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\begin{document}

\title{A seasonal pulse of ungulate neonates influences space use by carnivores
in a multi-predator, multi-prey system}



\author[1]{Joel  Ruprecht}%
\author[2]{Tavis Forrester}%
\author[3]{Nathan Jackson}%
\author[2]{Darren Clark}%
\author[4]{Michael Wisdom}%
\author[4]{Mary Rowland}%
\author[2]{Joshua Smith}%
\author[3]{Kelley Stewart}%
\author[1]{Taal Levi}%
\affil[1]{Oregon State University}%
\affil[2]{Oregon Department of Fish and Wildlife}%
\affil[3]{University of Nevada Reno}%
\affil[4]{USDA Forest Service Pacific Northwest Research Station}%


\vspace{-1em}



  
  \date{May 27, 2024}


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\selectlanguage{english}
\begin{abstract}
Understanding the extent to which predators engage in active search for
prey versus incidentally encountering them is important because active
search can exert a stabilizing force on prey populations by alleviating
predation pressure on low-density prey and increasing it for
high-density prey. Parturition of many large herbivores occurs during a
short and predictable temporal window in which young are highly
vulnerable to predation. Our study aims to determine how a suite of
carnivores responds to the seasonal pulse of newborn ungulates using
contemporaneous GPS locations of four species of predators and two
species of prey. We used step-selection functions to assess whether
coyotes, cougars, black bears, and bobcats actively searched for
parturient females in a low-density population of mule deer and a
high-density population of elk. We then assessed whether searching
carnivores shifted their habitat use toward areas exhibiting a high
probability of encountering neonates. None of the four carnivore species
encountered parturient mule deer more often than expected by chance
suggesting that predation of young resulted from incidental encounters.
By contrast, we determined that cougar and male bear movements
positioned them in proximity of parturient elk more often than expected
by chance which is evidence of searching behavior. Although both male
bears and cougars searched for neonates, only male bears used elk
parturition habitat in a way that dynamically tracked the phenology of
the elk birth pulse suggesting that maximizing encounters with juvenile
elk was a motivation when selecting resources. Our results support the
existence of a stabilizing mechanism to prey populations through active
search behavior by predators because carnivores in our study searched
for the high-density prey species (elk) but ignored the low-density
species (mule deer). We conclude that prey density must be high enough
to warrant active search, and that there is high interspecific and
intersexual variability in foraging strategies among large mammalian
predators and their prey.%
\end{abstract}%



\sloppy


\textbf{INTRODUCTION}

Although the distinction between active search and incidental encounter
of prey is key to understanding predator-prey dynamics, whether, and
under what conditions predators actively search for particular prey
species is poorly understood. Diet breadth theory suggests that
predators seeking to maximize their rate of energy acquisition should
have a more generalist prey profile until the encounter rate with the
most profitable prey item crosses a critical threshold that makes it
suboptimal to include lower-profitability prey in their diet (MacArthur
\& Pianka 1966; Figure 1; Supporting Information Text S1). Diet
specialization on abundant prey is necessarily associated with active
search for that prey, but as the density of the focal prey species
declines, additional species enter the diet which reduces the rate of
acquisition of the focal prey. A switch from active search for a prey
species at high density to incidental encounter of the same species at
low density can have stabilizing effects on prey population dynamics
(Murdoch 1969) and results in the canonical sigmoid Type III functional
response that is associated with many of the most interesting dynamics
in predator-prey systems including alternative stable states,
bifurcations, and predator pits (Holling 1959; Messier 1994;
Levi\emph{et al.} 2015).

The density-dependent response of predators that is evidence for active
search can be found by observing disproportionate predation in years in
which a given prey species is at high density. However, in many systems
prey densities vary predictably within a year due to a birth pulse that
provides a uniquely vulnerable life stage for predators. A classic case
of this phenomenon is the seasonal pulse of songbird nests (Schmidt,
Goheen \& Naumann 2001; Vigallon \& Marzluff 2005), and both active
search (Pelech, Smith \& Boutin 2010) and incidental encounter (Schmidt
2004) strategies have been documented as a function of nest density,
vulnerability, and maternal vigilance or defense (Schmidt 1999). In
addition to songbirds, large herbivore systems worldwide feature a
predictable birth pulse of neonates that are vulnerable to predators
across a wide body size gradient. Although mortality of ungulate
neonates has been studied extensively (Linnell, Aanes \& Andersen 1995),
it is still largely unknown whether, and under what conditions predators
engage in active search behavior during the birth pulse, which has
important implications for prey population dynamics.

The propensity of carnivores to target neonates likely depends on
factors intrinsic to both the predator and prey. For predators, this may
vary by body size, hunting proficiency or mode, and ability to cope with
maternal defense by the large herbivore. For example, ungulate neonates
are highly vulnerable to predation immediately following parturition
from a suite of carnivores, but quickly become sufficiently vagile to
elude those that are less predaceous or of smaller body size. Thus,
species such as bears and many mesopredators experience a particularly
short resource pulse of neonates (Linnell, Aanes \& Andersen 1995; Zager
\& Beecham 2006; Griffin \emph{et al.} 2011) (Figure 1a, b). In
contrast, the birth pulse may be less consequential to the largest
felids and canids that can efficiently capture large-bodied ungulates
throughout the first year of life and beyond (Figure 1c). Even within a
species, the response of predators to the ungulate birth pulse may vary
by individual or sex as has been shown in bears (Jacoby \emph{et
al.}1999; Zager \& Beecham 2006; Rayl \emph{et al.} 2015).

Because predatory behavior during the ungulate birth pulse is influenced
by idiosyncratic combinations of factors intrinsic to both predators and
prey, studies involving multiple carnivore and multiple ungulate species
will be needed to elucidate the generality of search behavior. Previous
research has largely focused on identifying spatial shifts in habitat
use by bears (but see Bastille-Rousseau \emph{et al} . 2016;
Svoboda\emph{et al} . 2019) toward birthing grounds or areas on the
landscape more likely to contain neonates, which has resulted in
different conclusions wherein both active search (Rayl \emph{et al} .
2018) and incidental encounter (Bastille-Rousseau \emph{et al.} 2011;
Bowersock\emph{et al.} 2021) were inferred. Much stronger inference is
possible using analytical methods that utilize spatiotemporal encounters
between individual predators and individual prey from contemporaneous
GPS telemetry data. Further, identifying general conditions associated
with incidental encounter and active search requires relocation data on
multiple species of predators and prey across gradients in body size,
abundance, and life histories.

Here we use contemporaneous GPS tracking data at the level of encounters
between individual predators and individual prey to assess whether
carnivores actively searched for or incidentally encountered ungulate
neonates in a multi-predator, multi-prey system. Each carnivore species
(cougar {[}\emph{Puma concolor} {]}, coyote {[}\emph{Canis latrans} {]},
black bear {[}\emph{Ursus americanus} {]}, bobcat {[}\emph{Lynx rufus}
{]}) varied in size, life history, and predatory ability, ranging from
large-bodied obligate predators to smaller-bodied omnivores, while prey
species (mule deer {[}\emph{Odocoileus hemionus} {]} and elk
{[}\emph{Cervus canadensis} {]}) varied dramatically in abundance. Our
primary objective was to determine whether predators encountered
parturient female ungulates more often than expected by chance,
indicating active search, while controlling for their habitat
preferences. If predators did indeed exhibit targeted search behavior, a
secondary objective was to determine whether a shift in space use toward
parturition habitat tracked the phenology of the birth pulse consistent
with an effort to maximize detections of neonates. We hypothesized that
the magnitude of response by predators to the birth pulse would be
greater toward elk than mule deer for all carnivore species because elk
were approximately 5 times more abundant than mule deer and could thus
cross the profitability threshold associated with specialization under
diet-breadth theory. We expected the carnivore species with a more
generalist diet profile (bears and coyotes) would alter their foraging
behaviors more strongly than cougars or bobcats because generalist
consumers are more fluid in their response to changing resources
(Ostfeld \& Keesing 2000; Yang et al. 2008). Bears are the least
carnivorous of these taxa, and previous research suggests that male
bears are disproportionately predaceous (Rode, Robbins \& Shipley 2001,
Boertje \emph{et al.} 1988; Jacoby \emph{et al.} 1999), so we
additionally hypothesized that male bears would be more likely to
exhibit active search behavior. Further, cougars kill mule deer and elk
of all age classes year-round (Clark \emph{et al.} 2014), so we expected
that the ungulate birth pulse may be less consequential to cougars given
their adeptness at killing larger prey such that they may not exhibit a
change in behavior during the earliest neonatal period. Finally, we
hypothesized that bobcats would show the weakest response, since they
rarely consume elk and mule deer in our study area (Ruprecht \emph{et
al.} 2021b).

\textbf{MATERIALS AND METHODS}

\textbf{Study area.}

Our study was conducted in the Blue Mountains of northeastern Oregon
centered at the Starkey Experimental Forest and Range between 2016 and
2019 (Figure 2). The major habitat types in the study area include
grasslands, riparian areas, open forest dominated by ponderosa pine
(\emph{Pinus ponderosa} ), and closed forest consisting of a mixture of
Douglas fir (\emph{Pseudotsuga menziesii} ), grand fir (\emph{Abies
grandis} ), larch (\emph{Larix occidentalis} ), ponderosa pine and
lodgepole pine (\emph{Pinus contorta} ). Riparian areas sustain willows
(\emph{Salix} spp.), hawthorn (\emph{Crataegus} spp.), Rocky Mountain
maple (\emph{Acer glabrum} ), and other shrub species in low quantities.
Starkey Experimental Forest and Range and adjacent public lands support
an assemblage of native and domestic large herbivores including mule
deer, white-tailed deer (\emph{Odocoileus virginianus} ), elk, and
seasonally grazed domestic cattle (\emph{Bos taurus;} Rowland \emph{et
al.} 1997). Carnivore species include black bears, coyotes, cougars, and
bobcats. Gray wolves (\emph{Canis lupus} ) are colonizing the area but
currently occur only occasionally and unpredictably in the study area.

We used global positioning system (GPS) telemetry data from 9 cougars
(representing 11 animal years), 17 coyotes (21 animal years), 11 black
bears (18 animal years), 6 bobcats (7 animal years), 25 adult female
mule deer (45 animal years), and 59 adult female elk (89 animal years).
GPS positions were recorded every 2 or 3 hours for carnivores, every 30
minutes for elk, and every 60 or 90 minutes for deer. Details on capture
and handling of carnivores, elk, and mule deer can be found in
Ruprecht\emph{et al.} (2021a), Wisdom \emph{et al.} (1993) and Jackson
\emph{et al.} (2021), respectively. All animal capture and handling
adhered to protocols approved by the USDA Forest Service, Starkey
Experimental Forest Institutional Animal Care and Use Committee
(IACUC~No. 92-F-0004; protocol \#STKY-16-01) and followed the guidelines
of the American Society of Mammalogists for the use of wild mammals in
research~(Sikes 2016).

\textbf{Identifying elk and mule deer parturition events.}

We inferred elk parturition events from GPS-collared elk between 2016
and 2019 using the rolling minimum convex polygon (MCP) method described
by Nicholson \emph{et al.} (2019) to estimate large herbivore
parturition events based on localized movements. We assigned a
parturition event for elk as the first day a rolling MCP (based on a
24-hour window) decreased to \textless{}30 hectares or less for a
minimum of 120 hours. If these conditions were not met, we assumed the
elk did not give birth. We validated the method using independent elk
GPS locations with known birth dates and locations (\emph{N} = 30) from
a previous study in the same area (Long et al. 2016). The mean
discrepancy between birth dates determined from field investigations by
Long et al. (2016) and birth dates predicted by the rolling MCP method
was 18 hours.

Parturition events of mule deer were determined either by 1) monitoring
GPS-collared adult females for localized movement and then searching the
area for neonates where a cluster of GPS locations had formed, 2) using
vaginal implant transmitters (details in Jackson \emph{et al.} (2021)),
or 3) using the rolling MCP inference method (Nicholson \emph{et
al.}2019). For the rolling MCP method, we assigned a parturition event
for deer as the first day a rolling MCP (based on a 24-hour window) was
\textless{}15 hectares or less for a minimum of 120 hours. We validated
the rolling MCP method for 14 deer parturition events determined from
field investigations and found a mean discrepancy of 33 hours.

\textbf{Objective 1: determining whether predator movements indicated
active search for parturient ungulates}

We determined whether predators were actively searching for parturient
female ungulates by assessing whether their actual movements (hereafter
``steps,'' or the Euclidean distance between subsequent GPS relocations)
led to encounters with parturient females more often than hypothetical
steps that they could have taken but did not. To do so, we fit
step-selection functions (Fortin \emph{et al.} 2005) for each carnivore
species to estimate the relative probability of selecting a location on
the landscape, given its previous location and a suite of covariates at
the ending locations of both real and hypothetical (hereafter,
``random'') steps. We excluded data from individuals whose home ranges
did not overlap deer and elk relocations in Starkey Experimental Forest
and Range. The covariate of primary interest was whether the endpoint of
each observed or random step was within a 200-meter proximity of a
parturient female ungulate. By comparing whether the observed steps were
more often within close proximity of a parturient ungulate than were
random steps, we could assess whether predators detected neonates more
often than expected by incidental encounter, which is evidence of active
search behavior. We restricted the analysis to include location data of
each female ungulate in the 30 days after a parturition event was
predicted to occur and fit separate models for deer and elk for each of
the four carnivore species (8 models total). We compared each real step
(coded 1) with 20 random steps (coded 0; Latombe \emph{et al} . 2014)
and fit models using conditional logistic regression. The random
locations were generated by taking random draws from the fitted
distributions of step lengths and turning angles (Gamma and von Mises
distributions, respectively; Avgar \emph{et al.} 2016) constructed from
GPS data for each predator species and projecting the random locations
for each GPS position onto the landscape given the previous location. To
control for the possibility that observed steps landed in close
proximity to an ungulate simply because of the predator's preference for
certain landscape or vegetative features, we included additional
covariates known to influence carnivore movements (Ruprecht \emph{et
al.} 2021b): canopy cover (derived from LEMMA's generalized nearest
neighbor model; Ohmann \emph{et al.} 2011), potential vegetation type (a
factor variable with classes for open forest, closed forest, grassland,
and other), ruggedness (using the vector ruggedness measure, a composite
index of terrain encompassing both slope and aspect; Sappington,
Longshore \& Thompson 2007), the distance to nearest open road (natural
log transformed), and distance to nearest perennial water source
(natural log transformed). All continuous variables were centered to
have a mean of 0 and scaled to have a standard deviation of 1. The
step-selection function took the form\(w(x)\ \sim\ exp(\beta_{1}\times\text{parturient\ deer\ or\ elk\ presence}+\ \beta_{2}\times\text{canopy\ cover}+\ \beta_{3}\times p\text{otential\ vegetation\ type}\ +\ \beta_{4}\times\text{ruggedness}\ +\ \beta_{5}\times ln(\text{distance\ to\ road})\ +\ \beta_{6}\times ln(\text{distance\ to\ perennial\ water\ source})\ +\ \beta_{7}\times ln(\text{step\ length})\ +\ \beta_{8}\times cosine(\text{turning\ angle}))\). Because the
response to neonates can differ by sex of bears (Rayl\emph{et al.}
2015), we fit additional models for male and female bears separately. We
did not fit additional sex-specific models for cougars, coyotes, or
bobcats, however, because we had no evidence \emph{a priori}that
predation of neonates would differ between the sexes for those species.

\textbf{Objective 2: determining whether use of parturition habitat by
searching predators tracked the phenology of the birth pulse}

One strategy for predators to maximize encounters with neonates is to
shift habitat use to areas with a high probability of selection by
parturient female ungulates. To this end, we constructed a resource
selection function (RSF; Manly \emph{et al.} (2007)) using GPS locations
of adult female elk in the 7 days immediately following a parturition
event with landscape and vegetative characteristics hypothesized to
influence location of parturition sites in our area based on previous
research (Johnson \emph{et al.} 2000, Stewart \emph{et al.} 2002, Long,
Rachlow \& Kie 2008). The resource selection function for elk
parturition habitat took the form\(w(x)\ \sim\ exp(\beta_{1}\times\text{canopy\ cover}\ +\ \beta_{2}\times ln(\text{distance\ to\ open\ road})+\ \beta_{3}\times ln(\text{distance\ to\ perennial\ water\ source})\ +\ \beta_{4}\times\text{ruggedness}\ +\ \beta_{5}\times\text{shrub\ cover}\ +\ \beta_{6}\times\text{forb\ cover}\ +\ \beta_{7}\times\text{slope}\ +\ \beta_{8}\times\text{aspect}\ +\ \beta_{9}\times\text{elevation}\ +\ \beta_{10}\times\text{potential\ vegetation\ type})\), where \emph{w}
(\emph{x} ) is the relative probability of selection for adult female
elk during the first 7 days following parturition. Percent shrub and
forb cover variables were derived from LEMMA's generalized nearest
neighbor model (Ohmann \emph{et al.} 2011); slope, aspect, and elevation
were drawn from a digital elevation model; and other covariates are as
described above. We paired each used elk location (coded as 1) with 10
randomly generated locations representing locations available to but not
used by elk (coded as 0) and used a generalized linear model with a
binomial error distribution and logit link to model the relative
probability of selection. Given that our objective was to create a
spatially-explicit map of the study area predicting the areas with a
high probability of selection by parturient ungulates and not make
inference on the specific resources that they selected for, we did not
conduct model selection and instead used the global model for
predictions. Each 30 x 30 m pixel in the resulting predictive map
projected onto the study area represented \emph{w} (\emph{x} ), or the
RSF score for parturition habitat. We then calculated the mean value of
the RSF scores across all GPS locations for each carnivore species that
exhibited active search behavior (determined from the previous analysis)
on a weekly basis from 15 April to 31 to determine whether predators
shifted habitat use toward places likely to be inhabited by ungulate
neonates. We predicted that predator use of habitat used for parturition
by elk would decline later in the season if predators were attempting to
maximize encounters with neonatal elk by shifting habitat use. Weekly
mean RSF scores represented each predator's use of predicted parturition
habitat with higher values indicating higher use of parturition habitat,
where ``use'' is a measure of the investment in a set of resource units
by an animal during a sampling period (Lele \emph{et al.} 2013).

We used the weekly average elk parturition RSF score at carnivore GPS
relocations as the response variable in a generalized linear mixed model
and used Julian week (i.e. the number of weeks elapsing since January 1)
as a predictor to assess how carnivore use of elk parturition habitat
changed throughout the season. We included a random intercept for animal
ID to control for differences in the mean elk parturition RSF score
available within individual predator home ranges. We fit models with
both linear and quadratic effects of Julian week as predictors. We
hypothesized that if a quadratic effect of Julian week on use of
parturition habitat tracked the phenology of the birth pulse, it would
be indicative of an effort of predators to alter habitat use to maximize
encounters with neonates immediately following parturition.
Alternatively, lack of a quadratic relationship between predator use of
parturition habitat and Julian week could indicate the predator does not
spend time in areas where neonates are likely to be immediately
following parturition, or that the predator may actively hunt older,
more mobile neonates or other age classes of prey. We used likelihood
ratio tests to compare whether the quadratic effect of Julian week was
supported over a linear effect.

\textbf{RESULTS}

We identified 45 parturition events for deer (14 determined from field
investigations and 31 determined using the rolling MCP method) and 89
parturition sites for elk (all determined using the rolling MCP method)
between 2016 and 2019 (Figure 2c). We estimated 27 May (range: 10 May to
25 June) as the mean parturition date for elk and 02 June (range: 21 May
to 28 June) as the mean parturition date for deer across all 4 years in
our study.

\textbf{Step-selection functions to infer active search behavior}

Of the four carnivore species, none made movements such that they
encountered parturient mule deer (within a 200-meter proximity) in the
first 30 days post parturition more often than the random movements
generated in the step-selection function (Figure 3a; Figure 4a; Tables
S1--S2) suggesting they were not actively searching for mule deer
neonates. We documented no GPS-collared cougars or bobcats within 200
meters of a GPS-collared mule deer at the time a simultaneous fix was
taken during the 30 days following parturition so models could not be
fit for these species. For elk, only two carnivore species exhibited
movements that positioned them in proximity of elk post-parturition more
often than did hypothetical movements, cougars (\selectlanguage{greek}β\selectlanguage{english}\textsubscript{elk
presence} = 0.94, \emph{P} = 0.001; Figure 3b; Table S3) and bears,
although for bears the result was marginally significant
(\selectlanguage{greek}β\selectlanguage{english}\textsubscript{elk presence} = 0.30, \emph{P} = 0.059; Figure 3b;
Table S3). Sex-specific analysis revealed that male bears were more
likely to encounter elk than expected by chance (\selectlanguage{greek}β\selectlanguage{english}\textsubscript{elk
presence} = 0.56, \emph{P} = 0.004, \emph{N} = 7 bears; Figure 4b; Table
S4) while there was no evidence supporting this effect for female bears
(\selectlanguage{greek}β\selectlanguage{english}\textsubscript{elk presence} = -0.45, \emph{P} = 0.24, \emph{N} = 4
bears; Figure 4b, Table S4). Projecting model predictions onto the
landscape spatially and overlaying GPS locations of post-parturient
female elk in the 30 days post birth further revealed similarities
between areas used by neonatal elk and areas selected for by male bears
and cougars as documented by the high degree of spatial overlap (Figure
5a,c). Female bears, however, generally did not select for areas that
overlapped with elk neonates (Figure 5b), suggesting their space use
decisions were driven more heavily by other resources that were
unrelated to elk.

\textbf{Carnivore use of parturition habitat}

We hypothesized that the use of predicted parturition habitat by
actively-searching predators would track the phenology of the birth
pulse such that they would use areas that maximized encounters with
neonates when they were most available. Of the species concluded to
exhibit active search for neonates (cougars and bears responding to elk
calves), linear mixed-models suggested that only male bears followed the
expected quadratic pattern for use of parturition habitat coincident
with peak parturition date (\selectlanguage{greek}β\selectlanguage{english}\textsubscript{Julian week} =
0.027,\emph{P} = 0.03; \selectlanguage{greek}β\selectlanguage{english}\textsubscript{Julian week}\textsuperscript{2} =
-0.028, \emph{P} = 0.03; Figure 6b) wherein the quadratic terms were
supported over a linear term (likelihood ratio test, \emph{P} = 0.03)
for the effect of Julian week on use of calving habitat. To assess
whether this result could be spuriously driven by bears selecting for
parturition habitat for other reasons such as bottom-up forage
acquisition, we tested whether female bears with similar vegetation
requirements as male bears also responded to parturition habitat but
found no support for a quadratic response (likelihood ratio
test,\emph{P} = 0.62; Figure 6c). For cougars, use of predicted
parturition habitat was also better explained by a linear term for
Julian week (likelihood ratio test \emph{P} = 0.32; Figure 6d).

\textbf{DISCUSSION}

We found that of four carnivore species, only two appeared to actively
search for elk and none searched for mule deer neonates. The fact that
no carnivores encountered parturient mule deer more often than expected
by chance was consistent with our predictions that the young of less
abundant species would not be targeted (Figure 1b); mule deer are at
least 5 times less abundant than elk in this ecosystem (Oregon
Department of Fish and Wildlife, unpublished data). This result suggests
that mule deer fawn mortalities in this study area (Jackson \emph{et
al.} 2021) are likely the result of fortuitous encounters (from the
perspective of the predator) and that risk to mule deer from incidental
predation may thus depend on the amount of overlap between deer and elk
parturition habitat for predators that are primarily searching for elk
calves. Our finding that two of the four carnivore species actively
searched for elk (the more abundant species) partially aligned with our
expectations that a predatory response would be greater toward the more
abundant prey species. We also expected the more generalist carnivores
(bears and coyotes, which are highly omnivorous) would exhibit a more
fluid response to an ephemeral prey source. This hypothesis was
supported for bears but not coyotes. The lack of response of bobcats and
coyotes to both elk and deer may be explained for several reasons.
First, elk calves are large prey items for mesopredators such as coyotes
and bobcats particularly when subject to maternal defense from elk.
While mule deer young are much smaller, their rarity on the landscape
may not have warranted search behavior. Nonetheless, we can speculate
that had mule deer been the more abundant species in this area, we may
have observed some level of search behavior by coyotes and/or bobcats.
Second, bobcats are efficient predators of small prey while coyotes in
this system gain a substantial amount of protein via scavenging
(Ruprecht et al. 2021b), both of which potentially reduce the need to
pursue neonates. Finally, our sample size of collared bobcats was small
(\emph{N} = 6) so results may have been subject to Type II error for
that species.

Our analyses to evaluate whether carnivores' use of elk parturition
habitat tracked the phenology of the birth pulse revealed further
contrasting behaviors among the predators in our study. Use of elk
parturition habitat by male bears was best explained by a model with a
quadratic effect of Julian week, with its maximum aligning almost
perfectly with the peak of the birth pulse (Figure 6b). This result
suggests that male bears exhibited a spatial shift in habitat consistent
with an effort to maximize encounters with elk neonates immediately
following parturition, which is logical given that bears are limited by
a short window in which they can efficiently hunt neonates. This idea is
further supported in that the number of encounters between GPS-collared
bears and parturient elk in the 30 days post-parturition peaked between
7-10 days after an elk gave birth. By contrast, the quadratic effect was
not supported for cougars (Figure 6d). Although previous research has
shown that juvenile elk constitute a large fraction of the diets of
cougars (Clark \emph{et al.} 2014), several aspects of cougar predatory
behavior may explain why cougars did not exhibit a quadratic effect
indicative of searching areas used by neonates. First, because elk
become solitary to give birth before rejoining the herd several weeks
later (Paquet \& Brook 2004), it may be inefficient for cougars to
target solitary mother-young pairs when they would have access to more
individuals by pursuing larger herds of mixed age classes. Such
``nursery herds'' (Paquet \& Brook 2004) would present na\selectlanguage{ngerman}ïve prey such
as yearling elk that may have recently lost maternal guidance, or
vulnerable young of the year after the mother-young pair rejoined the
herd after parturition. The number of encounters between GPS-collared
cougars and parturient elk in the 30 days post birth was greatest around
20 days after an elk gave birth which further supports the idea that
cougars pursued calves only after they had matured for several weeks. We
were initially concerned that the apparent use of parturition habitat by
bears coinciding with the birth pulse could be driven by selection for
other dynamic resources such as green vegetation that was correlated
with elk parturition habitat, causing a spurious result. However, only
male bears exhibited this pattern, and we would expect females to
exhibit the same response to bottom-up resources.

Although we are unaware of previous research on search behavior of
cougars toward ungulate neonates, our work both aligns and contrasts
with patterns described for black bears and coyotes elsewhere. The
density of elk neonates in our study area was closer in magnitude to the
number of caribou calves in the study by Rayl \emph{et al.} (2018) that
determined bears actively searched for neonates than it was to the study
by Bastille-Rousseau \emph{et al.} (2011), in which bears
opportunistically encountered neonates. Our finding that male bears were
much more likely to encounter neonates than were females also aligns
with Rayl \emph{et al.} (2015) who found that male bears were more
likely to visit caribou calving grounds than were females. Further,
several other studies have documented higher predation or meat
consumption by male black bears than females (Boertje \emph{et al.}1988;
Jacoby \emph{et al.} 1999), which should be expected given that previous
research has shown that larger, male bears require more animal-borne
protein to gain weight than do smaller, female bears (Rode, Robbins \&
Shipley 2001). Our results did not suggest that coyotes actively
searched for elk calves which accords with a cause-specific mortality
study of elk calves in this region that found coyote predation to be
minor (Johnson \emph{et al.} 2019). In other ecosystems, however,
coyotes have been implicated as nontrivial sources of mortality for elk
calves (Barber-Meyer, Mech \& White 2008) although there is mounting
evidence that coyote predation on mule deer neonates occurs largely only
when small mammal populations are low (Hamlin \emph{et al.} 1984;
Hurley\emph{et al.} 2011). We unfortunately did not have sufficient data
on occurrence and abundance of alternative prey to assess whether this
occurred in our study.

It is important to view the distinction between active search and
incidental encounter in light of the effects that predator population
dynamics may have on prey. If predators employ active search behavior,
then a reduction in predator density may not yield increased neonate
survival because neonates spared by that individual become targets for
the remaining pool of searching predators (unless prey density is such
that predation is limited by handling time or satiation). But if neonate
predation occurs because of incidental encounters, then a reduction in
predator density benefits a focal prey species by reducing encounter
rates both because each prey is less likely to be incidentally
encountered per unit time and because predators spend time handling
other species. Although population growth rates of ungulates are most
sensitive to survival of adult females, this demographic rate is
consistently high and stable (Gaillard, Festa-Bianchet \& Yoccoz 1998)
and many ungulate populations are instead limited by insufficient
recruitment due to low neonate survival (Raithel, Kauffman \& Pletscher
2007). Thus, knowledge of how different species of carnivores search or
encounter different species of prey will be needed to determine the
extent to which predator control would be an effective strategy for
managing ungulate populations.

A necessary assumption in our study was that predator and adult female
ungulate locations within a 200-meter proximity at the time of
simultaneous GPS recordings constituted an encounter with an ungulate
neonate in the weeks after birth. This assumption was required because
we did not have GPS transmitters on neonates and thus assumed the
location of the adult female was a reasonable proxy for the location of
the neonate. This assumption certainly introduced some amount of data
contamination that may have obscured a stronger signal than what we
observed. Although our dataset was unique in that it included
contemporaneous GPS recordings on four species of carnivores and two
species of ungulates, with fix intervals up to three hours on predator
GPS collars, we are certain to have missed additional encounters.
Another limitation in our study was that we were required to use
inference methods to predict some of the parturition events for deer and
all parturition events for elk which are subject to error in the exact
timing of births. Further, some number of neonates likely died in the
days following birth which our analysis could not consider. These
factors should only have acted to dilute any potential signals in the
data and not cause spurious correlations. Nonetheless, we caution that
our results are conservative and should be interpreted with the
possibility that Type II error may be present. These issues will be
minimized as GPS transmitters become sufficiently lightweight to be
placed on neonates and as battery life improves such that more frequent
GPS readings can be obtained on both predators and prey.

An emerging frontier in animal ecology is understanding if and how
behavior influences population dynamics. Consequently, elucidating how
predatory tactics (e.g. active search vs. incidental encounters) affect
prey populations should feature prominently in future research. Our
results suggest there was a behavioral response by two of the four
carnivores toward elk, but no response by any of the carnivores toward
mule deer. This result combined with previous research suggests that the
foraging tactics by predators in response to a pulsed resource differ by
both predator and prey species, are likely ecosystem-specific, and can
change dynamically through time as the availability of vulnerable
neonates fluctuates.

\textbf{ACKNOWLEDGEMENTS}

We thank R. Long and M. Bianco for data assistance. We are grateful to
the Oregon Department of Fish and Wildlife, the USDA Forest Service
Pacific Northwest Research Station, Oregon State University, and the
Wildlife Restoration Act for funding and/or logistical support. We thank
research technicians and volunteers who assisted with fieldwork.

\textbf{DATA AVAILABILITY STATEMENT}

Data associated with this manuscript can be accessed at the Dryad data
repository.

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\textbf{FIGURES}\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image1/image1}

\end{center}
\end{figure}

\textbf{Figure 1:} Conceptual diagram showing birth pulse phenology and
the profitability of predator search behavior. Panels a) and b) are
representative of species that can only successfully capture neonates
during a limited time period (e.g., bears, coyotes, bobcats), beyond
which neonates mature to the point where they have escaped the majority
of predation. Panel a) represents a population with a high density of
neonates; the period in which the number of neonates available (blue
line) exceeds the critical density is the period when active search is
profitable. Panel b) represents a population with a low density of
neonates that never exceeds the critical density such that actively
searching is never the optimal strategy. Panel c) represents species
that can capture juvenile ungulates throughout their entire first year
of life (and beyond; e.g., cougars), such that it is profitable to
search as soon as the critical density has been exceeded.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image2/image2}

\end{center}
\end{figure}

\textbf{Figure 2:} Study area: a) the general location of study area in
northeast Oregon, USA, is indicated by the black dot. b) GPS telemetry
locations of carnivores (black bears: tan points, bobcats: green points,
cougars: dark blue points and coyotes: light blue points) used for
analysis. c) Starkey Experimental Forest and Range boundary (black
polygon) overlaid on the elk parturition habitat resource selection
function (white areas indicate areas with low probability of selection,
dark blue areas indicate high probability of selection). Tan points
represent elk birth sites.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image3/image3}

\end{center}
\end{figure}

\textbf{Figure 3:} Selection coefficients (exp(\selectlanguage{greek}β\selectlanguage{english}\textsubscript{ungulate
presence})) from step-selection functions assessing whether carnivores
(coyotes, cougars, black bears and bobcats) made movements that placed
them in the proximity of a) mule deer and b) elk more often than
expected by chance in northeastern Oregon, 2016-2019. Dots represent
point estimates for the selection coefficient for ungulate presence and
bars represent 95\% confidence intervals. The gray horizontal line at y
= 1 indicates indifference toward parturient ungulates; values above
this line indicate selection and values below the line indicate
avoidance. Cougars and bobcats did not encounter mule deer often enough
for models to converge.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image4/image4}

\end{center}
\end{figure}

\textbf{Figure 4:} Selection coefficients (exp(\selectlanguage{greek}β\selectlanguage{english}\textsubscript{ungulate
presence})) from step-selection functions assessing whether male and
female black bears made movements that placed them in 200-meter
proximity of parturient elk more often than expected by chance in
northeastern Oregon, 2016-2019. Dots represent point estimates for the
selection coefficient for elk presence and bars represent 95\%
confidence intervals. The gray horizontal line at y = 1 indicates
indifference toward parturient elk; values above this line indicate
selection and values below the line indicate avoidance.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image5/image5}

\end{center}
\end{figure}

\textbf{Figure 5} : Relative probability of selection for a) male black
bears, b) female black bears, and c) cougars in northeastern OR
(2016--2019) predicted from step-selection functions (darker shades of
brown indicating higher relative probability of selection for each
carnivore). In each panel, the GPS locations of telemetered adult female
elk in the 30 days post-parturition (blue points) are overlaid on the
relative probability of selection maps. The elk locations are displayed
identically in each panel but appear darker when they overlap pixels
with higher (i.e., darker shades of) relative probabilities of selection
for carnivores. The maps are presented as a visual aid to portray how
male bears and cougars, but not female bears, select for features of the
landscape that overlap with areas used by post-parturient elk. Maps for
all species can be found in the Supporting Information (Figures
S1--S10).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/image6/image6}

\end{center}
\end{figure}

\textbf{Figure 6:} Elk births and carnivore use of predicted elk
parturition habitat as a function of Julian week in northeastern Oregon,
2016-2019. a) The density of elk births as a function of Julian week.
Bars indicate counts of births per week and the blue curve is a normal
distribution fit to the data. The dashed tan line indicates the mean
birth date. b-d) Predictions from linear mixed models relating the
weekly average resource selection function (RSF) score for parturient
elk at carnivore GPS relocations for male bears (b), female bears (c),
and cougars (d) as a quadratic function of Julian week. The solid blue
lines display the model predictions for carnivore use of elk parturition
habitat and the gray shading represents its 95\% confidence
interval.\emph{P} -values correspond to the outcome of likelihood ratio
tests assessing whether the models containing quadratic terms for Julian
week were supported over models with only a linear term for Julian week.

\selectlanguage{english}
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