The use of photographic rates to estimate densities of tigers and
other cryptic mammals 
Animal Conservation (2001) 4, 75?79  ? 2001 The Zoological Society of London  Printed in the United Kingdom
INTRODUCTION
Since their development in the early 1980s camera
traps have become an important tool for monitoring rare,
cryptic species in a wide range of environments
(Champion, 1992; Griffiths & van Schaik, 1993; Karanth
& Nichols, 1998; Cutler & Swann, 1999). This technique
is used for species that can be individually identified to
assess population size, population turnover rates and
many aspects of species ecology (Karanth & Nichols,
1998) . However, in most camera trapping programmes
individually marked target species represent only a frac-
tion of the total species assemblage (e.g. tiger pho-
tographs represented 5% of the total number of pho-
tographs taken in one study (N. Franklin & R. Tilson,
unpubl. results). A technique that could use photographic
rates of non-identifiable individuals to estimate animal
density would greatly increase the use of these data. In
this paper, we compare the observed relationship
between photographic rates of tigers and their density
with the results of a random walk simulation of a two-
dimensional gas model (Lowen & Dunbar, 1994) in
order to assess the ability of camera trapping pro-
grammes to estimate animal densities and detect animals
at low densities.
All correspondence to: Dr C. Carbone, Institute of Zoology,
Zoological Society of London, Regent?s Park, London, NW1 4RY.
Tel: 020 7449 6634; Fax: 020 7483 2237;
E-mail: chris.carbone@ioz.ac.uk.
*Current address: Large Animal Research Group, Department of
Zoology, University of Cambridge, Downing Street, Cambridge.
C. Carbone1, S. Christie2, K. Conforti3, T. Coulson1*, N. Franklin4,5, J. R. Ginsberg6, M. Griffiths7, J. Holden8, 
K. Kawanishi9, M. Kinnaird6, R. Laidlaw6, A. Lynam6, D. W. Macdonald10, D. Martyr8, C. McDougal11, 
L. Nath10, T. O?Brien6, J. Seidensticker3, D. J. L. Smith12, M. Sunquist9, R. Tilson5 and W. N. Wan Shahruddin6
Authorship in alphabetical order
1Institute of Zoology, Zoological Society of London, Regent?s Park, London NW1 4RY, UK
2London Zoo, Zoological Society of London, Regent?s Park, London NW1 4RY, UK
3Smithsonian National Zoological Park, Washington DC 2008, USA
4Department of Biology, University of York, York YO1 5DD, UK
5Sumatran Tiger Project, PO Box 190, Metro, Lampung 34101, Sumatra, Indonesia
6Wildlife Conservation Society, International Programs, 2300 Southern Boulevard, Bronx, New York, NY 10460?1099, USA
7Leuser Development Programme, Jl. Dr. Mansyur 68, Medan 20154, Sumatra, Indonesia
8Fauna and Flora International, Great Eastern House, Tenison Road, Cambridge CB1 2DT, UK
9Department of Wildlife Ecology and Conservation, University of Florida, PO Box 110430, Gainesville, FL, USA
10Wildlife Conservation Research Unit, Department of Zoology, University of Oxford, South Parks Road, Oxford, OX1 3PS, UK
11Tiger Tops, PO Box 242, Kathmandu, Nepal
12Dept of Fisheries and Wildlife, 200 Hodson Hall, 1980 Folwell Avenue, St Paul, MN 55108, USA
(Received 4 May 2000; accepted 14 September 2000)
Abstract
The monitoring and management of species depends on reliable population estimates, and this can be
both difficult and very costly for cryptic large vertebrates that live in forested habitats. Recently devel-
oped camera trapping techniques have already been shown to be an effective means of making
mark?recapture estimates of individually identifiable animals (e.g. tigers). Camera traps also provide
a new method for surveying animal abundance. Through computer simulations, and an analysis of
the rates of camera trap capture from 19 studies of tigers across the species? range, we show that the
number of camera days/tiger photograph correlates with independent estimates of tiger density. This
statistic does not rely on individual identity and is particularly useful for estimating the population
density of species that are not individually identifiable. Finally, we used the comparison between
observed trapping rates and the computer simulations to estimate the minimum effort required to
determine that tigers, or other species, do not exist in an area, a measure that is critical for conser-
vation planning.
METHODS
Camera trapping data
Camera trapping data were obtained from studies in
India, Nepal, Thailand, Malaysia and Indonesia
(Table 1). Photographic rate was defined as the number
of camera days (24 h) per tiger (? 1 year old) photo-
graph summed across all camera traps in the study
(see Table 1). Tiger density (expressed as the number of
tigers/100 km2) was estimated from the number of indi-
vidually identified tigers photographed divided by the
estimated sampling area of the study.
Previous studies have used a more robust measure of
population size based on a mark?recapture method
(Karanth & Nichols, 1998). These estimates were not
available for most of the studies used in this analysis.
However, in five studies, where both mark?recapture and
total number identified estimates were available, these
were strongly correlated (see e.g. Table 3 in Karanth &
Nichols, 1998). In addition, tigers were typically pho-
tographed five times over the course of the study and it
seems reasonable to assume therefore that most of the
population had been identified. We feel justified, there-
fore, in using estimates based on the total number iden-
tified for all of the 19 studies. In 15 studies, sampling
area was estimated as the area covered by the traps plus
an additional boundary layer estimated from tiger move-
ment distance (see Table 1). In the remaining four stud-
ies, information on the movement patterns of tigers and
park boundaries was used to estimate sample area.
Excluding these four studies did not significantly alter
the results (see below).
Random walk simulation
The observed relationship between photographic rates
and density was compared with the relationship obtained
from a random walk simulation. We did not expect a
simple random walk model to represent the complexi-
ties of tiger ranging patterns, but we used the model to
interpret the observed data more generally. The simula-
tions were based on a circular field of 10 000 km2 and
76 C. CARBONE ET AL.
Table 1. Data obtained from 19 studies, based in five countries
Location Country Source Total Total no. Total no. Sampling Tiger Number
camera photos tigers area density of
days (? 1 yr) (km2) (no./ days/tiger 
(24 h) 100km2) photo
Kanha India U. Karanth pers. comm. 937.11 87 26 2822 9.22 10.8
Kaziranga India U. Karanth pers. comm. 644.21 80 22 1672 13.17 8.1
Nagarahole India U. Karanth pers. comm. 1092.31 76 25 243.42 10.27 14.4
Pench India U. Karanth pers. comm. 919.61 42 5 121.62 4.11 21.9
Bandhavgarh, India India L. Nath (unpubl. data) 357.21 106 15 1053 14.29 3.4
Way Kambas Indonesia N. Franklin & R. Tilson 5030 126 18 3502 5.14 39.9
(annual average) (unpubl. data)
Gunung Leuser Indonesia Griffiths (1994) 2686 45 10 5503 1.82 59.7
Bukit Barisan Selatan Indonesia T. O?Brian & M. Kinnaird 4064 19 9 8362 1.08 213.9
(unpubl. data)
Kerinchi Seblat Indonesia D. Martyr & J. Holden 5316 623 16 8003 2.00 85.7
(unpubl. data)
Chitwan (1996?97) Nepal C. McDougal et al. 5611 120 25.5 1613 15.84 4.7
(unpubl. data)
Halabala Wildlife Thailand A. Lynam (unpubl. data) 999 92 2 166.72 1.20 111.0
Sanctuary, Narathiwat 
Province
Queen Sirikit Reserve Thailand A. Lynam (unpubl. data) 683 172 3 166.72 1.80 40.2
Forest, Yala Province
Phu Khieo Wildlife Thailand A. Lynam (unpubl. data) 989 32 1 86.22 1.16 329.7
Sanctuary, Chaiyaphum 
Province
Khao Yai National  Thailand A. Lynam (unpubl. data) 647 22 1 83.32 1.20 323.5
Park, Nakhon 
Ratchasima Province
Temenggor Forest Malaysia R. Laidlaw & Wan 812 82 2 86.22 2.32 101.5
Reserve, Perak Shahruddin (unpubl. data)
Bintang Hijau Forest Malaysia R. Laidlaw & Wan 776 72 2 202.02 0.99 110.9
Reserve, Perak Shahruddin (unpubl. data)
Gunung Tebu Forest Malaysia R. Laidlaw & Wan 807 12 1 188.72 0.53 67.3
Reserve, Terngganu9 Shahruddin (unpubl. data)
Ulu Temaing Forest Malaysia R. Laidlaw & Wan 563 15 2 210.52 0.95 37.5
Reserve, Kelantan9 Shahruddin (unpubl. data)
Taman Negara Malaysia K. Kawanishi & M. 18291 6 4 338.22 1.18 304.8
Sunquist (unpubl. data)
Mean tiger densities represent the total number of tigers (? 1 year) identified over the course of the study, divided by the sampling area. Camera photographic rate was cal-
culated from the total number of days the cameras were active divided by the total number of tiger photographs obtained (discarding duplicates of the same individual dur-
ing one visit to the trap).
1Camera traps were run on a 14?16h/day schedule and these rates were converted to a 24h/day rate.
2Sampling area was based on the area covered by the camera traps, which included a boundary layer estimated using half of the mean maximum distance travelled by tigers
within the study area (see Karanth & Nichols, 1998).
3Sampling area based on tiger home ranges and park boundaries.
simulated tiger density was varied within this field from
0.5/100 km2 to 100/100 km2. One camera trap was
located in the centre. Each day the tigers moved to a
new position by randomly assigning a straight-line dis-
tance with a mean of either 3, 10 or 40 km (standard
deviation of 1.0). The lower two values of daily distance
were chosen to approximate observed total daily dis-
tances estimated for tigers (including deviations from the
straight line distance). For example, in the Russian Far
East one male and one female averaged a total distance
of 9.6 km and 7 km/day, respectively, between kills
(Yudakov & Nikolaev, 1987). This represents an upper
limit because tigers typically remain near each kill for a
day or more. In India, males and females moved on aver-
age 4.2 and 1.4 km/day (estimated straight line distance,
Chundawat, Gogate & Johnsingh, 1999). The simula-
tions based on a daily distance of 40 km provided cap-
ture rates that were close to the observed capture rates
(see below) and these were carried out to illustrate the
sensitivity of the model predictions to travel distance.
The simulated daily distance was varied according to a
normal distribution with a standard deviation of 1.0 and
negative values converted to zeros. Tiger movements
were restricted to the area of the field and positions that
fell outside this area were re-selected. When the tiger?s
start or end positions, or the line of travel between posi-
tions, fell within the radius of detection (4 m) of the cam-
era trap, a photograph was recorded. These photos were
summed over 1000 days for each density and daily
range. We also examined the proportion (number out of
100 runs) of camera trapping programmes (1000 cam-
era trap days each) that were successful at obtaining one
or more photographs at low simulated animal densities.
Comparing observed data and simulated data
Nineteen values were randomly selected from each set
of simulated data (3, 10 and 40 km moved/day). The
slopes and intercepts between the observed and simu-
lated data were compared (y = trap days/photograph,
x = number of tigers/100 km2). This was done in a gen-
eral linear model with a normal error structure with sim-
ulation/observation fitted as a factor. A significant
interaction term between the effects of density (contin-
uous variable) and the simulation/observation factor
would highlight a significance difference between
slopes. There was no significant difference between
slopes and we dropped the simulation/observation fac-
tor from the final model (see Results, below).
RESULTS
Across 19 field studies, there was a significant relation-
ship between photographic rates of tigers (number of
camera days/tiger photograph) and tiger density
(tigers/100 km2); y = 140.33 x?1.116; F(1,17) = 47.43; r2 =
0.72.1; P < 0.001; (Fig. 1(a)). Removing the four stud-
ies that used park boundaries to estimate sampling area
did not alter this result substantially; y = 133.89 x?0.971;
F(1,13) = 21.12; r2 = 0.61.9; P < 0.002; (Fig. 1(a)). The
slope and form of the function estimated from the
observed results was very similar to the relationship
achieved from a random walk simulation (daily distance
= 3 km, power curve regression, y = 2866.4x?0.957; r2 =
0.81; daily distance = 10 km, power curve regression,
y = 703.1x?0.938; r2 = 0.96) (Fig. 1(b)). These relation-
ships differ significantly in intercept but not in slope;
F(4,71) = 1.43, P = 0.242. Dropping the simulation/obser-
vation factor from the model we got: F(3,74) = 117.77, P
< 0.001. This suggested that photographic rates are asso-
ciated with tiger densities in a way that reflects a ran-
dom process, but that the observed photographic rates
were much higher than expected from the random walk
model at equivalent densities. Two factors may be con-
tributing to the differences between the model and the
observed relationships. Firstly, tigers may use only a
fraction of the total area inside their home range (e.g.
Miquelle et al., 1999); and/or tigers move much greater
distances than we assume. A mean daily distance of 40
km was needed to produce photographic rates similar to
the observed rates (y = 146.8x?1.03; r2 = 0.96) (Fig. 1(b))
and this represents an unrealistically high long term
average travel distance for this species. It seems rea-
sonable to assume therefore, that the differences between
the predicted and observed photographic rates reflect the
fact that camera traps are placed in areas where tigers
and other large mammals are known to occur.
We used the ratio of the regression constants in the
predicted and observed equations (predicted/observed)
to provide a correction factor between the simulated and
observed capture rates (i.e. 2886.4/143.9 = 19.9 and
703.1/143.9 = 4.9 (average of 12.4) for 3 km and 10 km,
respectively). With these correction factors, we could
use the model simulation to interpret the performance of
camera trapping programmes at very low ?animal? den-
sities. Our random walk model predicted that pro-
grammes running for 1000 camera days had a 95%
chance of obtaining at least one photograph at simulated
animal densities of between roughly two and five indi-
viduals/100 km2, assuming even use of the habitat
(Fig. 2). If we applied the same correction factors esti-
mated above for the two sets of simulations (19.9 for 3
km and 4.5 for 10 km) this would correspond to tiger
densities of between 0.38 and 0.71/100 km2. If we
increased the trapping effort to 10 000 trap days, we pre-
dicted that tiger presence could be determined with the
same confidence level down to a density of
0.05/100 km2.
DISCUSSION
Overall there is a good correlation between the photo-
graphic rate measured in terms of days per tiger photo-
graph and tiger density. The relationship holds despite
variations in methodology and terrain among field sites,
indicating that estimates of average photographic rates
of unknown individuals may provide a robust measure
of tiger densities. The fact that the observed relationship
scales similarly to the simple random walk model
suggests that, on average, tiger movements are evenly
77Photographic rates and mammal densities
distributed over a fraction of the total home range area.
This is not surprising. We know that although the camera
location on a large scale may be chosen to meet specific
statistical objectives, on a local scale sites are chosen in
order to maximize encounter rates (Karanth, 1999). This
is done by placing cameras in locations close to tiger
markings or on trails, roads and ridges that represent
routes of travel for many species.
Because the statistic used does not rely on individual
identity, the method can, in principle, be used on a wide
range of species. For studies on tigers, camera traps are
typically distributed over an area of between 150 and
350 km2 (Table 1) and the cameras may be several km
apart. Based on our results and the camera distributions
used for tigers, we expect that this technique would be
most effective for species that are relatively wide rang-
ing, (?1 km/day), with a minimum animal density of 
two or more per 100 km2 (Fig. 1(a)) and which are soli-
tary or found in very small groups. Many large forest
dwelling mammals meet such conditions. In addition,
many of these species will be found at far higher den-
sities than the tiger densities used in this study and this
should lead to a reduction in the variation in the photo-
graphic rate index. Given that only a small fraction of
the species photographed by camera traps are individu-
ally identifiable, this technique could greatly increase the
use of camera trap data for estimating large mammal
abundance. However, the effective use of this technique
will depend on our ability to obtain independent esti-
mates of animal density at representative sites in com-
bination with camera-trapping data in order to calibrate
the photographic rates (e.g. T. O?Brien & M. Kinnaird,
unpubl. data).
Systematic sampling of tiger populations through the
use of mark?recapture will usually give a more accurate
estimate of tiger population number. This method 
also allows a measurement error to be estimated for a
particular site and can be used in areas with both high
and low densities of animals (K. U. Karanth, pers com;
78 C. CARBONE ET AL.
Fig. 1. (a) The number of camera days/tiger photograph plot-
ted against estimated tiger density (see Methods for details).
Each point represents the mean tiger density and photographic
rates outlined in Table 1. The top two lines represent the
regression lines for the simulated data illustrated in Fig. 1(b)
(3 km, top continuous line; 10 km, bottom dashed line). The
bottom line is the regression line for the camera trap data (this
regression line is also plotted with the 40 km per day (open
diamonds) simulated data in Fig. 1(b). Simulated capture rates
for animal densities of 0.5?100/km2 assuming a mean daily
distance of 3 km (filled diamonds), 10 km (grey diamonds)
and 40 km (open diamonds). The simulations based on a daily
distance of 40 km were made to provide capture rates that
were near the observed rates. Each point represents the means
from 1000 camera trapping days. The slopes of the simulated
data do not differ significantly from the observed relationship
(see Fig. 1(a) and see the text for details).
Fig. 2. The % of simulated camera trapping programmes
(number out of 100 runs, 1000 camera days each) that obtained
at least one photograph against animal density (N/100 km2)
assuming a daily travel distance of 3 km (grey line) and 10 km
(black line). The vertical arrows represent the approximate
density at which there is a 95% chance of obtaining one pho-
tograph. The mean number of days per photograph at these
densities is 391.8 and 246.3 days (for daily travel distances of
3 km and 10 km respectively). The corresponding tiger densi-
ties based on the ratio of the simulated and observed capture
rates would be approximately 0.4 and 0.7 tigers/100 km2 (see
text for details). 
Karanth & Nichols, 1998). Thus, we would recommend
that, where possible, scientists design sampling proto-
cols that use mark?recapture methods to estimate ani-
mal population densities. The method described in this
paper is clearly appropriate for rapid assessments, and
is critical in developing methods to estimate the density
of animals other than tigers which cannot be individu-
ally identified from their markings.
Finally, by comparing observed trapping rates with
the results of our computer simulations, we were able to
calculate the sampling effort required to determine
whether tigers were present in an area. Our analysis sug-
gested that camera trapping programmes (running for
1000 or more camera days) may be successful in esti-
mating presence or absence of tigers in densely forested
habitats at very low densities (0.4 to 0.7 tigers/100 km2).
By increasing the trapping effort to 10 000 trap days we
predict that tiger presence could be detected down to a
density of 0.05 tigers/100 km2.
This research has important implications for the con-
servation of tigers and other large carnivores. The tiger
is a habitat generalist ranging across 14 countries. Like
many large carnivores, its distribution and population
viability is linked with the distribution and abundance
of large prey (Carbone et al., 1999; Karanth & Stith,
1999). The amount of potential habitat that is actually
occupied by tigers is unknown, and nearly all potential
and occupied tiger habitat, including protected areas, is
undergoing substantial change (Dinerstain et al., 1997).
With the procedures we describe here we have, for the
first time, a rapid, quantifiable, non-invasive means to
assess both tiger and prey numbers and identify land-
scape patterns and conditions that determine the distri-
bution of viable tiger populations.
Acknowledgements
We thank Ullas Karanth, Jim Nichols and Georgina
Mace for comments on earlier drafts of the manuscript.
Funding sources for the 19 tiger studies included the
Save The Tiger Fund, Esso UK plc, the Tiger
Foundation, the Zoological Society of London, the
Wildlife Conservation Society, Disney Wildlife
Conservation Fund, University of Florida, WWF-Japan,
WWF-UK, WWF-Netherlands, SFWS, Care for the Rare
program of Justerini & Brooks Ltd. and the International
Trust for Nature Conservation.
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