Evaluating capture–recapture population and density estimation of tigers in a population with known parameters

Evaluating capture–recapture population and densityestimation of tigers in a population with known parameters

R. K. Sharma1, Y. Jhala1, Q. Qureshi1, J. Vattakaven1, R. Gopal2 & K. Nayak3

1 Wildlife Institute of India, Dehradun, India

2 Project Tiger, Government of India, New Delhi, India

3 Kanha Tiger Reserve, Madhya Pradesh, India

Keywords

1/2 MMDM; bias and precision; camera

density; effective trapping area; home-range

radius; Kanha Tiger Reserve India; sampling

cost; spatial likelihood density estimation.

Correspondence

Yadvendradev Jhala, Wildlife Institute of

India, Dehradun, India. Tel: +91 135

2640112 to 2640115; Fax: +91 135

2640117

Email: [email protected]

Received 29 September 2008; accepted 22

July 2009

doi:10.1111/j.1469-1795.2009.00305.x

Abstract

Conservation strategies for endangered species require accurate and precise

estimates of abundance. Unfortunately, obtaining unbiased estimates can be

difficult due to inappropriate estimator models and study design. We evaluate

population–density estimators for tigers Panthera tigris in Kanha Tiger Reserve,

India, using camera traps in conjunction with telemetry (n=6) in a known

minimum population of 14 tigers. An effort of 462 trap nights over 42 days yielded

44 photographs of 12 adult tigers. Using closed population estimators, the best-fit

model (program CAPTURE) accounted for individual heterogeneity (Mh). The least

biased and precise population estimate (n (SE) [n]) was obtained by the Mh

Jackknife 1 (JK1) [14 (1.89)] in program CARE-2. Tiger density (D (SE) [D]) per

100 km2 was estimated at 13 (2.08) when the effective trapping area was estimated

using the half mean maximum distance moved (1/2 MMDM), 8.1 (2.08), using the

home-range radius, 7.8 (1.59), with the full MMDM and 8.0 (3.0) with the spatial

likelihood method in program DENSITY 4.1. The actual density of collared tigers

(3.27 per 100 km2) was closely estimated by home-range radius at 3.9 (0.76), full

MMDM at 3.48 (0.81) and spatial likelihood at 3.78 (1.54), but overestimated by

1/2 MMDM at 6 (0.81) tigers per 100 km2. Sampling costs (Rs. 450 per camera

day) increased linearly with camera density, while the precision of population

estimates leveled off at 25 cameras per 100 km2. At simulated low tiger densities, a

camera density of 50 per 100 km2 with an effort of 8 trap nights km�2 provided

95% confidence coverage, but estimates lacked precision.

Introduction

The tiger Panthera tigris epitomizes wilderness values and

acts as an umbrella species for the conservation of biodiver-

sity in several forest systems of South Asia. As top preda-

tors, tigers play a vital role in regulating and perpetuating

ecological processes and systems (Terborgh, 1991; Sunquist,

Karanth & Sunquist, 1999). Tigers, being highly adaptable,

exist in a wide range of forest types, and climatic regimes

and subsist on diverse prey (Schaller, 1967; Sunquist et al.,

1999). However, today tigers occupy a mere 7% of their

historic range and in the past decade, tiger-occupied habi-

tats in Asia have declined by 40% (Sanderson et al., 2006;

Dinerstein et al., 2007). Tigers are in a precarious state and

threats to their survival do not seem to be declining despite

international and regional conservation efforts.

Estimating the abundance of a species is essential for

monitoring and evaluating conservation programs. But

population estimation of carnivores is a difficult task owing

to their large ranges, low densities and cryptic nature (Mills,

1996). A mark–recapture framework (Otis et al., 1978) using

camera traps (Chapman, 1927; Champion, 1992; Griffiths &

van Schaik, 1993) has been the scientific method of choice

for estimating tiger abundance (Karanth, 1995; Karanth &

Nichols, 1998). The method relies on identifying photo-

captured tigers individually based on their unique stripe

patterns. Acquiring this information in a capture–recapture

experimental design permits the estimation of population

size. Tiger density is then computed by dividing the esti-

mated population size by the effective trapping area esti-

mated by adding a buffer strip of half the mean maximum

distance moved (1/2 MMDM) by recaptured tigers to the

trapping grid (Karanth, Kumar & Nichols, 2002). Avail-

ability of good mark–recapture estimators implemented in

user-friendly software programs (Otis et al., 1978; White

et al., 1978; White & Burnham, 2000; Chao & Yang, 2003;

Efford, Dawson & Robbins, 2004) has made the method

popular with field ecologists. Large carnivore population

estimates using mark–recapture models are limited by small

sample sizes in comparison with sample sizes possible for

other taxa and those recommended through simulation

studies (White et al., 1982). This limitation probably com-

promises the precision of the population and density esti-

mates as rarely do field estimates have a coefficient of

Animal Conservation 13 (2010) 94–103 c� 2009 The Authors. Journal compilation c� 2009 The Zoological Society of London94

Animal Conservation. Print ISSN 1367-9430

mailto:[email protected]

variation o10% (e.g. see Karanth, 1995; Trolle & Kery,

2003; Karanth et al., 2004; Silver et al., 2004; Soisalo &

Cavalcanti, 2006; Wang & Macdonald, 2009). Despite these

limitations, the mark–recapture approach is most widely

used for estimating the population size of large carnivores as

statistically robust alternative approaches are lacking (Kar-

anth et al., 2003). Few studies have actually evaluated the

appropriateness of mark–recapture models in field situa-

tions for obtaining unbiased estimates of population size

and density of carnivores (Wegge, Pokheral & Jnawali,

2004; Soisalo & Cavalcanti, 2006; Dillon & Kelly, 2007;

Maffei & Noss, 2008). Information on population and

density of endangered carnivores is needed for guiding

conservation investment, management and policy. Over-

estimates can provide a false sense of population well-being

and may compromise conservation objectives through inac-

tion and lack of resource allocation.

We conducted a camera trap capture– recapture study in

conjunction with an ongoing long-term study on tiger

ecology using GPS telemetry in Kanha Tiger Reserve,

central India. The study area was an intensive tourism zone

where tigers have been regularly monitored by mahouts

from elephant back, trackers and through tourist photogra-

phy. Thus, we had a unique opportunity of estimating the

minimum population size of tigers in the study area a priori

with reasonable certainty. Telemetry-based range data were

used to obtain an independent estimate of tiger density.

Herein, we use this information to evaluate the precision

and bias of various capture– recapture population and

density estimation procedures for large carnivores with field

data on tigers that we use as a model dataset.

Methods

Study area

The study was carried out in a part of the Kanha Tiger

Reserve in the state of Madhya Pradesh, Central India.

Kanha Tiger Reserve is a typical geo-physiographical repre-

sentative of the Central Indian Highlands and is located in

the eastern part of the Satpura Range known as the Maikal

Hills at coordinates 221450N and 801450E (Schaller, 1967)

(Fig. 1). Kanha receives an average annual rainfall of

around 1200mm and the temperature ranges from �3 to

Figure 1 Minimum convex polygons defining the camera-trapped area and ranges of six radio-collared tigers Panthera tigris. The map insets show

the location of Kanha Tiger Reserve within the state of Madhya Pradesh, India.

Animal Conservation 13 (2010) 94–103 c� 2009 The Authors. Journal compilation c� 2009 The Zoological Society of London 95

Evaluating capture–recapture population and density estimation of tigersR. K. Sharma et al.

40 1C. Kanha has tropical moist deciduous forest dominated

by sal Shorea robusta and tropical mixed deciduous forest

(Champion & Seth, 1968). It has been recognized as an

important tiger reserve for long-term conservation of tigers

(Wikramanayake et al., 1998; Jhala, Gopal & Qureshi,

2008).

Major prey species were chital Axis axis, sambar Cervus

unicolor, barasingha Cervus duvaucelli branderi, barking

deerMuntiacus muntjak, chousingha Tetracerus quadricorni,

gaur Bos gaurus, langur Semnopithecus entellus and wild pig

Sus scrofa. Carnivores included jackal Canis aureus, sloth

bear Ursus ursinus, wild dog Cuon alpinus, leopard Panthera

pardus and tiger P. tigris.

Field methods

We deployed camera traps in about 60 km2 of tiger habitat

of Kanha Tiger Reserve. Telemetry data from six tigers (two

males and four females) that used the camera trap study area

were used to estimate home-range radius and effective

trapping area.

Determining minimum population size a priori

The study area formed a part of the tourism zone of the

Tiger Reserve. On an average, about 100 tourist vehicles

traversed the study area daily, primarily to see and photo-

graph tigers. Traditionally, each morning, tigers were

tracked within the study area with the assistance of five to

eight elephants and experienced mahouts and trackers for

tourism and management purposes. Tigers in the tourism

zone have thus become habituated to being observed and

followed from vehicles and elephants and are known indivi-

dually by mahouts and nature guides. Researchers using

telemetry (GPS, satellite and VHF) on tigers regularly

located and photographed tigers for monitoring movement

patterns, behavior and demography. Whenever tigers were

located by mahouts, nature guides or researchers, their

locations were communicated to Sharma or Vattakaven by

wireless radio, who later photographed these tigers from

elephant back. Herein, we use this information, along with

photographs taken by tourists, to arrive at the minimum

number of tigers a priori and independently from the camera

trap study. From this exercise, we were reasonably certain

that there were 14 individual tigers (nine females, five males)

and five cubs (o1 year) using the trapping grid. There was a

possibility that the study area was traversed by occasional

transient tigers during the course of the camera trapping

exercise because the study area was surrounded by tiger

habitat. Therefore, we consider the known adult tiger

population of 14 as a minimum population.

Home-range estimation

We used telemetry location data from two male tigers and

four tigresses who occupied the camera trapping grid (Fig.

1) for this paper. The GPS schedule on two GPS collars on

male tigers was programmed to record fixes every 4 h so as

to have independence of location data (White & Garrott,

1990). Location data for tigresses equipped with VHF

transmitters were obtained by homing in on elephant back

and recording coordinates by a hand-held GPS unit at

different times of the day and night. Each tiger had over 70

(71–472) locations that were used for home-range estima-

tion. We computed 95% fixed kernel (Worton, 1989) and

100% minimum convex polygon (MCP) home ranges

(Mohr, 1947) for each of the six tigers using Home-Range

Extension for ArcViewTM (Rodgers & Carr, 1998).

Camera trap survey

We carried out a reconnaissance survey for a period of

1month to identify optimal camera trap locations within the

study area so as to capture as many different individuals and

to obtain as many photo-captures of each individual as

possible. Trap locations were selected based on cues such as

scats, pugmarks, scrapes, rake marks, etc. The survey

yielded 40 potential trap sites, which were then monitored

through track plots to determine their usage by tigers.

Finally, we selected 33 best trap sites for deploying cameras.

Camera placement approached an approximate systematic

coverage of the study area and the average distance between

camera locations was 1.5 km to ensure that there were no

major gaps in the sampled area. The size of theMCP formed

by joining the outermost camera locations was 59.2 km2.

We used 11 TrailmastersTM (TM 1550) active infrared

trail monitoring systems (Goodson Associates Inc., Lenexa,

KS, USA), which use an invisible infrared beam across the

trail between the transmitter and the receiver. The cameras

were placed at a distance of 5m on both sides from the

center of the trail to obtain good-quality full-frame pictures

of tigers. The camera delay was kept at minimum (6 s) to

minimize the chance of missing photo-captures of tigers

traveling in pairs or groups, for example mating pairs or a

mother with cubs. Camera traps were camouflaged to avoid

detection by tigers. No bait or lure was used to attract the

tigers toward the camera stations. Camera traps were

monitored on a daily basis and data were recorded in a

standard format.

We divided the study area into three blocks and set traps

at 11 sites in a block on a daily basis. Cameras were moved

from one block to another every day so that the entire study

area was covered in a 3-day period. Each sampling occasion

combined captures from 3 consecutive days of trapping

covering one ‘pass’ over the entire study area. Cameras were

operated from 17:00 to 09:00 h. There were 14 sampling

occasions spanning 42 days, involving a total effort of 462

trap nights.

Each film roll was assigned a unique ID and a daily log of

data was maintained, enabling us to correctly assign a tiger

photograph to a specific date, time and location. Each tiger

photograph was carefully examined for the position and

shape of stripes on the flanks, limbs, forequarters and tail

(Schaller, 1967; McDougal, 1977; Karanth, 1995; Franklin

et al., 1999) and matched with the known tigers using the

study area.


Evaluating capture–recapture population and density estimation of tigers R. K. Sharma et al.

Analytical methods

Population and density estimation

Individual capture histories for the identified tigers were

constructed using a standard ‘X-matrix format’ (Otis et al.,

1978; Nichols, 1992), where rows represented the capture

histories of each captured individual and columns repre-

sented captures on each occasion. Population closure was

formally tested using program CloseTest (Stanley & Burn-

ham, 1999). We used the model selection procedure built in

program CAPTURE that uses a series of goodness-of-fit tests,

followed by discriminant function analysis to decide be-

tween the null (M0), heterogeneity (Mh), behavior (Mb),

time effects (Mt) and a combination of these models (White

et al., 1978, 1982; Rexstad & Burnham, 1991) for determin-

ing the best-fit model for our data. We used program CARE-2

(Chao & Yang, 2003) to estimate population size as the

program provides a large number of estimators with up-

dated algorithms (Chao, 2001; Chao & Huggins, 2005). The

conventional models of Otis et al. (1978) are based on the

full likelihood parameterization with three types of para-

meters viz. probability of first capture (pi), the probability of

recapture (ci) and population estimate (n). On the other

hand, the Huggins (1991) model estimates population size

and also provides an insight into the capture process by

incorporating covariates in the analysis. In the Huggins

model the likelihood is conditioned only on the number of

animals detected to avoid the difficulty of estimating the

covariates of uncaptured animals. Thus, population size n in

the Huggins model is a derived parameter (Chao &Huggins,

2005). We use tiger gender as a covariate for the Huggins

model in CARE-2. Male and female tigers have different

ranging patterns and this attribute was likely to account for

the variability of capture probabilities. The Huggins model,

through the use of covariates that likely account for varia-

bility in capture probabilities, was presumed to provide

more accurate and precise estimates of population size.

Because we knew the minimum population size of tigers

operating within the camera trapping grid, we used this

unique opportunity to compare the population estimates

and confidence interval coverage obtained by various esti-

mators of the best model and null model M0 for their

precision and bias.

The abundance estimate (n) determined to be most pre-

cise and least biased was then used to compute an estimate

of tiger density [D = n /A (W) ]. We compared the estimates

of densities obtained by different methods of estimating

buffer width with actual tiger density obtained from home-

range data. In this paper, we examine estimates of tiger

density based on (1) the 1/2 MMDM method, in which the

buffer (W) was average of half of the MMDM by recap-

tured tigers (Wilson & Anderson, 1985; Karanth & Nichols,

1998; Karanth et al., 2002); (2) the full MMDM method, in

which the buffer (W) was the average of the MMDM by

recaptured tigers (Parmenter et al., 2003); (3) home-range

radius method, wherein a buffer width (W) equal to the

average of the home-range radius of the radio-collared tigers

was added to the sampled area (Dice, 1938, 1941); (4) a

likelihood-based framework, where density was computed

directly from the spatial capture histories of camera traps

(Borchers & Efford, 2008). The traditional density estima-

tion methods rely on adding an arbitrary boundary strip

around the trap location polygon to determine the effective

trapping area, whereas the spatial likelihood method uses a

two-model approach. The first sub-model simulates the

animal distribution from individual spatial capture histories

by estimating each animal’s range and center of activity

using a Poisson distribution. The second sub-model simu-

lates the capture process, which, in the case of camera traps

(proximity detectors), permits the animal to be detected at a

trap and yet leaves it free to visit other traps. Multiple

detections of several animals are possible at a detector on

any occasion. The probability density functions for detec-

tions of animals based on distance from activity centers are

modeled using hazard rate, half-normal or exponential

detection functions (Efford, Borchers & Byrom, 2008) and

are analogous to distance sampling (Buckland et al.,

2001).This analysis was peformed using software DENSITY

4.1 (Efford, 2007).

The home-range radius for each of the tigers was com-

puted by assuming that the home range approximated a

circle. The average of the home-range radius of six collared

tigers was then used as the buffer width. For this analysis,

we considered the density derived from the home-range

radius approach as the baseline to compare the density

estimates obtained by other methods.

To further compare only the effect of various methods of

computing effective trapping area on tiger density, we

conducted an analysis considering a hypothetical situation,

wherein the six collared tigers constituted the entire popula-

tion. In that case, the combined area covered by the six

collared tigers (95% fixed kernel home range) would be the

effective trapping area for the density computation. Density

estimates for these six radio-collared tigers using various

estimators listed above for estimating effective trapping area

were compared with the actual (home-range-based) density.

We did not include variation associated with population

estimates in this analysis of tiger density.

Effect of camera and tiger density on

population estimates

To understand the effect of camera density on population

estimates, we simulated varying camera densities by ran-

domly dropping camera traps along with their capture data.

Hundred different simulations were performed for each

camera trap density of 8, 17, 25, 34 and 42 camera traps per

100 km2. We computed the cost of sampling at various

camera densities by accounting for cost of equipment, film

and processing, wages of research team and vehicle cost. We

then evaluated the precision of estimates against costs.

Because Kanha had a relatively high density of tigers

(Karanth & Nichols, 1998) in comparison with other tiger-

bearing forests, our results would have little applicability in



low tiger density forests. To determine what camera trap

density would be required to estimate tiger populations that

occur at low densities, we simulated a low tiger density

scenario by dropping the capture histories of all but two

tigers picked at random from the population of camera-

trapped tigers. We estimated the population size of this

simulated two-tiger population using varying camera trap

densities. Hundred simulations were performed for each set

of camera trap density and a different set of two tigers.

Results

Population estimates

A sampling effort of 462 camera trap nights spread over

42 days (14 sampling occasions) yielded 44 photographs of

12 unique individual tigers (eight females and four males).

Three cubs (o1 year) were also captured thrice: once with

the mother and twice without the mother. The number of

unique adult individuals (12) stabilized on the 20th day of

sampling with 20 photo-captures (Fig. 2). Camera traps

could not detect two tigers; one male and a non-breeding

female, which were known to be operating within the

trapping grid.

The program CloseTest (Stanley & Burnham, 1999)

supported the population closure assumption (w2=1.50,

P=0.22). The population estimation study was of a short

duration (42 days) compared with the long life span of tigers

(Sunquist, 1981; Smith, 1993) and we only considered adult

tigers for the purpose of population estimation. The mini-

mum number of adult tigers operating in the study area was

known to be 14 with reasonable certainty. During the course

of the study, no new tiger was observed, nor did any of the

radio-collared tigers disperse from the study area. There-

fore, it would be reasonable to assume that the population

was closed.

The model selection procedure in CAPTURE rated Mh

(model incorporating individual heterogeneity) as the best

fit (rated 1), followed closely by M0, the null model (rated

0.99). The population estimates generated by Mh varied

from 12 to 15 with a coefficient of variation ranging between

5 and 21% (Table 1). Among the Mh estimators, the first-

order Jackknife estimator (Mh JK1) was least biased and

reasonably precise (Table 1). With analysis using gender as a

covariate in CARE-2, AIC criteria listed model M0

(AIC=185.85), closely followed by Huggins model Mh2

(AIC=186.72), as the best-fit models. Tiger gender was not

a significant covariate, although tigresses had a higher

probability of being captured in comparison with male

tigers. Individual capture probabilities of tigers were reason-

ably high, with 0.24 for model M0 and 0.22 using model Mh

(IntJK).

Camera trap density

At low camera densities of 8 cameras per 100 km2 the

population estimates were severely negatively biased (Fig.

3). Population estimates and precision (% CV) stabilized at

a density of 25 cameras per 100 km2 and changed only

marginally as the camera density increased to 51 cameras

per 100 km2 (Fig. 3). The precision of the population

estimates was the lowest (33% CV) at low camera densities

and the highest at a high camera density (14% CV). The costFigure 2 Rate of tiger Panthera tigris photographs and cumulative

number of unique tigers camera trapped in Kanha Tiger Reserve.

Table 1 Population estimates of tigers Panthera tigris using various

estimators of the best-fit model incorporating individual heterogeneity

(Mh) and the null model M0

Model

Population

estimate

Standard

error

% coefficient

of variation

Confidence

interval % bias

Mh2 12 0.59 4.79 12–16 �14.28

Mh (SC1) 13 1.01 7.77 12–18 �7.14

Mh (SC2) 13 0.97 7.46 12–16 �7.14

Mh (JK1) 14 1.89 13.50 12–20 0.0

Mh (JK2) 15 3.13 20.87 13–27 7.14

Mh (IntJK) 14 1.89 13.50 12–72 0.0

M0 (CMLE) 12 0.73 6.08 12–14 �14.28

M0 (UMLE) 12 0.62 5.17 12–12 �14.28

For details on estimators, please refer to Chao & Yang (2003).

Mh2, Huggins heterogeneity model (Huggins, 1991); SC1, sample

coverage 1; SC2, sample coverage 2; JK1, first order Jackknife; JK2,

second order Jackknife; Int JK, interpolated Jackknife; CMLE, condi-

tional maximum likelihood estimator; UMLE, unconditional maximum

likelihood estimator.

Figure 3 Tiger Panthera tigris population estimates obtained by the

first-order Jackknife estimator of model Mh executed in program

CARE-2 with 95% confidence limits plotted against camera trap density

(camera units per 100 km2). The minimum known population of 14

tigers is shown as a reference line.



of operating a camera was computed at 450 Indian rupees

(US$11.25) per camera per day. Gain in precision and

reduction in bias were disproportionably low after a camera

density of 25 per 100km2 as the cost increased linearly with

an increase in the camera density (Fig. 4).

In the case of the simulated population of two tigers (low

tiger density scenario), population estimates were negatively

biased and only 34% of the simulated estimates actually

contained the true population within their 95% confidence

intervals at a low camera density (8 per 100 km2). With high

camera densities of 50 per 100 km2, 100% of the estimates

contained the true population of two tigers within their 95%

confidence interval. However, the precision of the population

estimates was poor even with a high camera density (Fig. 4).

Home-range estimates

The average 100% MCP home range of the six tigers was

41.2 (SE=19.6) km2; the average 95% fixed kernel range was

41.8 (SE=21.97) km2. Male range size [102 (SE=9) km2] was

10 times larger than that of females [10.46 (SE=2.6) km2]

and extended beyond the trapping polygon (Fig. 1).

Tiger densities and effective trapping area

Using population size obtained from Mh JK1, tiger density

estimates were obtained by buffering the camera trap MCP

with (1) 1/2MMDM estimated at 1.59 (SE=0.28) km was 13

(SE=2.08) per 100 km2, (2) full MMDM estimated at 3.19

(SE=0.57) km was 7.8 (SE=1.59) per 100 km2, (3) home-

range radius estimated at 3.05 (SE=0.80) km was 8.1

(SE=2.08) per 100 km2, (4) using a spatial likelihood-based

approach of computing density directly from trapping data

was 8 (SE=3) per 100 km2 (Table 2).

The actual area used by the six radio-collared tigers was

183 km2 (Fig. 1), yielding a density of 3.27 tigers per

100 km2. Density estimates for the six radio-collared tigers

using (1) 1/2 MMDM estimated at 1.53 (SE=0.28) km was 6

(SE=0.81) tigers per 100 km2, (2) full MMDM estimated at

3.06 (SE=0.57) km was 3.48 (SE=0.81) tigers per 100 km2,

(3) home-range radius estimated at 3.05 (SE=0.80) km was

3.49 (SE=0.76) tigers per 100 km2, (4) using the spatial

likelihood-based approach of computing density directly

from trapping data was 3.78 (SE=1.54) tigers per 100 km2

(Table 3).

Discussion and conclusions

Photographic capture of tigers

The overall probability of capturing a tiger present in the

study area (Mtþ1=n) was fairly high (86%). The unique

individuals captured through camera traps (n=12) reached

an asymptote on the 20th day of sampling, suggesting an

adequacy of sampling effort. Initial field work and monitor-

ing of probable camera locations through track plots before

camera deployment greatly enhanced our chances of photo-

capturing tigers. Camera traps failed to capture all the

individuals (minimum known population size of 14) using

the study area even after prolonged sampling after the

asymptote (Fig. 2). This suggests that the total counts even

with intensive sampling by camera traps are difficult to

achieve in natural populations. The rate of obtaining tiger

pictures per day during the initial part of the study [slope

(SE)=1.33 (0.03)] was significantly more than the latter part

of the study [0.78 (0.04), Po0.001], suggesting a trap-

Figure 4 Gain in precision in terms of coefficient of variation of

population estimates when sampling a simulated low and high tiger

Panthera tigris density area along with the cost of sampling with

increasing trapping effort.

Table 2 Estimates of effectively sampled areas obtained by buffering

camera trap polygon by different approaches and resultant density

estimates of tigers Panthera tigris

Density estimation approach

Buffer

width

(km)

Effectively

sampled

area

Density

(tigers

per 100 km2)

1/2 MMDM 1.59 111 12.53�2.09

Full MMDM 3.19 179 7.77�1.58

Home-range radius 3.05 188 7.39�1.99

Spatial likelihood (DENSITY 4.1�) – – 8.0�3.0

�Efford (2007).

MMDM, mean maximum distance moved by recaptured tigers.

Table 3 Estimates of effectively sampled areas obtained by buffering

camera trap area by different approaches and resultant density

estimates of the six radio-collared tiger Panthera tigris population

Density estimation approach

Buffer

width

(km)

Effectively

sampled

area

Density

(tigers per

100 km2)

1/2 MMDM 1.53 108.31 5.53� 0.81

Full MMDM 3.06 172.12 3.48� 0.81

Home-range radius 3.05 171.66 3.49� 0.76

Spatial likelihood (DENSITY 4.1�) – – 3.78� 1.54

Actual density fpopulation

size (6)/total home-range areag182.94 3.27� 0.0

�Efford (2007).

MMDM, mean maximum distance moved by recaptured tigers.



shyness response (Fig. 2). We monitored the pugmark trails

of tigers along camera trap locations everyday and observed

three instances of active trap avoidance in which tigers

circumvented the camera traps to avoid being captured. We

attempted to minimize trap shyness by camouflaging cam-

eras and whenever camera avoidance at a particular trap

location was recorded from track signs, we moved the

camera location by 50–100m to another suitable location.

In our study, cameras were moved daily between blocks;

thus, continued exposure of tigers to cameras at the same

location was minimized. Our data as well as those of Wegge

et al. (2004) suggest that trap shyness in tigers can be a major

concern and therefore fixing cameras permanently at a

location for long durations should be avoided. Although

there were two tigresses with cubs in the study area, cubs of

only one female were photo-captured. This suggests that

camera traps are poor at detecting cubs as young cubs are

confined to a small area and rarely accompany mothers

(Chundawat, 2004).

Population estimation

The disparity in capture probabilities between tigers and

tigresses can be partly attributed to disparity in the exposure

of the genders to traps. Males ranged over large areas,

beyond the boundaries of trapping grid, thus decreasing the

amount of time they spent in the trapping grid and hence

their chance of encountering a camera. Female home ranges,

on the other hand, were largely within the trapping grid,

increasing their chances of encountering a trap. This high-

lights the importance of having a large study area in relation

to the home-range size of tigers to minimize such biases

(White et al., 1982; Maffei & Noss, 2008). Because of high

individual capture probabilities, the model selection proce-

dure of CAPTURE as well as the AIC criteria did not discrimi-

nate much between the null model and the models that

incorporated individual heterogeneity. The Huggins model,

which incorporates covariates, is believed to perform well

under conditions of a small sample size and heterogeneity of

capture probabilities (Chao & Huggins, 2005). In our case,

the population estimates of the Huggins model were precise

but negatively biased. This could be because tiger gender

alone may not have captured the entire heterogeneity in

capture probabilities. Rarely can camera trap studies estimate

the covariates (gender, age and social status) that are likely to

influence individual heterogeneity. Thus, inclusion of relevant

covariates is a difficult task for tiger population estimates.

Heterogeneity models using Jackknife were least biased, had

a confidence interval coverage of the known population and

some estimators were reasonably precise as well (e.g.Mh JK1,

Table 1). Our data suggest that trap shyness, gender biases in

photo-captures and individual heterogeneity can be a major

source of variability in tiger population estimates. Through a

good design, researchers may be able to control for the first

two but individual heterogeneity in natural populations

would still need to be accounted for through appropriate

model selection.

Density estimates

We had home-range data from six tigers, constituting 50%

of the camera trapped population. Besides, the sex ratio of

collared tigers (two male tigers and four tigresses) was fairly

representative of the camera-trapped population sex ratio

that is four male tigers and eight tigresses. Thus, we believe

that we were justified in generalizing their home-range

estimates for the entire population. We also conducted a

separate density estimation considering only the six collared

tigers as the population, thereby eliminating the need for

assumptions and variability associated with population

estimates. Dice (1938) and Stickel (1954) speculated that

the density estimates obtained using the 1/2 MMDM

approach would overestimate actual density. Tiger density

estimates using the MMDM method, home-range radius

and spatial likelihood approach were close to the actual

density. Soisalo & Cavalcanti (2006) obtained similar results

for Jaguars Panthera onca and Dillon & Kelly (2008) for

ocelots Leopardus pardalis.

The best approach in the absence of telemetry-based

home-range data is to use the spatial capture histories of

camera traps in a likelihood-based density estimation frame-

work (Borchers & Efford, 2008; Efford et al., 2008; Royle

et al., 2008). Because the spatial likelihood approach is not

dependent on adding a buffer to the trapping polygon for

estimating the effective trapping area, the resultant esti-

mates are least biased by trap layout and density (Efford,

2004). With our data, the tiger density estimated by this

approach was similar to estimates obtained from the home-

range data (Tables 2 and 3).

Effect of camera trap density, layout anddensity of tigers on population estimates

Simulating a varying camera density scenario suggests that a

minimum of 34 cameras 100 km�2 would be required to

estimate population size with reasonable accuracy and

precision at tiger densities observed within our study site.

As expected, the precision of population estimates increases

with an increase in the density of camera traps (by increasing

recapture rates), albeit only marginally beyond a certain

point, but the cost of operating cameras increases in a linear

fashion. This clearly suggests a tradeoff that a biologist may

have to look for between attaining a desired level of preci-

sion and investment in resources and effort.

In case of a low tiger density (o2 per 100 km2), research-

ers may be able to obtain an estimate of population size with

high camera trap densities. However, these estimates are

likely to lack precision and would have little value for

monitoring population trends.

We recommend a systematic approach of camera place-

ment (Silver et al., 2004), preferably at a density of 425

traps per 100 km2 for medium to high tiger density areas

with a minimum effort of 4 trap nights km�2 and 450

cameras per 100 km2 in areas of low tiger density (c. o2

tigers per 100 km2) with a minimum effort of over 8 trap

nights km�2. We also recommend that the shape of the



trapping grid approaches that of a circle and be sufficiently

large (Garshelis, 2000) to capture the maximum distances

moved by male tigers. A study on ocelots (Maffei & Noss,

2008) suggests that the camera trap area should cover a

minimum of three to four average home ranges. In this study

the trapping area met the size criteria for tigresses but male

tigers had much larger ranges in comparison with our

trapping area (Fig. 1). The above recommendations would

ensure a uniform coverage of the study area and would

provide a fair chance for all the tigers to be photo captured.

Such a design would be specifically useful to photo-capture

sub-adult tigers, which, as an avoidance behavior, use

marginal, non-typical tiger habitat like ridge tops and rarely

venture on well-used prominent trails (Y. Jhala and Q.

Qureshi, pers. obs.). We believe that mark–recapture popu-

lation estimates provide a robust estimate of population size

for most source populations of tigers (high- to medium-

density populations) and should become a regular monitor-

ing tool in most, if not all tiger reserves. Our results would

likely be applicable to other large- and medium-sized carni-

vores so as to provide decision makers and wildlife man-

agers with an accurate and precise assessment of their status.

Acknowledgments

This study was funded by the Project Tiger Directorate,

Government of India, and the Wildlife Institute of India.

We are grateful to the Director and Dean, Wildlife Institute

of India, the Chief Wildlife Warden, Forest Department of

Madhya Pradesh and especially the staff of Kanha Tiger

Reserve for facilitation and permissions. We thank our field

assistants for their sincere efforts.

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Evaluating capture–recapture population and density estimation of tigers in a population with known parameters