 m. The majority of the area was managed by the United States Forest Service, interspersed with Arizona
State Trust, Arizona State Parks, and private lands. Topography varied from rolling hills and high benches to steep,
rugged cliffs, hogbacks, canyons, and vertical rock faces (Krausman 2017). Vegetation communities formed a
floristic continuum along an increasing elevation gradient, and included Sonoran Desert scrub, desert grassland,
open oak woodland, pine‐oak woodland, pine‐oak forest, pine forest, montane fir forest, and subalpine forest
FIGURE 1 Study areas used to examine bighorn sheep habitat selection and factors influencing the risk of
bighorn sheep mortality due to mountain lion predation, Arizona, USA, 2013–2017
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(Krausman 2017). Vegetation associations important to bighorn sheep in the Catalina study area included Palo
verde‐saguaro mountain slopes, nonprecipitous open oak woodland, precipitous open oak woodland, and riparian
woodland (Gionfriddo and Krausman 1986, Krausman 2017). Predators included mountain lion, bobcat, coyote,
gray fox, golden eagle, and black bear. Historically, desert bighorn sheep (O. c. mexicana) occupied the Catalina site
and the herd was estimated at 220 individuals in 1927 (Krausman et al. 1979). The population declined steadily until
the late 1990s, when the herd was considered extirpated (Krausman et al. 1995, Cain et al. 2005, Krausman 2017).
The specific reasons for the decline of the herd are unknown but likely causes include urbanization, habitat
fragmentation, human recreation pressures, and fire suppression (Krausman 2017). The Catalina site was occupied
by other ungulates including javelina, Coues' white‐tailed deer (O. virginianus couesi), and mule deer. Climate in the
Catalina area was characterized by a bimodal precipitation pattern with rains occurring in winter and during summer
monsoons, and mean annual precipitation was 32.3 cm. Yearly mean maximum monthly temperatures ranged from
19.3°C in December to 38.1°C in July. Yearly mean minimum monthly temperatures ranged from 1.2°C in
December to 22.2°C in July (Western Regional Climate Center 2018b). To model bighorn sheep habitat selection
we delineated 2 seasons corresponding to winter (Nov–Apr) and summer (May–Oct).
METHODS
Bighorn sheep translocation, monitoring, and mortality investigations
In November 2013 and November 2014, Arizona Game and Fish Department (AZGFD) personnel captured 80
bighorn sheep in the Black Mountains in northwestern Arizona using a net gun fired from a helicopter (Krausman
et al. 1985) and released them in occupied bighorn sheep habitat in the Arrastra study area as part of a population
augmentation effort. Of the 80 bighorn sheep, 21 (5 males, 16 females) from the 2013 release and 22 (4 males,
18 females) from the 2014 release were fitted with combination very high frequency (VHF) and global positioning
system (GPS) radio‐collars, with an 8‐hour mortality sensor and a pre‐programmed drop‐off mechanism (model
GlobalStar Track S, Lotek Wireless, Newmarket, Ontario, Canada). We programmed collars to record approximately
4 GPS locations/day, on a 5‐hour rotating schedule. In November 2013 and November 2014, AZGFD personnel
captured 60 bighorn sheep in the Plomosa and Trigo Mountains in southwestern Arizona and the Superstition
Mountains in central Arizona in the same manner, and released them into historical bighorn sheep habitat in the
Catalina study area as part of a reintroduction project. Of the 60 reintroduced bighorn sheep, 30 (6 males,
24 females) from the 2013 release and 30 (7 males, 23 females) from the 2014 release were fitted with combination
VHF‐GPS radio‐collars with a 10‐hour mortality sensor and a pre‐programmed drop‐off mechanism (model Iridium
Track M, Lotek Wireless). We programmed the collars to record 4 locations/day on a fixed schedule at 0000, 0600,
1200, and 1800. We also fit all bighorn sheep with a colored and uniquely numbered ear tag.
We began monitoring all individuals immediately after release via daily GPS location uploads, mortality alerts
transmitted via text message and email, and VHF monitoring. We investigated bighorn sheep mortalities following a
VHF mortality signal or mortality alert received via text message and email, and estimated date of death using the
last normal (live) VHF telemetry signal, GPS data, and examination of carcasses. We determined cause of mortality
using field necropsies, field inspections of mortality sites, and previous observations of animal condition. We
collected nasal swabs and heart, liver, lung, kidney, and muscle tissue samples during field necropsies, when
recoverable, and submitted samples to the Washington Animal Disease Diagnostic Lab (Pullman, WA, USA) for
histologic and bacteriological testing for common bighorn sheep pathogens. We categorized causes of mortality as
1) mountain lion predation, 2) non‐predation and identifiable cause (e.g., disease), 3) non‐predation and no iden-
tifiable cause (i.e., unknown), and 4) predation not attributable to mountain lion. We classified mortalities as
mountain lion predation if we observed ≥2 of the following: bite marks on the sheep's neck, a mountain lion scat, a
photographic record of a mountain lion visiting the carcass shortly after the animal's death, a cached pile of remains,
MOUNTAIN LIONS AND BIGHORN SHEEP
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a trail where the prey had been dragged or carried, fresh mountain lion tracks at the site of the carcass, mountain
lion scrapes in the soil, hair plucked from the carcass, large leg bones crushed or broken, and consumption of skull
bones from the nose to the base of the horns (Hayes et al. 2000).
Environmental variables used in habitat selection analysis and risk modeling
We considered environmental and behavioral variables hypothesized to influence bighorn sheep habitat selection
and mortality risk due to mountain lion predation (Table 1). We used topographic measures of terrain ruggedness,
slope, topographic position index (TPI; Risenhoover and Bailey 1985, Berger 1991, Hoglander et al. 2015), and
distance to the land cover type cliff‐rock‐scree. We quantified terrain ruggedness in a geographic information
system (GIS; ArcGIS version 10.3, Esri, Redlands, CA, USA) using a vector ruggedness measurement (VRM;
Sappington et al. 2007) calculated with a 150‐m moving neighborhood window in the Benthic Terrain Modeler GIS
extension (Benthic Terrain Modeler version 3.0, https://coast.noaa.gov, accessed 13 Mar 2017). We calculated
percent slope using the DEM surface tools package (DEM Surface Tools version 2.1.375, jennessent.com, accessed
TABLE 1 Environmental and behavioral variables considered for habitat selection (HS) and Anderson‐Gill
proportional hazards models (A‐G) for bighorn sheep at the Catalina and Arrastra study sites, Arizona, USA,
2013–2017. Environmental or behavioral variable abbreviations are indicated in parentheses
Environmental or behavioral variable Unit of measure Source of data Model
Group size (size) Continuous
(mean)
Visual observations A‐G
Source population (source) Categorical Bighorn translocation records A‐G
Sex (sex) Categorical Bighorn translocation records A‐G
Vector ruggedness
measurement (VRM)
Index 30‐m digital elevation model HS, A‐G
Slope (slope) % 30‐m digital elevation model HS, A‐G
Topographic position index (TPI) Index 30‐m digital elevation model HS, A‐G
Visual obstruction (vegetative
obstruction, topographic
obstruction, total obstruction)
% Cover pole HS, A‐G
Normalized difference vegetation
index (NDVI)
Index Moderate‐resolution Imaging
Spectroradiometer satellite data
HS, A‐G
Desert scrub and grassland
(scrub‐grassland)
Distance to (m) Southwest Regional Gap Analysis Project HS, A‐G
Chaparral and shrubland (chaparral) Distance to (m) Southwest Regional Gap Analysis Project HS, A‐G
Forest and woodland
(forest‐woodland)
Distance to (m) Southwest Regional Gap Analysis Project HS, A‐G
Riparian (riparian) Distance to (m) LANDFIRE HS, A‐G
Cliff, rock, scree (cliff‐rock‐scree) Distance to (m) Southwest Regional Gap Analysis Project HS, A‐G
Perennial water (water) Distance to (m) National Hydrography Dataset, field
observations, Arizona Game and Fish
Department databases
HS, A‐G
Solar radiation (solar radiation) Index 30‐m digital elevation model HS, A‐G
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JONES ET AL.
13 Mar 2018) in a GIS. We calculated a 4‐position TPI, namely canyon bottoms, gentle slopes, steep slopes, and
ridges, using the Land Facet Corridor Design extension to the GIS (Land Facet Corridor Designer version 1.2.884,
jennessent.com, accessed 13 Mar 2018), which we treated as a 4‐level factor in the analysis. We used the
Southwest Regional Gap Analysis Project (gapanalysis.usgs.gov, accessed 1 Sep 2017) to classify the nearest cliff‐
rock‐scree land cover type, and measured the Euclidean distance from the center of each 30‐m
2
cell to the
nearest cliff‐rock‐scree land cover type. We derived VRM, slope, and TPI covariates from a 30‐m digital elevation
model obtained from United States Geological Survey National Elevation Dataset (ned.usgs.gov, accessed 13
Mar 2018).
Visual obstruction has been hypothesized to influence both habitat selection and mortality risk because bighorn
rely on vision to detect and evade predators (Hansen 1980b, Wakelyn 1987, Etchberger et al. 1989). We recorded
horizontal obstruction at randomly selected locations and at randomly selected bighorn sheep GPS locations within
defined available habitat and sampling units (defined below). We placed a 2‐m cover pole (Griffith and Youtie 1988)
at each location, established a 20‐m transect in each cardinal direction, and recorded the number of 0.1‐m bands
within each 0.5‐m section that were ≥25% obstructed when viewed at a height of 88 cm (to simulate adult bighorn
sheep eye height; Hansen 1980b) from the end of each transect. For each obstructed band, we noted whether it
was primarily obstructed by vegetation or topography. For analysis, we converted the number of bands obstructed
to a percentage and considered total horizontal obstruction, vegetative horizontal obstruction, and topographic
horizontal obstruction.
We also measured group size, which may serve as a primary determinant of predation risk for bighorn sheep
(Berger 1978, Mooring et al. 2004, Rieucau and Martin 2008). We attempted to VHF track and observe each
collared bighorn sheep once per month and used spotting scopes and binoculars to identify individuals in a group
via unique ear tag numbers. During each observation, we recorded group size and the number of adult females,
adult males, female yearlings, male yearlings, lambs, and total group size.
Normalized difference vegetation index (NDVI) is an indicator of vegetation productivity and an index of plant
green‐up or senescence (Pettorelli et al. 2005, Sesnie et al. 2012), which may influence bighorn sheep habitat
selection. We used 250‐m resolution, 16‐day Moderate‐resolution Imaging Spectroradiometer (MODIS) satellite
data, obtained via USGS EarthExplorer (earthexplorer.usgs.gov, accessed 28 Aug 2017) to calculate NDVI metrics.
We used the raster algebra tool in ArcGIS 10.3 to calculate average NDVI values for time periods defined by our
survival and habitat selection analysis periods.
Predation risk and a prey species' habitat selection may also be influenced by a predator's resource selection
and spatial distribution. Previous research has reported that mountain lions use some vegetation associations and
landforms such as woodlands, chaparral, riparian areas, gentle slopes, and canyon bottoms, preferentially (Dickson
et al. 2005, Dickson and Beier 2007, Nicholson et al. 2014). We therefore used a GIS and the Southwest Regional
Gap Analysis Project (gapanalysis.usgs.gov, accessed 1 Sep 2017) to classify the following vegetation associations:
desert scrub and grassland, chaparral and shrubland, and forest and woodland. We used LANDFIRE (land-
fire.cr.usgs.gov, accessed 1 Sep 2017) to classify riparian areas. We then measured the Euclidean distance from the
center of each 30‐m
2
cell to each of these 4 vegetation associations.
Free water availability may influence bighorn sheep distribution (Leslie and Douglas 1979, Turner and
Weaver 1980) and proximity to water has been hypothesized to increase bighorn sheep predation risk
(Broyles 1995). We used AZGFD databases, field observations, and the National Hydrography Dataset
(nhd.usgs.gov, accessed 1 Sep 2017) to identify perennial water sources, and used a GIS to measure the
Euclidean distance from the center of each 30‐m
2
cell to the nearest perennial water source. We used the
area solar radiation tool in ArcGIS 10.3 to calculate yearly‐averaged insolation for each 30‐m
2
cell. Prior to
modeling, we standardized all continuous covariates by setting their mean to 0 and standard deviation to 1
(Schielzeth 2010). We calculated a Pearson correlation coefficient (r) matrix for all continuous environmental
variables to evaluate multicollinearity, and did not use environmental variables in the same model if pairwise
|r|≥0.5.
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Analysis of habitat selection
We conducted a habitat selection analysis to evaluate bighorn sheep habitat selection patterns as they relate to
presumed predator avoidance strategies. We used a negative binomial resource selection probability function
(RSPF) to estimate how environmental variables affected the relative probability of use of sampling units (Sawyer
et al. 2006,2009; Nielson and Sawyer 2013). We used a generalized linear model with a negative binomial error
distribution (GLM; Cameron and Trivedi 2013) because it accounts for the intensity of resource use, whereas a
traditional logistic model does not (Nielson and Sawyer 2013).
Defining available habitat and sampling units
We defined available habitat at the population level by pooling all sheep locations by season and, for each season,
calculated a utilization distribution (Van Winkle 1975) using a squares cross‐validation bandwidth and 95% isopleth
in the Geospatial Modeling Environment (version 0.7.4.0, www.spatialecology.com/gme, accessed 12 Feb 2018).
We chose a utilization distribution with a squares cross‐validation bandwidth to define available habitat because it
produced contiguous population‐level home range boundaries but was more restricted than minimum convex
polygons, which tended to include large areas where no bighorn sheep locations were present as available habitat,
including urban areas at the Catalina site. Prior to analysis, we evaluated 3 different sizes of non‐overlapping
circular sampling units (Nielson and Sawyer 2013) with diameters of 50 m, 100 m, and 150 m. For each sampling
unit diameter size, we summed sheep relocations per sampling unit and calculated the mean value of environmental
variables per sampling unit for each season. Of the 3 options for sampling unit diameter, we chose a 100‐m
diameter because this option appeared, based on a visual assessment, to be sensitive to changes in bighorn sheep
habitat selection, judged by sampling units that contained 0 bighorn sheep relocations adjacent to sampling units
that contained ≥1 bighorn sheep relocations. Additionally, rootograms indicated that the counts of relocations
approximated a negative binomial distribution (Kleiber and Zeileis 2016, Roberts et al. 2017), and visual inspection
of histogram plots of environmental variables showed that 100‐m diameter sampling plots captured meaningful
spatial variability in habitat conditions (Nielson and Sawyer 2013).
Candidate habitat selection models
Bighorn sheep habitat selection strategies may vary by sex and season (Leslie and Douglas 1979, Bleich et al. 1997)
so we split data by sex and 2 seasons corresponding to winter (Nov–Apr) and summer (May–Oct). Additionally, we
anticipated that translocated bighorn sheep might exhibit aberrant habitat use patterns until they become familiar
with their new surroundings, so we excluded the first 6 months of each animal's data in our habitat selection
analyses. In total, this resulted in 4 sex‐seasons (hereafter, season), pooled across years: female winter, male winter,
female summer, and male summer. Under hypothesis 1 and 2, we identified mechanisms of bighorn sheep predator
avoidance strategies and the distribution of food and cover resources on the landscape to formulate 35 candidate
habitat selection models (Appendix A). The bighorn sheep predator avoidance strategy mechanism included
combinations of the following variables: horizontal obstruction, slope, VRM, distance to cliff‐rock‐scree, and to-
pographic position index (Table A1). The bighorn sheep resource acquisition mechanism included combinations of
the following variables: distance to perennial water, distance to desert scrub and grassland, distance to riparian,
distance to chaparral and shrubland, distance to forest and woodland, solar radiation, and NDVI (Table A2). We also
developed candidate habitat selection models that included environmental variables from both the resource ac-
quisition and predator avoidance strategies mechanisms (Table A3). We included quadratic terms for slope and
ruggedness because it has been reported previously that bighorn sheep select areas with intermediate ruggedness
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JONES ET AL.
and slope (Hoglander et al. 2015, Karsch et al. 2016). We included only one form of horizontal obstruction covariate
per model to differentiate the potential effect of obstruction due to vegetation only, topography only, or total
obstruction.
Resource selection probability functions
We modeled habitat selection in each season with an RSPF using a negative binomial GLM (Sawyer et al. 2006,
2009). We treated the count of bighorn sheep locations in each 100‐m diameter sampling unit as the response
variable, and the mean value of each environmental variable in each 100‐m diameter sampling unit as the predictor
variables. We bootstrapped (n= 1,000 bootstrap samples) individual animals with replacement for each season to
account for among‐animal variation, and to correctly treat the individual animal as the experimental unit (Goldstein
et al. 2010, Nielson and Sawyer 2013). We pooled location data from all bootstrapped individuals by summing all
locations per sampling unit for each season (Goldstein et al. 2010, Nielson and Sawyer 2013). We used the number
of locations from each bootstrap sample as the offset term in the negative binomial GLM, which rescales the
response as a relative frequency of use (Sawyer et al. 2009). We then used the 1,000 bootstrap samples for each
season to fit a priori candidate models using a negative binomial GLM. For each GLM, we estimated coefficients and
standard deviations for each variable and calculated the Akaike's Information Criterion corrected for small sample
sizes (AIC
c
; Burnham and Anderson 2002) values for each model. We estimated standard errors of the coefficients
by averaging the standard deviations from each bootstrap run. We used AIC
c
values from a single random model fit
for each candidate model to rank the a priori models by AIC
c
weights, which indicate the amount of support for each
model (Anderson 2007). We considered models with ΔAIC
c
< 10 to be well‐supported and selected as top models
those with ΔAIC
c
< 2 (Burnham and Anderson 2002). We used program R (R Core Team 2018) and the aods3
package (Lesnoff and Lancelot 2018) to fit negative binomial regression models.
Habitat selection model validation
We used the continuous Boyce index (Boyce et al. 2002, Hirzel et al. 2006) to validate the predictive power of our
top‐supported habitat selection models. The Boyce index divides a map of model predictions into bins and then
compares the ratio of the predicted proportion of presences (assuming no habitat selection) in the same bin (Guisan
et al. 2017). The Boyce index is then the Spearman rank correlation coefficient between the predicted‐to‐expected
ratio and the bin number. The Boyce index can take values between −1 and 1, where values trending towards 1
indicate better predictive power of a model (Guisan et al. 2017). To develop predictive maps, we used the raster
algebra tool in ArcGIS 10.6 to multiply each RSPF coefficient against a raster of each environmental variable, then
summed the products. We included the offset term to re‐scale the predictions as a relative frequency of use
(Sawyer et al. 2009). We then used the ecospat package (version 3.2; Di Cola et al. 2017) in program R to calculate
the Boyce index, with the number of bins set to 10 (Hirzel et al. 2006). We used 80% of bighorn sheep relocations
for each season to fit a habitat selection model, the remaining 20% of bighorn sheep relocations to validate the
model, and repeated the process 5 times (Hirzel et al. 2006, Johnson and Gillingham 2008). We then calculated the
mean and 95% confidence interval of the Boyce index for each season.
Analysis of risk of mortality
We used the Andersen‐Gill (A‐G; Andersen and Gill 1982) formulation of the Cox proportional hazards model (Cox
1972) to examine time‐varying continuous and categorical covariates that we hypothesized might influence bighorn
MOUNTAIN LIONS AND BIGHORN SHEEP
|
9
sheep risk of mortality due to mountain lion predation. We used 3 competing hypotheses to develop candidate risk
models, postulating that bighorn sheep risk of mortality due to mountain lion predation may be primarily influenced
by bighorn sheep predator avoidance strategies, mountain lion presence, and bighorn sheep translocation history
(Appendix B). The bighorn sheep predator avoidance strategy hypothesis included combinations of the following
variables: horizontal obstruction due to vegetation, horizontal obstruction due to topography, total horizontal
obstruction, slope, VRM, distance to cliff‐rock‐scree, topographic position index, NDVI, group size, and sex
(Table B1). Because mountain lion space use may be influenced by vegetation associations and topography (Dickson
et al. 2005, Dickson and Beier 2007, Nicholson et al. 2014), candidate models for the mountain lion presence
hypothesis included combinations of the following variables: distance to desert scrub and grassland, distance to
chaparral and shrubland, distance to forest and woodland, distance to riparian, distance to perennial water, VRM,
topographic position index, and solar radiation (Table B2). The bighorn sheep translocation history hypothesis
included the following environmental and biological variables in a single model: source population, sex, release
cohort (e.g., all individuals released into the Catalina site in 2014), and whether a cohort was released into habitat
with bighorn sheep already present. We included only one form of horizontal obstruction covariate per model to
differentiate the potential effect of obstruction due to vegetation only, topography only, or total obstruction. We
used the same AIC
c
guidelines as in our habitat selection models (Burnham and Anderson 2002) to compare 53 total
candidate A‐G models. We estimated A‐G model coefficients in program R using the survival package
(Therneau 2018).
The A‐G proportional hazards model is parameterized in terms of the hazard ratio (HR), which represents the
proportionate change in the instantaneous mortality rate due to a unit change in the respective covariate
(Kleinbaum 1996, Johnson et al. 2004, Eacker et al. 2016). An HR > 1 indicates a decrease in survival as
the predictor variable increases, whereas a HR < 1 indicates an increase in survival as the value of the predictor
variable increases. Confidence intervals for the HR that include 1 suggest no relationship between mortality rate
and the predictor or, alternatively, suggest imprecise estimates or weak inferences (Johnson et al. 2004).
To incorporate time‐varying covariates, we specified a time scale of a week‐long interval of risk (hereafter,
interval; Kleinbaum 1996) with stop and censoring variables for each interval indicating whether an animal died or
was censored during that interval (Therneau and Grambsch 2000). We right‐censored individuals that were lost
because of radio‐collar failure on the last interval for which those animals recorded ≥1 GPS location. We right‐
censored all individuals after collars were released via the pre‐programmed drop‐off mechanism. We calculated
mean covariate values associated with GPS locations for a given bighorn sheep for each interval of risk. We were
unable to obtain a group size observation for each individual in each week‐long interval of risk, so we assigned the
observed mean monthly group size for every individual to each week‐long interval of risk within that month.
Therefore, our final data were structured so that each row represented an individual bighorn sheep for a given
interval of risk with column covariate values describing the average environmental and behavioral conditions
associated with that bighorn sheep for the interval of risk.
An important assumption in our risk models was that the mean behavioral and environmental conditions used
for each interval of risk accurately reflected instantaneous variation in predation risk. For example, if a bighorn
sheep was in gentle terrain during the first part of a week and steep terrain for the rest of the same week, the mean
value of slope could be a misrepresentation of the environmental conditions to which that bighorn was exposed for
the week. To explore this assumption, we plotted the means and variation of environmental variables used in the
proportional hazards models from bighorn sheep for the weeks in which they were killed by a mountain lion.
Similarly, we assumed the stability of bighorn sheep group within a month accurately characterized bighorn sheep
group size at a week‐long interval risks. We explored this assumption by plotting the means and variation of group
size for bighorn sheep observed ≥3 times in one month.
The principal assumption of the A‐G model is that the HR for a given individual is proportional to the HR for
any other individual and remains constant over time for covariates (Johnson et al. 2004, Hosmer et al. 2008).
We tested for non‐proportionality in the HRs using a correlation test between the scaled Schoenfeld residuals and
10
|
JONES ET AL.
log‐transformed survival times (Therneau and Grambsch 2000). When we detected a violation of the assumption
for a given covariate, we fit a time × covariate interaction and report the results as a post hoc analysis (Therneau and
Grambsch 2000). We plotted Martingale residuals against continuous covariates to assess non‐linearity and de-
viance residuals to assess model outliers, and evaluated the assumption that censoring was unrelated to survival
(i.e., non‐informative; Johnson et al. 2004, Hosmer et al. 2008, Eacker et al. 2016) by attempting to locate radio‐
collared individuals via VHF when GPS uploads from a collar failed. We combined the Arrastra and Catalina study
sites for analysis because of the limited number of mortalities; however, because bighorn sheep risk of mortality
due to mountain lion predation may have varied between study sites, we used the coxme package (Therneau 2021)
in program R to fit post hoc models using study site as a random effect for the best‐supported fixed effects models.
We used multivariate imputation by chained equations (van Buuren 2007) with the mice package (version 3.13.0;
van Buuren and Groothuis‐Oudshoorn 2011) in program R to impute missing covariate values. Multivariate im-
putation by chained equations iteratively solves a series of conditional regression models to stochastically impute
missing covariate values (van Buuren 2007) and maintains the mean and standard deviation of the original data set
while preserving the maximum amount of usable data.
RESULTS
Bighorn sheep habitat selection
For females in winter, we used 21,623 locations from 52 individuals with a mean of 0.52 locations per sampling unit
(SD = 3.02, range = 0 –137). For females in summer, we used 27,529 locations from 63 individuals with a mean of
0.41 locations per sampling unit (SD = 1.88, range = 0–75). For males in winter, we used 3,700 locations from 12
individuals with a mean of 0.35 relocations per sampling unit (SD = 1.32, range = 0–28). For males in summer, we
used 4,617 locations from 15 individuals with a mean of 0.45 locations per sampling unit (SD = 1.37, range = 0–25).
At the Catalina site, we recorded 2,736 horizontal obstruction measurements in 1,416 sampling units, with a mean
of 1.93 (SD =0.45) horizontal obstruction measurements per sampling unit. At the Arrastra study site, we recorded
3,074 horizontal obstruction measurements in 1,534 sampling units, with a mean of 2.00 (SD = 0.31) horizontal
obstruction measurements per sampling unit. Collar fix rate averaged across individuals at the Catalina site was
90.16% ± 5.55%, and collar fix rate averaged across individuals at the Arrastra site was 94.99% ± 2.90%. We did not
address GPS location accuracy in RSPFs because the sampling units were larger than the GPS spatial error averaged
across individual bighorn sheep (Nielson and Sawyer 2013).
Top habitat selection models for female bighorn sheep were different between winter and summer, and there was
strong support for the top female habitat selection models in both seasons (Table 2; Burnham and Anderson 2002). The
top models for male bighorn sheep were also different between winter and summer, and there was strong support for
the top male habitat selection models in both seasons (Table 2; Burnham and Anderson 2002). The Boyce index for the
female winter model was 0.87 (95% CI = 0.84–0.91), for the female summer model was 0.86 (95% CI =0.84–0.88), for
the male winter model was 0.85 (95% CI = 0.78–0.92), and for the male summer model was 0.87 (95% CI = 0.80–0.93),
indicating a strong positive correlation between RSPF predictions and bighorn sheep GPS relocations.
In winter, females selected areas with less vegetative obstruction, moderately rugged and steep areas, and
areas with increased distance to perennial water (Figures 2A,3A, and 4A). In winter, females selected steeper slopes
and ridgetops over canyon bottoms and gentle slopes, and selected ridgetops over all other topographic positions.
They did not select differently between canyon bottoms and gentle slopes. Females also selected areas with greater
solar radiation in winter but did not select areas with higher NDVI values.
Similar to winter habitat selection, in summer female bighorn sheep selected some features associated with
predator avoidance, including less vegetative obstruction, areas closer to desert scrub and grassland (Figure 2B),
and moderately rugged and steep areas (i.e., selection was lowest at low and high ruggedness and slope values;
MOUNTAIN LIONS AND BIGHORN SHEEP
|
11
Figures 3B and 4B). Females in summer also selected canyon bottoms over gentle slopes, steep slopes over canyon
bottoms and gentle slopes, and ridgetops over canyon bottoms, gentle slopes, and steep slopes (Figure 2B). Ad-
ditionally, female sheep selected areas of higher NDVI values, and areas with increased distance to perennial water.
In winter, males also selected some features associated with predator avoidance, including moderately rugged
and steep areas, and areas with less vegetative obstruction (Figures 2C, 3C, and 4C). Males also selected areas with
greater solar radiation and increased distance to perennial water but did not select areas with higher NDVI values
(Figure 2). During winter, males also did not show any difference in selection between canyon bottoms, gentle
slopes, and steep slopes but did select ridgetops. In summer, males did not select for rugged areas but did select for
intermediate slopes (Figures 3D and 4D). Males in summer also selected desert scrub and grassland and areas with
less vegetative obstruction, areas with higher NDVI values, and increased distance from perennial water
(Figure 2D). Males did not show any difference in selection between canyon bottoms, gentle slopes, and steep
slopes but did select for ridgetops in summer.
Bighorn sheep risk of mortality modeling
We included 93 collared bighorn sheep (18 males and 75 females) in our risk of mortality models and recorded 31
mortalities due to mountain lion predation over 7,263 intervals of risk, which we used to fit 53 A‐G models. A total
of 21 bighorn sheep were killed by mountain lions at the Catalina site (5 males, 16 females), and 10 bighorn sheep
(1 male, 9 females) were killed by mountains lions at the Arrastra site. Twelve bighorn sheep mortalities had no signs
of mountain lion predation and were categorized as unknown sources of mortality. Six bighorn sheep mortalities
had no signs of mountain lion predation and post‐mortem lung tissue samples tested positive for Mycoplasma
ovipneumoniae bacterium. We categorized these mortalities as non‐predation and an identifiable cause (disease).
From the 2013 release at the Catalina site, 15 bighorn sheep were killed within the first 4 months post‐release
(4 males, 11 females), and from the 2014 release at the Catalina site, 2 female bighorn sheep were killed within the
TABLE 2 Top models predicting bighorn sheep habitat selection at the population level within the Catalina and
Arrastra sites, Arizona, USA, 2013–2017. Model covariates, number of parameters in each model (K), Akaike's
Information Criterion corrected for small sample sizes (AIC
c
), ΔAIC
c
, and Akaike weights (ω
i
) are reported.
Differences in AIC
c
between the top model and all other candidate models for female bighorn sheep in the winter,
female bighorn sheep in the summer, male bighorn sheep in the winter, and male bighorn sheep in the summer >10
AIC
c
. Environmental variables include distance to perennial water (distance to water), a vector ruggedness
measurement (VRM), the quadratic form of VRM, solar radiation, distance to desert scrub and grassland (desert
scrub and grassland), slope, the quadratic form of slope, vegetative obstruction, and normalized difference
vegetation index (NDVI). Topographic position index is a 4‐level factor comprised of canyon bottoms, gentle
slopes, steep slopes, and ridgetops
Season Model structure AIC
c
ΔAIC
c
Kω
i
Female winter Vegetative obstruction + VRM + VRM
2
+ slope + slope
2
+ topographic
position index + NDVI + distance to water + solar radiation
271,400 0 13 0.99
Female summer Vegetative obstruction + VRM + VRM
2
+ slope + slope
2
+ topographic
position index + distance to desert scrub‐grassland + distance to
water + NDVI
439,900 0 13 0.99
Male winter Vegetative obstruction + VRM + VRM
2
+ slope + slope
2
+ topographic
position index + NDVI + distance to water + solar radiation
446,970 0 13 0.99
Male summer Vegetative obstruction + VRM + VRM
2
+ slope + slope
2
+ topographic
position index + distance to desert scrub‐grassland + distance to
water + NDVI
54,250 0 13 0.99
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JONES ET AL.
first 4 months post‐release. At the Arrastra site, 1 female bighorn sheep was killed by a mountain lion within the
first 4 months post‐release in 2013 and 2014. We were only able to collect 3 post‐mortem lung tissue samples and
7 post‐mortem nasal swabs from bighorn sheep killed by mountain lions because carcasses were often consumed
prior to our mortality investigation. Zero of these biological samples tested positive for Mycoplasma ovipneumoniae
bacterium. Because of incomplete disease sampling from lion‐killed sheep, we were unable to evaluate the effect of
disease in the A‐G models. We right‐censored the 18 mortalities due to factors other than mountain lion predation
and right‐censored 17 other bighorn sheep because of radio‐collar failure. We right‐censored all other individuals
after collars dropped off via a pre‐programmed release mechanism. All bighorn sheep that were censored because
of radio‐collar failure were subsequently confirmed alive via opportunistic visual observation after the interval for
which they were right‐censored; therefore, the assumption of non‐informative censoring was met.
We used a mean of 25.1 ± 7.27 (SD) and 22.1 ± 11.99 (SD) locations per individual per interval of risk at the
Catalina and Arrastra study sites, respectively, to derive environmental variable values for remote‐sensed covariates
(e.g., VRM, slope). We measured horizontal obstruction at 1,206 bighorn sheep GPS relocations at the Catalina site,
and 1,301 bighorn sheep GPS locations at the Arrastra site. We used a mean of 6.05 ± 5.37 (SD) and 7.52 ± 5.96
(SD) horizontal visibility measurements per individual per interval of risk at the Catalina and Arrastra study sites,
respectively. We recorded a mean of 2.3 ± 1.95 (SD; n= 1,230) visual observations of group size per bighorn sheep
per month at the Catalina site, and a mean of 1.06 ± 0.86 (SD; n= 809) visual observations of group size per
FIGURE 2 Parameter estimates of top‐ranked models examining male and female bighorn sheep habitat
selection in winter and summer periods at the Arrastra and Catalina study sites in Arizona, USA, 2013–2017.
Estimates are from the top‐ranked model for females in the winter (A), females in the summer (B), males in the
winter (C), and males in the summer (D). Positive and negative coefficients indicate bighorn selection and avoidance,
respectively, for environmental variables. Error bars indicate 95% confidence intervals. Environmental variables
include distance to perennial water (distance to water), a vector ruggedness measurement (VRM), the quadratic
form of a vector ruggedness measurement, solar radiation, distance to desert scrub and grassland (desert scrub and
grassland), slope, the quadratic form of slope, vegetative obstruction, and normalized difference vegetation index
(NDVI). Canyon bottom was the reference category for the topographic position index environmental variable,
which also included categorical variables of gentle slope, steep slope, and ridgetop
MOUNTAIN LIONS AND BIGHORN SHEEP
|
13
individual per month at the Arrastra site. We imputed 3.2% of the covariate values in the group size dataset and
5.3% of the covariate values for the horizontal visibility dataset.
We observed initially that the VRM covariate in models with ΔAIC
c
< 2 violated the proportional hazards
assumption. A visual examination of the smoothed plots of scaled Schoenfeld residuals versus time showed in-
creased mortality with increased values of VRM for the 4 months immediately after translocation for the initial
cohort released at the Catalina site. After this 4‐month period, the smoothed line of the Schoenfeld residuals
decreased and remained flat, indicating decreased risk of mortality with increased values of VRM. We attributed
this pattern in the Schoenfeld residuals to the first release cohort of bighorn sheep making aberrant movements
in areas outside of historical bighorn sheep habitat in the Catalina Mountains during the first 4 months after
release, after which bighorn sheep occupied areas more representative of historical bighorn sheep habitat
FIGURE 3 Relationship between bighorn sheep habitat selection and terrain ruggedness for females in the
winter (A), females in the summer (B), males in the winter (C), and males in the summer (D) at the Arrastra and
Catalina sites in Arizona, USA, 2013–2017. Prediction probabilities represent the probability of use of any given
sampling unit in a given bighorn sheep season. We estimated probability of use for the range of terrain ruggedness
values using the top fitted habitat selection model for each season and holding all other environmental variables in
the fitted model to their means
14
|
JONES ET AL.
(AZGFD, unpublished data). We surmised that these aberrant movements were because animals were released into
vacant bighorn sheep habitat. Therefore, to address the proportional hazards assumption violation in the VRM
environmental variable, we fit a categorical release into vacant habitat covariate representing individuals at the
Catalina site from the first release cohort, during the first 4 months after that release. We then fit a release into
vacant habitat × time interaction for candidate models with ΔAIC
c
< 2 and evaluated the resulting post hoc models.
The top proportional hazards model contained VRM, slope, group size, and sex, and the second‐ranked model
included vegetative obstruction, VRM, slope, group size, and sex (Table 3). The third‐ranked model included total
obstruction, VRM, slope, group size, and sex. We report AIC
c
metrics for the top 3 models (Table 3), but we retained
and report coefficient estimates for only the most parsimonious model because the top‐ranked model was a more
parsimonious model nested within the more complex second‐and third‐ranked models (Roberts et al. 2011). In our
FIGURE 4 Relationship between bighorn sheep habitat selection and percent slope for females in the winter (A),
females in the summer (B), males in the winter (C), and males in the summer (D) at the Arrastra and Catalina site in
Arizona, USA, 2013–2017. Prediction probabilities represent the probability of use of any given sampling unit in a
given bighorn sheep season. We estimated probability of use for the range of slope values using the top fitted habitat
selection model for each season and holding all other environmental variables in the fitted model to their means
MOUNTAIN LIONS AND BIGHORN SHEEP
|
15
final model, group size had the strongest risk effect based on the HR, and as group size increased, bighorn sheep
mortality risk decreased (HR = 0.17, 95% CI = 0.07–0.44, P< 0.005; Table 4; Figure 5). The second‐ranked risk
effect was VRM, and as values of VRM increased, mortality risk decreased (HR = 0.33, 95% CI = 0.3–0.86, P= 0.02).
Slope was the last risk effect, and bighorn sheep mortality risk decreased as values for slope increased (HR = 0.43,
95% CI = 0.21–0.85, P= 0.01). Sex, with male as the reference group, had little explanatory power (HR = 0.67,
CI = 0.24–1.92, P= 0.46). The VRM × release into vacant habitat covariate interaction removed the proportional
hazards assumption violation for VRM in the post hoc models. Relationships between environmental and behavioral
variables and mortality due to mountain lion predation were static between candidate and post hoc models, as
confidence intervals for each environmental and behavioral variable overlapped between the top‐ranked candidate
and top‐ranked post hoc models and signs on each environmental and behavioral estimate remained the same.
Additionally, candidate models and analogous post hoc models maintained the same AIC
c
rankings. Similarly, the
ΔAIC
c
between top‐ranked candidate models and analogous post hoc models with the addition of study site as a
random effect did not improve model fit (ΔAIC
c
= 2). Because the top‐ranked model candidate models were more
parsimonious models nested within the more complex post hoc models, we concluded there was no difference in
bighorn sheep mortality risk between study sites (Roberts et al. 2011). Finally, we interpreted the plotted means
and variation of environmental variables used in the proportional hazards models (Figure 6) and group size (Figure 7)
as showing an acceptable degree of variation, such that the use of mean values for each interval of risk was justified.
DISCUSSION
In this study, we synthesized aspects of bighorn sheep biology that have traditionally been evaluated in-
dependently. Specifically, we evaluated habitat selection, grouping behavior, and predation risk in a combined way
that allowed us to test the effectiveness of presumed predator avoidance strategies. Although these strategies have
TABLE 4 Standardized coefficient estimates, hazard ratios, 95% confidence intervals (CI) for hazard ratios, and
significance values (P) for the top Andersen‐Gill proportional hazards model examining bighorn sheep risk of
mortality due to lion predation at the Arrastra and Catalina study sites, Arizona, USA, 2013–2017. Environmental
or behavioral variables includes a vector ruggedness index (VRM), slope, group size, and sex. For the sex variable,
male was the reference group
Environmental or behavioral variable Estimate SE Hazard ratio 95% CI P
VRM −1.09 0.48 0.33 0.13–0.86 0.02
Slope −0.83 0.34 0.43 0.21–0.85 0.01
Group size −1.72 0.46 0.17 0.07–0.44 <0.005
Sex −0.38 0.52 0.67 0.24–1.92 0.46
TABLE 3 Top 3 Andersen‐Gill proportional hazard models showing Akaike's Information Criterion with an
adjustment for small sample size (AIC
c
), difference in AIC
c
(ΔAIC
c
)
,
and model weights (ω
i
) for bighorn sheep at the
Arrastra and Catalina study sites, Arizona, USA, 2013–2017. Environmental or behavioral variables includes a
vector ruggedness index (VRM), slope, group size, and sex. For the sex variable, male was the reference group
Model structure AIC
c
ΔAIC
c
ω
i
VRM + slope + group size + sex 185.00 0.00 0.33
Vegetative obstruction + VRM + slope + group size + sex 186.09 1.09 0.19
Total obstruction + VRM + slope + group size + sex 186.94 1.94 0.17
16
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JONES ET AL.
often been referred to in previous bighorn sheep literature, this is, to our best knowledge, the first study that tested
the effect of these strategies on bighorn sheep risk of mortality due to mountain lion predation.
Hypothesis 1 was supported because bighorn sheep generally selected habitat in concordance with presumed
predator avoidance strategies and, consistent with prediction 1, males and females in both seasons selected for
FIGURE 5 Unstandardized hazard ratios at bighorn sheep group sizes of 1–10 individuals at the Arrastra and
Catalina sites in Arizona, USA, 2013–2017
FIGURE 6 Means and standard deviation of environmental covariates from bighorn relocations during interval
of risks for which bighorn were killed by a mountain lion at the Arrastra and Catalina study sites in Arizona, USA,
2013–2017
MOUNTAIN LIONS AND BIGHORN SHEEP
|
17
areas with less horizontal obstruction. Additionally, males in the winter and females in both seasons selected for
intermediate slopes and ruggedness, and generally selected these areas rather than gentle terrain. Hypothesis 2 and
prediction 2 were partially supported because females demonstrated a trade‐off between forage resources and
security cover during the winter, which coincided with periods of sexual segregation in our study populations.
Contrary to prediction 2, males showed no trade‐off in forage resources for security cover during periods of sexual
segregation. Related to hypothesis 3, we found that the risk of lion predation was more strongly influenced by
bighorn sheep predator avoidance strategies (prediction 3) than by vegetation associations and landforms pre-
ferentially used by mountain lions (prediction 4) or by the translocation history of bighorn sheep (prediction 5).
Consistent with prediction 3, rugged and steep areas and larger group size reduced the risk of mountain lion
predation. Contrary to prediction 3, we did not identify a relationship between topographic or vegetative horizontal
obstruction and risk of mountain lion predation.
One hypothesized anti‐predator strategy of bighorn sheep is the use of steep and rugged terrain, where
bighorn sheep can presumably outmaneuver predators (Bleich et al. 1997, Geist 1999). This strategy may be a result
of co‐evolution with coursing predators (Festa‐Bianchet 1991) and might not be as effective against ambush
predators such as mountain lions. In this sense, it has been hypothesized that the evolutionary response to coursing
predators has resulted in an ecological trap when mountain lions become the dominant predator (Rominger 2017).
Numerous studies have reported on the relationship between bighorn sheep habitat selection and topographic
features (Geist 1971, McQuivey 1978, McCarty and Bailey 1994, McKinney et al. 2003, Hoglander et al. 2015), and
the importance of ruggedness and slope in bighorn sheep habitat selection is widely accepted (Risenhoover and
Bailey 1985). Our study demonstrates that bighorn sheep selection of rugged and steep topographic features does
reduce the risk of mortality due to mountain lion predation. Therefore, even if bighorn sheep selection strategies
evolved in response to coursing predators, their habitat selection patterns relative to topographic features provide
protection against mountain lions.
FIGURE 7 Means and standard deviation of bighorn group size for individuals observed at least 3 times per
month at the Arrastra and Catalina study sites in Arizona, USA, 2013–2017
18
|
JONES ET AL.
While our study demonstrated a generally positive relationship between habitat selection and ruggedness and
slope, bighorn sheep do not necessarily select the most rugged and steep terrain available. This indicates that while
steep and precipitous terrain represents an important component of bighorn sheep habitat, bighorn sheep may, in
some of their range, select for intermediate levels of slope and ruggedness. This is similar to findings by Hoglander
et al. (2015), who reported that bighorn sheep in southwestern Arizona selected for intermediate values of rug-
gedness and slope. Additionally, even though bighorn sheep in our study selected areas with intermediate values of
slope and ruggedness, relative to availability, these areas still conferred a lower risk of mortality due to mountain
lion predation. Potentially, use of steeper and more rugged terrain may be associated with lower forage availability,
or may increase risk of mortality from mountain lions if bighorn sheep mobility is limited in these areas.
During periods of sexual segregation, females minimize predation risk to themselves and their lambs by se-
lecting rugged and steep terrain during periods of parturition and lamb rearing, even if this results in a foraging cost.
In contrast, males select areas with increased forage resources to increase their body condition and mating success,
potentially at increased predation risk (Festa‐Bianchet 1988, Bleich et al. 1997, Mooring et al. 2003). In our study,
winter (Nov–Apr) included gestation, parturition, and early lamb rearing, and thus included the primary period of
sexual segregation. We found partial support for hypothesis 2, suggesting that female bighorn sheep in our study
selected habitat during periods of sexual segregation to minimize predation risk and maximize reproductive fitness.
We did not, however, observe males trading security cover to exploit forage resources during the primary period of
sexual segregation. Under hypothesis 2, we used NDVI metrics as a measure of forage availability, derived from
250‐m resolution, 16‐day MODIS satellite images, averaged across habitat selection analysis periods. This is a
relatively coarse scale at which to measure NDVI, and may not reflect finer temporal (Hoagland et al. 2018), or
spatial patterns in bighorn forage availability. This coarse scale of analysis may explain the lack of relationship
between male bighorn and NDVI metrics during the primary period of sexual segregation.
Our prediction 1 aligned with the hypothesis that bighorn select habitat with greater visibility as a predator
avoidance strategy (Risenhoover and Bailey 1985,Wakelyn1987,Etchbergeretal.1989). In our risk analysis, we did
not identify any relationship between topographic or vegetative horizontal obstruction and bighorn sheep mortality
risk. Given that habitat selection generally includes avoidance of risk (McLoughlin et al. 2005, Thomson et al. 2006), we
expected that decreased obstruction would decrease predation risk. One possible explanation for the lack of an
observed relationship is that mountain lions hunt primarily at night (Beier et al. 1995,Pierceetal.1998), whereas
bighorn sheep are primarily active during the day. Therefore, the visual field of a bighorn sheep may be inconsequential
to mediating predation risk during the night when mountain lions are most active. Another possibility is that group size,
ruggedness, and slope are the primary determinants of predation risk for bighorn sheep, and while bighorn sheep select
for areas with less obstruction, we were not able to statistically detect the effect of topographic or vegetative
horizontal obstruction on predation risk. A final possibility is that bighorn sheep in our study had previously established
their home ranges in areas with low obstruction, and there wasn't enough variation in horizontal obstruction within
their home ranges to detect a difference in predation risk related to horizontal obstruction. Previous research on heart
rates in free‐ranging bighorn sheep reported increased rates when bighorn sheep were in areas of high visual ob-
struction (MacArthur et al. 1979, Hayes et al. 1994), suggesting a higher perceived risk by bighorn sheep in these areas.
Although we did not identify a relationship between horizontal obstruction and bighorn sheep risk of mountain lion
predation, we found that it influenced habitat selection. Our study therefore suggests that restoration of bighorn sheep
habitat should include efforts to increase horizontal visibility, which could increase the availability or quality of bighorn
sheep habitat. Restoration efforts to increase horizontal visibility are especially important in areas with fire‐adapted
vegetation communities, where fire suppression has resulted in vegetation encroachment, decreasing bighorn visibility
and lowering habitat quality (Wakelyn 1987,Etchbergeretal.1989, Krausman et al. 2001, Bleich et al. 2008).
Gregarious behavior by bighorn sheep is an anti‐predator strategy through group alertness (Hamilton 1971). As
predicted, our risk models indicated that bighorn sheep risk of mortality decreased as group size increased, where the
unstandardized hazard ratio for group size predicted mortality to decrease 30% for every additional individual in a group
(Table 4; unstandardized hazard ratio obtained by back‐transforming the standardized hazard ratio). Using bighorn sheep
MOUNTAIN LIONS AND BIGHORN SHEEP
|
19
vigilance behavior as an indicator of an individual's perceived risk of predation, Berger (1978) and Mooring et al. (2004)
concluded that group size was a primary determinant of risk, with increased group size conferring safety. While
increased group size confers increased safety, Berger (1978) and Berger and Cunningham (1988) reported a reduced
benefit in groups larger than 5–10 individuals. Similarly, Mooring et al. (2004) reported a decreased anti‐predator benefit
of group size beyond groups of 5–10 animals, using vigilance as an index of risk. We found a similar pattern of a
declining marginal benefit of increased group size to mountain lion predation risk at larger group sizes (Figure 5).
We did not find support for any models under the mountain lion presence framework of hypothesis 3. Previous
research on other ungulates found that risk of lion predation was influenced by mountain lion distribution or
abundance. For example, Atwood et al. (2009) reported that mule deer risk of predation was largely a function of
mountain lion resource selection, and Eacker et al. (2016) reported elk (Cervus canadensis) calf survival was best
predicted by exposure to mountain lion predation risk. Under hypothesis 3, we developed A‐G candidate models
that included vegetation associations and landforms reported to influence mountain lion habitat selection. In-
corporating mountain lion resource selection functions as an environmental variable in bighorn sheep risk models
would enhance our understanding of the link between mountain lion distribution and bighorn sheep mortality risk.
Future research on bighorn sheep‐mountain lion interactions would also benefit from evaluation of the relationship
between predation risk and mountain lion abundance, distribution, and resource selection patterns.
Our study included translocated animals, with one cohort released into vacant historical habitat. Initially,
translocated bighorn sheep experienced a higher mortality risk in rugged areas, possibly due to high visual ob-
struction or unfamiliarity with escape routes in a new home range; however, we were able to control for this effect
by including a time × VRM interaction and, ultimately, bighorn sheep were at decreased risk of mortality due to
mountain lion predation in areas with increased ruggedness.
Our study, to the best of our knowledge, is the first to evaluate the effectiveness of bighorn sheep predator
avoidance strategies in mitigating the risk of mortality due to mountain lion predation through a mortality risk model. Our
study validates several long‐held hypotheses about bighorn sheep predator avoidance strategies. These include the
importance of topographic features and increased group size as factors that reduce bighorn sheep risk of mortality due to
mountain lion predation, and the importance slope, ruggedness, and reduced vegetative obstruction as important
components of bighorn sheep habitat. This increased knowledge of bighorn sheep habitat selection and factors influ-
encing risk of mortality due to mountain lion predation suggests several pertinent and actionable management strategies.
MANAGEMENT IMPLICATIONS
Bighorn sheep select areas that are unobstructed by vegetation, and we suggest that management actions that
increase horizontal visibility will likely increase the suitability and availability of bighorn sheep habitat. Our findings
also indicate that areas with intermediate levels of ruggedness and slope may provide the best bighorn sheep
habitat. Management actions that decrease visual obstruction in these areas may therefore yield the greatest
improvement in bighorn sheep habitat quality. Additionally, managers should evaluate slope and ruggedness when
selecting future translocation areas and release sites, especially when reintroducing bighorn sheep to vacant ha-
bitat. Finally, because increased group size may reduce predation risk, augmentation of low‐density bighorn sheep
populations may decrease individual predation risk, and increasing the number of bighorn sheep in each translo-
cation may help to increase group sizes after release, thereby decreasing mortality risk.
ACKNOWLEDGMENTS
B. D. Brochu was instrumental in facilitating the re‐introduction of bighorn sheep to the Catalina Mountains and
also assisted with field work. E. M. Butler facilitated the bighorn sheep augmentations at the Arrastra Mountain
Wilderness study site. N. J. Jackson, M. J. Guerena, B. M. Webber, S. I. Martinez, G. J. Samsill, N. A. Ratliff, C. B.
Piper, E. T. Cini, K. A. Herbstreit, L. R. Frear, A. C. Stewart, J. R. Sheehey, R. Y. Yee, S. G. Whitmore, I. Garcia,
20
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JONES ET AL.
W. Eckels, K. D. Bristow, and M. L. Crabb provided field support. S. Boe provided GIS support. T. C. Theimer and 2
anonymous reviewers provided a helpful review of the draft manuscript. Funding for this project was provided by a
Pittman‐Robertson Federal Aid in Wildlife Restoration Grant. Additional funding was provided by Safari Club
International and the Arizona Desert Bighorn Sheep Society.
ETHICS STATEMENT
All animal capture and handling procedures were included in capture plans approved by AZGFD.
DATA AVAILABILITY STATEMENT
Data available on request from the authors.
ORCID
Matthew J. Clement http://orcid.org/0000-0003-4231-7949
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APPENDIX A: HABITAT SELECTION CANDIDATE MODELS
TABLE A1 Candidate models (model number) of habitat selection by desert bighorn sheep based on predator
avoidance mechanisms during the summer and winter seasons at the Catalina and Arrastra study sites, 2013–2017.
Squared term indicates the quadratic form of a variable
Model number Model structure
a
Predator avoidance hypothesis
1 Total obstruction + VRM + VRM
2
+ slope + slope
2
2 Vegetative obstruction + VRM + VRM
2
+ slope + slope
2
3 Topographic obstruction + VRM + VRM
2
+ slope + slope
2
4 Total obstruction + cliff‐rock‐scree
5 Vegetative obstruction + cliff‐rock‐scree
6 Topographic obstruction + cliff‐rock‐scree
7 Total obstruction + topographic position index
8 Vegetative obstruction + topographic position index
9 Topographic obstruction + topographic position index
10 Total obstruction + VRM + VRM
2
+ slope + slope
2
+ topographic position index + cliff‐rock‐scree
11 Vegetative obstruction + VRM + VRM
2
+ slope + slope
2
+ topographic
position index + cliff‐rock‐scree
12 Topographic obstruction + VRM + VRM
2
+ slope + slope
2
+ topographic
position index + cliff‐rock‐scree
a
Horizontal obstruction due to vegetation and topography (total obstruction); horizontal obstruction due to vegetation
(vegetative obstruction); horizontal obstruction due to topography (topographic obstruction); slope (slope); a vector
ruggedness measure (VRM); distance to cliff, rock, scree (cliff‐rock‐scree); and topographic position index.
TABLE A2 Candidate models (model number) of habitat selection by desert bighorn sheep based on
obtainment of resources mechanisms during the summer and winter seasons, at the Catalina and Arrastra study
sites, 2013–2017
Model number Model structure
a
Resource acquisition hypothesis
1 Water + scrub‐grassland
2 Water + chaparral scrub
3 Water + forest‐woodland
4 Water + desert scrub‐grassland + NDVI
5 Water + chaparral scrub + NDVI
6 Water + forest‐woodland + NDVI
7 Water + scrub‐grassland + chaparral scrub + forest‐woodland
8 Water + scrub‐grassland + chaparral scrub + forest‐woodland + NDVI + solar radiation
a
Normalized difference vegetation index (NDVI); distance to perennial water (water); solar radiation (solar radiation);
distance to desert scrub and grassland (scrub‐grassland); distance to chaparral scrub (chaparral); and distance to forest and
woodland (forest‐woodland).
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TABLE A3 Candidate models (model number) of habitat selection by male and female desert bighorn sheep
based on predator avoidance and obtainment of resources mechanisms during the summer and winter seasons at
the Catalina and Arrastra study sites, 2013–2017. Squared term indicates the quadratic form of a variable. The top
performing model is indicated with an asterisk (*)
Model number Model structure
a
Predator avoidance and resource acquisition hypothesis
1 Total obstruction + VRM + VRM
2
+ topographic position index + NDVI + water + solar radiation
2 Vegetative obstruction + VRM + VRM
2
+ topographic position index + NDVI + water + solar
radiation
3 Topographic obstruction + VRM + VRM
2
+ topographic position index + NDVI + water + solar
radiation
4 Total obstruction + cliff‐rock‐scree + NDVI + water + solar radiation
5 Vegetative obstruction + cliff‐rock‐scree + NDVI + water + solar radiation
6 Topographic obstruction + cliff‐rock‐scree + NDVI + water + solar radiation
7 Total obstruction + VRM + VRM
2
+ slope + slope
2
+ NDVI + water + solar radiation
8 *Vegetative obstruction + VRM + VRM
2
+ slope + slope
2
+ NDVI + water + solar radiation
9 Topographic obstruction + VRM + VRM
2
+ slope + slope
2
+ NDVI + water + solar radiation
10 Total obstruction + VRM + VRM
2
+ slope + slope
2
+ topographic position index + NDVI + water +
solar radiation
11 Vegetative obstruction + VRM + VRM
2
+ slope + slope
2
+ topographic position index + NDVI + water
+ solar radiation
12 Topographic obstruction + VRM + VRM
2
+ slope + slope
2
+ topographic position index +
NDVI + water + solar radiation
13 Total obstruction + water + scrub‐grassland + chaparral + forest‐woodland + VRM + VRM
2
+ slope +
slope
2
+ topographic position index + NDVI
14 Vegetative obstruction + water + scrub‐grassland + chaparral + forest‐woodland +
VRM + VRM
2
+ slope + slope
2
+ topographic position index + NDVI
15 Topographic obstruction + water + scrub‐grassland + chaparral + forest‐woodland +
VRM + VRM
2
+ slope + slope
2
+ topographic position index + NDVI
a
Horizontal obstruction due to vegetation and topography (total obstruction); horizontal obstruction due to vegetation
(vegetative obstruction); horizontal obstruction due to topography (topographic obstruction); slope (slope); a vector
ruggedness measure (VRM); distance to cliff‐rock‐scree (cliff‐rock‐scree); topographic position index, normalized difference
vegetation index (NDVI); distance to perennial water (water); solar radiation (solar radiation); distance to desert scrub and
grassland (scrub‐grassland); distance to chaparral scrub (chaparral); and distance to forest and woodland (forest‐woodland).
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APPENDIX B: PREDATION RISK CANDIDATE MODELS
TABLE B1 Cox proportional hazards models (model number) used to examine bighorn sheep risk of mortality
due to mountain lion predation under the predator avoidance mechanism at the Arrastra and Catalina study sites,
2013–2017. The top performing model is indicated with an asterisk (*)
Model number Model
a
Predator avoidance hypothesis
1 Total obstruction + VRM + slope + sex
2 Vegetative obstruction + VRM + slope + sex
3 Topographic obstruction + VRM + slope + sex
4 Total obstruction + VRM + slope + group size + sex
5 Vegetative obstruction + VRM + slope + group size + sex
6 Topographic obstruction + VRM + slope + group size + sex
7 *VRM + slope + group size + sex
8 Topographic position index + group size + sex
9 Cliff‐rock‐scree + group size + sex
10 VRM + topographic position index + group size + sex
11 VRM + topographic position index + slope + group size + sex
12 Total obstruction + topographic position index + sex
13 Vegetative obstruction + topographic position index + sex
14 Topographic obstruction + topographic position index + sex
15 Total obstruction + cliff‐rock‐scree + sex
16 Vegetative obstruction + cliff‐rock‐scree + sex
17 Topographic obstruction + cliff‐rock‐scree + sex
18 Total obstruction + topographic position index + group size + sex
19 Vegetative obstruction + topographic position index + group size + sex
20 Topographic obstruction + topographic position index + group size + sex
21 Total obstruction + cliff‐rock‐scree + group size + sex
22 Vegetative obstruction + cliff‐rock‐scree + group size + sex
23 Topographic obstruction + cliff‐rock‐scree + group size + sex
24 VRM + slope + topographic position index + sex
25 Total obstruction + VRM + slope + NDVI + sex
26 Vegetative obstruction + VRM + slope + NDVI + sex
27 Topographic obstruction + VRM + slope + NDVI + sex
28 Total obstruction + topographic position index + NDVI + group size + sex
29 Vegetative obstruction + topographic position index + NDVI + group size + sex
(Continues)
MOUNTAIN LIONS AND BIGHORN SHEEP
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TABLE B1 (Continued)
Model number Model
a
30 Topographic obstruction + topographic position index + NDVI + group size + sex
31 VRM + slope + NDVI + group size + sex
a
Horizontal obstruction due to vegetation and topography (total obstruction); horizontal obstruction due to vegetation
(vegetative obstruction); horizontal obstruction due to topography (topographic obstruction); slope (slope); a vector
ruggedness measure (VRM); distance to cliff‐rock‐scree (cliff‐rock‐scree); topographic position index; normalized difference
vegetation index (NDVI); group size (group size); and sex.
TABLE B2 Cox proportional hazards models (model number) used to examine bighorn sheep risk of mortality
due to mountain lion predation under the lion presence mechanism at the Arrastra and Catalina study sites,
2013–2017
Model number Model
a
Lion presence hypothesis
1 Riparian + sex
2 Forest‐woodland + sex
3 Chaparral + sex
4 Scrub and grassland + sex
5 VRM + riparian + sex
6 VRM + forest‐woodland + sex
7 VRM + chaparral + sex
8 VRM + scrub‐grassland + sex
9 Topographic position index + riparian + sex
10 Topographic position index + forest‐woodland + sex
11 Topographic position index + chaparral + sex
12 Topographic position index + scrub‐grassland + sex
13 VRM + riparian + water + sex
14 VRM + forest‐woodland + water + sex
15 VRM + scrub‐grassland + water + sex
16 VRM + topographic position index + forest ‐woodland + solar radiation + sex
17 VRM + topographic position index + riparian + solar radiation + sex
18 VRM + topographic position index + scrub‐grassland + solar radiation + sex
19 VRM + topographic position index+ chaparral + solar radiation + sex
20 VRM + topographic position index + riparian + water + sex
21 Distance forest‐woodland + chaparral + scrub‐grassland + riparian + sex
a
Desert scrub and grassland (desert scrub‐grassland), distance to chaparral and shrubland (chaparral), distance to forest and
woodland (forest‐woodland), distance to riparian (riparian), distance to perennial water (water); a vector ruggedness
measure (VRM); and solar radiation (solar radiation).
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