Improving the random encounter model method to estimate carnivore densities using data generated by conventional camera-trap design

Abstract

The random encounter model, a method for estimating animal density using camera traps without the need for individual recognition, has been developed over the past decade. A key assumption of this model is that cameras are placed randomly in relation to animal movements, requiring that cameras are not set only at sites thought to have high animal traffic. The aim of this study was to define a correction factor that allows the random encounter model to be applied in photo-trapping surveys in which cameras are placed along tracks to maximize capture probability. Our hypothesis was that applying such a correction factor would compensate for the different rates at which lynxes use tracks and the surrounding area, and should thus improve the estimates obtained with the random encounter model. We tested this using data from a well-known Iberian lynx Lynx pardinus population. Firstly, we estimated Iberian lynx densities using a traditional camera-trapping design followed by spatially explicit capture-recapture analyses. We estimated the differential use rate for tracks vs the surrounding area using data from a lynx equipped with a GPS collar, and subsequently calculated the correction factor. As expected, the random encounter model overestimated densities by %. However, the application of the correction factor improved the estimate and reduced the error to %. Although there are limitations to the application of the correction factor, the corrected random encounter model shows potential for density estimation of species for which individual identification is not possible.

Full text

Improving the random encounter model method
to estimate carnivore densities using data generated
by conventional camera-trap design
GERMÁN GARROTE,RAMÓN PÉREZ DE AYALA,ANTÓN ÁLVAREZ,JOSÉ M. MARTÍN
MANUEL RUIZ,SANTIAGO DE LILLO and M IGUEL A. SIMÓN
Abstract The random encounter model, a method for esti-
mating animal density using camera traps without the need
for individual recognition, has been developed over the past
decade. A key assumption of this model is that cameras are
placed randomly in relation to animal movements, requir-
ing that cameras are not set only at sites thought to have
high animal traffic. The aim of this study was to define
a correction factor that allows the random encounter
model to be applied in photo-trapping surveys in which
cameras are placed along tracks to maximize capture prob-
ability. Our hypothesis was that applying such a correction
factor would compensate for the different rates at which
lynxes use tracks and the surrounding area, and should
thus improve the estimates obtained with the random
encounter model. We tested this using data from a well-
known Iberian lynx Lynx pardinus population. Firstly, we
estimated Iberian lynx densities using a traditional camera-
trapping design followed by spatially explicit capture–
recapture analyses. We estimated the differential use rate
for tracks vs the surrounding area using data from a lynx
equipped with a GPS collar, and subsequently calculated
the correction factor. As expected, the random encounter
model overestimated densities by %. However, the ap-
plication of the correction factor improved the estimate and
reduced the error to %. Although there are limitations to
the application of the correction factor, the corrected
random encounter model shows potential for density
estimation of species for which individual identification is
not possible.
Keywords Camera traps, capture–recapture, carnivores,
correction factor, density estimation, Iberian lynx, Lynx
pardinus, random encounter model
Introduction
Methods that accurately estimate animal abundances or
densities can greatly enhance the ability to monitor
and manage populations (Garrote et al., ; Zero et al.,
). Camera traps are highly efficient in detecting elusive
mammals such as carnivores (Cutler & Swann, ) and
over the last decade they have been used widely for estimat-
ing population sizes of secretive but individually recogniz-
able animals (Foster & Harmsen, ). Population sizes of
the tiger Panthera tigris (Karanth & Nichols, ), jaguar
Panthera onca (Boron et al., ) and Iberian lynx Lynx
pardinus (Garrote et al., ) have been estimated success-
fully using capture–recapture analyses of camera-trapping
data. However, this method is of limited use for species
that do not have markings that allow for the identification
and enumeration of individuals (Villette et al., ).
As an alternative to capture–recapture analysis, photo-
graphic capture rates (photo captures per unit time) can
be used as a density index for species that cannot be indi-
vidually identified (Carbone et al., ). Nevertheless the
use of camera-trapping rates as an index of abundance has
been debated widely (Carbone et al., ; Jennelle et al.,
; Karanth et al., ;O’Brien et al., ; Harmsen
et al., ; Rovero et al., ). Although under certain cir-
cumstances camera-trap encounter indices may give accu-
rate estimates of relative abundance (O’Brien et al., ),
criticisms have noted that indices derived from camera-trap
data vary between species, habitats, seasons and/or camera
placements (Larrucea et al., ; Harmsen et al., ;
Cusack, et al., a,b; Mann et al., ). However,
Rowcliffe et al. () have developed a method for estimat-
ing animal density using camera traps without individual
recognition. This method is based on modelling random
encounters between animals and cameras and takes into
account variables affecting the trapping rate. The probability
that a camera detects an animal depends on the speed of the
animal (distance travelled in a given time), the exposure
time, the detection area of the camera and the number of an-
imals present. The random encounter model method has
been tested on only a few occasions against known densities
derived by other methods (Rovero & Marshall, ; Zero
et al., ; Anile et al., ; Cusack et al., a,b). Three
studies have tested the effectiveness of the random
encounter model as a method for estimating carnivore
GERMÁN GARROTE (Corresponding author, orcid.org/0000-0002-6974-4513),
JOSÉ M. MARTÍN,MANUEL RUIZ and SANTIAGO DE LILLO Agencia de Medio
Ambiente y Agua de Andalucía, c/ Johan Gutenberg s/n, Isla de la Cartuja,
41092 Seville, Spain. E-mail gergarrote@gmail.com
RAMÓN PÉREZ DE AYALA World Wildlife Fund–Spain, Madrid, Spain
ANTÓN ÁLVAREZ Instituto de Biología de la Conservación, Madrid, Spain
MIGUEL A. SIMÓN Consejería de Medio Ambiente de la Junta de Andalucía,
Jaén, Spain
Received  June . Revision requested August .
Accepted  December . First published online  December .
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use,
distribution, and reproduction in any medium, provided the original work is properly cited.
Oryx
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https://doi.org/10.1017/S0030605318001618 Published online by Cambridge University Press

populations (wildcat Felis silvestris, Anile et al., ; lion
Panthera leo, Cusack et al., a,b; European pine marten
Martes martes, Balestrieri et al., ). Overall, these studies
concluded that the random encounter model is a promising
method for obtaining density estimates and has the potential
to be applied widely, although further field tests for different
species and habitats are still needed.
A key assumption of the model is that cameras are placed
randomly in relation to animal movements, sampling parts of
the landscape in proportion to their coverage in the study
area, which means that they should not be placed to either
inflate or deflate encounter rates (Rowcliffe et al., ).
Therefore, to avoid inflated encounter rates and exaggerated
estimates, the random encounter model requires that cameras
are not set only at sites thought to have high animal traffic
(e.g. tracks, underpasses or water sources; Rowcliffe et al.,
). Because of this requirement, rare species such as carni-
vores may be detected too infrequently for density estimates
to be calculated (Rowcliffe et al., ). Many carnivore spe-
cies are more likely to be detected along tracks than with
random camera placements (Larrucea et al., ; Harmsen
et al., ;Blake&Mosquera,; Di Bitetti et al., ;
Cusack et al., a,b). Even with camera traps set along
roads, carnivore species have low detection rates because of
their naturally low densities, large home ranges and secretive
habits (Trolle & Kéry, ;O’Connell & Nichols, ). The
random arrangement of cameras in relation to animal move-
ments thus requiresa much greater sampling effort to achieve
detection rates that can be used to generate reliable estimates.
The aim of this study was to define a correction factor
that enables the random encounter model method to be ap-
plied to traditional photo-trapping surveys of carnivores,
with cameras placed on tracks to maximize capture prob-
ability. Our hypothesis was that if the differential use rate
between tracks and the rest of the area is known, then it is
possible to calculate a correction factor for expected devia-
tions from random encounter model density estimates that
are caused by the violation of the method’s key assumption.
We tested this hypothesis using data from a well-known
Iberian lynx population, a species with fur patterns that
allow identification of individual animals (Garrote et al.,
). Firstly, we estimated Iberian lynx densities using
spatially explicit capture–recapture. We then estimated the
differential use rate for tracks vs surrounding area using
GPS collar data, and calculated a correction factor. Finally,
we compared the density estimates from the original ran-
dom encounter model with those derived from the adjusted
model, to evaluate the usefulness of the correction factor.
Study area
We conducted our study on a private estate in the Sierra de
Andújar Natural Park, which lies within the known range of
the Sierra Morena Iberian lynx population in south-eastern
Spain (Simón et al., ;Fig. ).Theareaismanagedforbig
game hunting and has high densities of red deer Cervus
elaphus andwildboarSus scrofa. Altitudes range between
 and , m, and the vegetation consists primarily of well-
preserved Mediterranean forests dominated by oaks Quercus
ilex,Quercus faginea and Quercus suber, and scrublands with
Quercus coccifera,Pistacia lentiscus,Arbutus unedo,Phillyrea
angustifolia and Myrtus communis.
Methods
The estate collaborates with the long-term (. years)
Iberian lynx conservation programme, which uses intensive
camera trapping throughout the year to closely monitor
individuals within the population (Gil-Sánchez et al.,
). Data from continuously operating camera traps in
the estate showed that  Iberian lynxes occupied the
study area during the study period.
The camera-trap survey was carried out during Sep-
tember–October  and followed traditional protocols
used in Iberian lynx monitoring (Gil-Sánchez et al., )
that are designed to generate population estimates using
capture–recapture analysis (Garrote et al., ). We placed
the cameras on –m wide tracks that are built for use by
cars moving around the hunting estates. Cameras were po-
sitioned in trees or on poles c.  cm above ground level and
.m from the opposite side of the track. We discarded
records of animals detected beyond this .-m limit to fix
the detection radius required for the random encounter
model analysis. We used nine Moultrie M- camera traps
(PRADCO, Birmingham, USA) with a mean spacing of
. ±SE . km. Cameras operated continuously and the
delay period between photographs was set at  s. Every 
days we checked all cameras to ensure they were working
correctly and to download any photographs. No cameras
malfunctioned and therefore there were no gaps in the data.
We considered the density derived from spatially explicit
capture–recapture analysis as the baseline for comparison
with the density estimates obtained using the random
encounter model. Spatially explicit capture–recapture uses
two distinct submodels within its workflow to compute
densities (D). One submodel simulates an animal’s distribu-
tion from the capture history to give the individual’s activity
centre as an output, whereas the second simulates the cap-
ture process on the basis of the radial distance between the
estimated centre of activity and the traps (Efford et al.,
). Input data is in two files, one containing the name
and geographical coordinates of the detectors (cameras)
and another containing the capture histories (i.e. season,
animal identification, the occasion and the detector). We
set the trap detector type for the camera-trapping analysis
as proximity (allowing for multiple detections of the same
individual during the same event; Efford et al., ), the
distribution model as Poisson (assuming homogeneous
100 G. Garrote et al.
Oryx
, 2021, 55(1), 99–104 ©The Author(s), 2019. Published by Cambridge University Press on behalf of Fauna & Flora International doi:10.1017/S0030605318001618
https://doi.org/10.1017/S0030605318001618 Published online by Cambridge University Press

distribution of home range centres in the study; Borchers &
Efford, ), and the detection function as half-normal
(the capture probabilities decrease linearly with the distance
of the camera station from the centre of the individual’s
home range; Efford et al., ).
Following Jůnek et al. () we employed two models:
the null model, in which detection is affected only by the
use of space, and the -class finite mixture model, which al-
lows for the modelling of variation in detection probability
amongst individuals. We ranked candidate models using
the Akaike information criterion corrected for small samples
sizes (AICc). This analysis was performed using Density
.(Efford & Fewster, ).
Random encounter model parameterization
To convert camera-trapping rates into lynx density, we used
the equation:
D=y
t
p
vr(2+
u
)
following Rowcliffe et al. (), where yis the number of
independent photographic events, tthe total camera survey
effort, vthe average speed of animal movement, and rand
θthe radius and angle of the camera trap detection zone,
respectively.
We measured the arc θof the cameras through trials in
which we placed a scale with -cm divisions that could be
read in photographs at a distance of .m from the camera.
We activated the camera by walking in front of it and then
measured the width of the photograph with the scale. We
used trigonometry to infer the angle of the width of the
photograph and the distance from the scale. We found
that the camera radius was .m, i.e. the other side of the
track, thus reducing the possibility of an error associated
with variation in the radius. We assumed the mean speed
of movement of the Iberian lynx to be ±SE . km/day,
following Palomares et al. ().
We computed the overall variance in the random
encounter model density estimates using bootstrapping,
which incorporated the variance associated with the en-
counter rate (estimated by re-sampling camera locations
with , replicas; Rowcliffe et al., ; Cusack et al.,
a,b) and the standard errors associated with the esti-
mation of the speed parameter. Camera-related parameters
(Rowcliffe et al., ) were assumed to have no variance
(Zero et al., ).
Correction factor
The correction factor represents the lynxes’preference for
or avoidance of roads and is calculated as the ratio of road
availability to road use in the study area (Fig. ). The propor-
tional availability of roads was defined by the surface area
occupied by roads divided by the total size of the study
area. To estimate the surface area occupied by roads we
added a buffer of . m either side of the lines represent-
ing roads, resulting in a total width of .m (equal to the
camera-trap detection radius). The total size of the study
area, or effective trapping area, was defined as the minimum
convex polygon around camera-trap stations with an added
buffer strip of the mean maximum distance moved by
recaptured lynx (Parmenter et al., ). To estimate the
lynxes’use of roads, we used data from the only lynx in
the study area equipped with a GPS collar, which gives a
position signal every hours and has an activity sensor.
FIG. 1 (a) Location of the study
area in southern Spain, design
of the camera-trap grid, and
locations obtained from GPS
collar data for one Iberian lynx
Lynx pardinus. (b) Detail of
on-road and off-road Iberian
lynx localities.
Improving the random encounter model 101
Oryx
, 2021, 55(1), 99–104 ©The Author(s), 2019. Published by Cambridge University Press on behalf of Fauna & Flora International doi:10.1017/S0030605318001618
https://doi.org/10.1017/S0030605318001618 Published online by Cambridge University Press

We used GPS data from the same months as the camera
survey, but from the year following the camera-trapping
surveys (September–October ). We only used locations
recorded while the animal was active because the animal
has to be moving to be photo-trapped. With these data,
we determined and quantified the on-road and off-road
localizations. The proportional use of roads by lynxes
was defined as the number of on-road localizations out of
all localizations. We conducted all spatial analyses with
the geographical information system QGIS . (QGIS
Development Team, ). We calculated the correction
factor CF using the following equation:
CF =road availability
road use =
road surface
total surface
on-road localizations
total localizations
This factor corrects the random encounter model results
(REM) and gives the corrected random encounter model
result (REMc) as:
REMc =REM ×CF
We used bootstrapping to assign measures of accuracy to
the correction factor (re-sampling of the on-road and off-
road locations with replacements) and then calculated the
overall standard deviation and % confidence intervals for
corrected random encounter model estimates, as described
above. We carried out all analyses in R..(R Development
Core Team, ). As with the random encounter model
estimates, we generated two corrected random encounter
model estimates.
Results
Camera traps accumulated  trap days over a period of
 days and generated  Iberian lynx detections, resulting
in a total trapping rate of . captures/ trap days. We
identified all  lynxes previously known to inhabit the
area;  trap days ( days) were needed to capture all of
them. The mean maximum distance moved was , ±SE
 m, which implies a total size of the study area of , ha.
Spatially explicit capture–recapture surveys The null model
(AICc = .;ΔAIC = ;parameters) performed better
than the -class finite mixture model (AICc = .;
ΔAIC = .;parameters) and was used for the spatially
explicit capture–recapture analysis. The population density
estimates calculated using this model were . ±SE .
individuals/ ha (Table ). Movement parameter σwas
. ±SE . m.
Random encounter model The mean trapping rate in the
dataset for the camera traps was . ±SE . detections/
 trap days, resulting in a population density estimate of
. ±SE . individuals/ ha based on the random
encounter model.
Random encounter model with correction factor The total
road surface area was .ha out of a total area of
,.ha, which corresponds to a road availability of .%.
We recorded  GPS localizations for lynx on the move, of
which  were along roads; lynx road use was thus .%.
Consequently the correction factor value was . ±SE .
and the estimated % confidence interval was .–..
After applying the correction factor to the random encounter
model estimates, we obtained a density of . ±SE .
individuals/ ha (Table ). The random encounter model
without the correction factor overestimates the lynx density
by %. The corrected random encounter model greatly
improves the estimate as it only differs by % from the estimate
calculated using the spatially explicit capture–recapture null
model.
Discussion
Density estimates calculated with a random encounter
model, using data from conventional camera-trapping sur-
veys in which cameras are placed along tracks, resulted in
an overestimate of lynx density in our study area. This was
expected because the sampling design did not fulfil the key
assumption that cameras should be placed randomly in rela-
tion to animal movements (Rowcliffe et al., ). Our results
suggest that the application of a correction factor to the
random encounter model based on lynx road use greatly im-
proves the estimates. In addition, it allows us to use data from
conventional survey designs in which cameras are positioned
specifically to increase the capture probability; thus, the re-
quired sampling effort is less than in the standard random
encounter model methodology with random camera place-
ment. The random encounter model requires that cameras
should be deployed for as long as is necessary to obtain a
minimum of  photographs but preferably at least 
(Rowcliffe et al., ). In Rovero et al. () there is a
personal communication from Rowcliffe that suggests the
minimum number of photographs should be at least .
There are numerous studies of on-road vs off-road capture
rates that provide an indication of the sampling effort
needed to reach this number of captures. For instance, Di
Bitetti et al. () and Blake & Mosquera ()have
determined the on-road and off-road encounter rates for
TABLE 1 Density estimates (D) for a population of  Iberian lynxes
Lynx pardinus, obtained using different methodologies.
Method D±SE (95% CI)
Spatially explicit capture–recapture 0.31 ±0.13 (0.13–0.68)
Random encounter model 1.43 ±0.34 (0.42–3.74)
Corrected random encounter model 0.36 ±0.21 (0.10–0.94)
102 G. Garrote et al.
Oryx
, 2021, 55(1), 99–104 ©The Author(s), 2019. Published by Cambridge University Press on behalf of Fauna & Flora International doi:10.1017/S0030605318001618
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several mammal species. For the ocelot Leopardus pardalis
(similar in size to the Iberian lynx), capture rates are .–
. captures/ trap days off-road vs .–. captures/
 trap days on-road. These capture rates imply that
,–, trapping days off-road and – trapping
days on-road are required to obtain at least  captures.
The effort required off-road is thus – times greater than
on-road to achieve the same number of captures.
However, there are variations between carnivore species
in the detection probability along tracks vs random camera
placements. Although detection probability is greater along
roads and main tracks for medium-sized and large carni-
vores (e.g. jaguars and ocelots), detection probabilities for
small carnivores (e.g. Cape grey mongoose Galerella pulver-
ulenta and common genet Genetta genetta) tend to be the
same or greater with random camera placements (Wearn
et al., ; Di Bitetti et al., ; Mann et al., ).
Photo capture rates are influenced by habitat structure
and type, as well as by season (Larrucea et al., ;
Harmsen et al., ; Cusack et al., a,b; Mann et al.,
). For example, tracks in dense vegetation possess a
greater capacity for funnelling animals past a camera than
tracks in open areas where animals have more room to
wander off-track (Harmsen et al., ). Reproduction sta-
tus (in those species where it is seasonal) may also influence
the capture rate as it determines the movement range and
thus the capture probability (Nichols et al., ). Male
and female road use could also be different (Conde et al.,
) and individual differences may also occur. In our case
the correction factor was calculated using data from a single
male Iberian lynx. The inclusion of more individuals of both
sexes will improve the correction factor and thus the estimates
obtained. However, the use of GPS collars on a sufficient
number of individuals as a means of establishing a correction
factor for different species will often be logistically and eco-
nomically unviable. Thus, it would be advisable to examine
the possibility of establishing the correction factor for un-
marked species using on-road/off-road camera trap surveys.
Additionally, the identification of correction factors for differ-
ent species could make it possible to retrospectively estimate
abundance using previously collected camera-trap data.
Although the use of roads is not as pronounced in herbi-
vores as it is in carnivores, it has been observed in species such
as the South American tapir Tapirus terrestris (Di Bitetti et al.,
), Kirk’s dik-dik Madoqua kirkii and the hippopotamus
Hippopotamus amphibius (Cusack et al., a,b). The esti-
mates of herbivore densities established using a random en-
counter model (Zero et al., ; Caravaggi et al., )donot
take into account the possibility that species prefer to move
along roads, which could affect results. It is thus important
to carry out detailed studies of on-road vs off-road use by
species for which individuals cannot be identified, to establish
whether or not a correction factor needs to be applied when
estimating population densities.
The application of the proposed correction factor to
the random encounter model using conventional capture–
recapture camera-trap methodology improves the accuracy
and precision of lynx density estimates. The use of con-
ventional camera-trap design data vs random-design data
allows population estimates to be performed over shorter
study periods, thereby reducing project costs (White, ;
Garrote et al., ). Even though further studies (e.g. on
habitat influence and intersexual variation) are needed to
allow the correction factor to be used in other areas or spe-
cies, the corrected random encounter model shows potential
for estimating the density of species for which individual
identification is not possible.
Acknowledgements The study was supported by LIFE Project
10NAT/ES/570 (Recovery of the historical distribution of the
Iberian lynx (Lynx pardinus) in Spain and Portugal). We thank
Pedro Monterroso and Sonia Illanas for their collaboration.
Author contributions Study conception and design: GG; data
collection: GG, JMS, MR, SdL; data analysis: GG, RPdA, AA, MAS;
writing: all authors.
Conflict of interest None.
Ethical standards This research abided by the Oryx guide-
lines on ethical standards. All necessary permits were obtained
from Consejería de Medio Ambiente y Ordenación del Territorio
(Andalusian government).
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