Density estimation of sympatric carnivores using spatially explicit capture recapture methods and standard trapping grid

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1 Ecological Applications, 21(8), 2011, pp Ó 2011 by the Ecological Society of America Density estimation of sympatric carnivores using spatially explicit capture recapture methods and standard trapping grid TIMOTHY G. O BRIEN 1,3 AND MARGARET F. KINNAIRD 2 1 Wildlife Conservation Society, 2300 Southern Boulevard, Bronx, New York USA 2 Mpala Research Centre, P.O. Box 555, Nanyuki Kenya Abstract. Population density is an important state variable in ecology and monitoring of wildlife populations. In the study of large carnivores, traditional density estimation methods have relied on camera trapping to collect capture recapture data using sampling designs suited to a single target species and ad hoc methods to calculate the effective trapping area. We describe an application of spatially explicit capture recapture analysis to estimate density for four sympatric carnivore species using a standard spatial sampling grid, camera trap sampling, and maximum-likelihood estimation methods. We used camera traps deployed in four adjacent, sequential camera arrays to construct capture histories for leopard, aardwolf, spotted hyena, and striped hyena in an African savanna/scrub ecosystem. We considered two methods of constructing trapping histories: (1) a simultaneous layout in which all cameras are deployed and active for 21 trapping intervals of 24 h each; and (2) an incomplete layout in which cameras are considered deployed for 84 sampling intervals, but with only a fraction of traps active for a given sampling interval. We estimated density and confidence or profile likelihood intervals for each species using a mean maximum distance moved method and maximum-likelihood estimation procedures with model averaging. Maximum-likelihood densities ranged from 4.93/100 km 2 for spotted hyena to 12.03/100 km 2 for leopard. Estimates did not differ between simultaneous and incomplete trap layouts. Our approach demonstrates the utility and cost effectiveness of using maximum-likelihood density estimation methods in studies of sympatric species that are individually recognizable. Key words: aardwolf; Crocuta crocuta; DENSITY 4.4; Hyena hyena; leopard; maximum-likelihood density estimation; Panthera pardus; Proteles cristata; spotted hyena; striped hyena. INTRODUCTION Over the past 15 years, efforts to estimate abundance and density of striped and spotted cats often have relied on camera trapping and use of capture recapture analyses based on sampling designs tailored to photographing individual species in order to maximize the detection probability for that species (Karanth 1995, Karanth and Nichols 1998, 2010, Silver et al. 2004). Camera traps are passive detectors with automatic cameras attached to heat motion sensors that trigger a photograph when warm-bodied animals pass through the sensor beams. Camera traps stamp each photograph with a time and date so each photograph can be assigned to a sampling period. Paired camera traps at a sampling point photograph each side of an animal and allows unambiguous identification of stripe and spot patterns necessary for individual identification. Normally, sampling designs space camera points far enough apart to include a sufficient number of individuals of the target species, but close enough such that no individual within Manuscript received 1 December 2010; revised 12 May 2011; accepted 24 May 2011; final version received 25 June Corresponding Editor: J. J. Barber. 3 Present address: Mpala Research Centre, P.O. Box 555, Nanyuki Kenya. tobrien@wcs.org 2908 the trapping area has a zero probability of capture. Sampling typically entails moving cameras after a specified period of trapping to increase the number of trapping points (Karanth and Nichols 2002, 2010). For example, one might trap 100 points in four blocks of 25 points, each for a 10-day period, and each 24-hour period considered a sampling interval. The data are then treated as 100 trapping points sampled over 10 intervals. Under this scenario, an animal photographed in the first sampling block on day 7 and 9, and in the second sampling block on day 2 of trapping (actually day 12 of the study) would have a capture history of [ ]. Such an approach does not reflect the actual temporal capture history of individuals and may result in the loss of useful information and precision when an animal is photographed on the same sampling interval in different sampling blocks (e.g., day 2 in block 1 and day 12 in block 2; Efford et al. 2009b, Royle et al. 2009a, b). The design similarly restricts capture within a sampling block to one per individual per interval, precluding the real possibility of an animal being photographed at two or more points in a single sampling interval and again, resulting in the loss of potentially useful information. Recently, a new method of describing capture histories has been developed that corrects these shortcomings: the

2 December 2011 DENSITY ESTIMATION OF CARNIVORES 2909 incomplete trap layout (Borchers and Efford 2008, Royle et al. 2009b). Technically, capture recapture analysis estimates a population size, ˆN, that represents the population available for capture (N c ). This may not be an interesting quantity compared to the actual population size or density. Density estimation based on capture recapture abundance estimates has been an ad hoc process in which the effective trapping area (ETA) or Aˆc is estimated by calculating a convex polygon defined by the trapping grid and adding a buffer strip (Wilson and Anderson 1985) to the polygon. There are several ways to calculate buffer strips (Wilson and Anderson 1985, Parmenter et al. 2003, Soisalo and Cavalcanti 2006) and resulting ETA estimates vary by method, yielding different density estimates for the same abundance estimate (O Brien 2011). These methods also fail to ensure the spatial closure for a population, which is more difficult to achieve reliably than temporal closure in a typical abundance estimation approach (Royle et al. 2009a). Recently, inference-based procedures for estimating density using maximum-likelihood methods (Borchers and Efford 2008, Efford et al. 2009a) and Bayesian methods (Royle and Young 2008, Royle et al. 2009a, b) have become available that make use of the spatial distribution of captures. Both approaches use hierarchical models to model the detection process and the spatial distribution of animal home range centers. The maximum-likelihood method (Borchers and Efford 2008) assumes that the probability that an animal is caught in a camera trap at a given distance, d, from its home range center follows a two-parameter spatial detection function g(d) with parameters g 0, the detection probability when d ¼ 0, and a spatial scale r, a measure relating to home range width. The detection function usually is a monotonic decreasing function, such as a half-normal or negative exponential function. If a hazard function is specified (Buckland et al. 2001), an additional shape parameter, z, is required. Range centers are unknown but assumed to be Poisson-distributed with density D. Detection probability is therefore a function of distances and other covariates, as in line transect sampling (Buckland et al. 2001), relaxing the spacing requirements for trap placement in a typical capture recapture study. The density is calculated as ^D ¼ n/a, where n is the number of unique animals detected during the survey, and a is effective sampling area (ESA). ESA is defined as the size of an area in which the expected value of n is the same as the actual value of n for the survey when all animals within the area are detected and no animals outside the area are detected. The new methods allow for individuals that visit more than one camera point during a single trapping interval, and allow multiple individuals to visit a single camera point during one trapping interval. These methods also allow the efficient design of multispecies studies using camera traps. Estimating the density of secretive, often nocturnal, carnivores is an important part of wildlife conservation efforts, especially in ecosystems undergoing rapid change due to habitat conversion and population growth. In this paper, we used spatially explicit capture recapture analysis (SECR) to estimate the densities of sympatric, individually identifiable African carnivores using a single standardized camera trap spatial design. We compare SECR density estimates and ad hoc estimates, and evaluate two methods of treating capture histories. Study area Mpala Ranch is a 200-km 2 cattle ranch and wildlife conservancy in Laikipia County in northern Kenya ( N and E). Topographically, Mpala Ranch consists of rolling hills, an uplifted plateau, granitic inselbergs, and is bordered by rivers along more than half of its boundary. Annual rainfall averages 594 mm (years ) in the south and 430 mm (years ) in the north, with rains typically occurring during April May, August, and October November. Droughts are sporadic, but increasing in frequency (Franz 2007). The landscape is covered by bushland dominated by Acacia mellifera, A. etbaica, A. brevispica, and Grewia tenax, and by A. drepanolobium open woodland. Since the early 1900s, most of Laikipia has been owned by private and group ranches. Laikipia is one of the few areas in Kenya where wildlife persist without the benefit of government-supervised protected areas (Georgiadis et al. 2007). Cattle, sheep, and camels are stocked at intermediate densities (;13 livestock units/km 2 ) on Mpala Ranch, and are managed using traditional pastoral herding methods. Mpala hosts a diverse wildlife community including 24 carnivore species. Tolerance of carnivores in Laikipia Country varies by ranch management and owner, and by carnivore species of concern. Lethal predator control is widely practiced in the district (Woodroffe and Frank 2005), but.50% of Mpala s borders are shared with ranches that tolerate predators. METHODS We surveyed leopard (Panthera pardus; see Plate 1), cheetah (Acinonyx jubatus), African lion (Panthera leo), serval (Leptailurus serval), caracal (Caracal caracal), aardwolf (Proteles cristata), striped hyena (Hyena hyena), spotted hyena (Crocuta crocuta), and African wild dog (Lycaon pictus) on Mpala Ranch using Deercam film camera traps (Non-Typical, Park Falls, Wisconsin, USA) and standard camera trapping methods. We divided the ranch into sample units of 2 km 2, located the centroid of each unit using ArcView 3.2, and designated these points as potential trap points. Actual trap points were located at ecologically optimal sites within 50 m radius of the center point, typically on a road or active game trail. Once a point was located, we recorded the UTM coordinates using GPS. Two camera

3 2910 TIMOTHY G. O BRIEN AND MARGARET F. KINNAIRD Ecological Applications Vol. 21, No. 8 traps were mounted on posts approximately 6 10 m apart at each trap point, to photograph both sides of carnivores passing between the cameras. No lures or baits were used to attract carnivores, though this type of design does not preclude the use of lures. The sampling took place sequentially in three blocks of 25 points, and one block of 22 points. Each point was active for 21 sampling days between 8 January and 12 April Camera traps were checked on day 5, day 10, and day 15, and films and batteries were changed as needed. Each photograph was stamped with a time and date that facilitates assigning photographic events to sampling intervals. All carnivore photographs were independently assessed by two people. We then developed regular and spatial capture histories for each individual in a species. Regular capture histories for each individual consisted of a series of 1 s representing a capture during a sampling interval and 0 s indicating no capture. The vector [ ], for instance, indicates that an individual was captured on days 2 and 7 of a 10-day sampling period. Capture histories for all individuals were then compiled into a matrix of capture histories with one line of the matrix per individual history. A spatial capture history for an individual takes the form of a matrix in which the each capture is a vector that identifies the individual, the day of the sampling interval, and the location of the trap. These individual matrices were then joined into a large detection matrix with each detection of each individual georeferenced to a trap location. We calculated ad hoc and maximum-likelihood density estimates based on a standard treatment of data (Karanth and Nichols 2002, 2010) in which day 1 in each sampling block was considered the first sampling interval, and the entire sampling effort added to 21 days. We refer to this as a simultaneous trap layout. We then considered a second design that treated the four blocks of 21-day samples as a continuous 84-day sample, but with most trapping points unavailable during a given sampling interval. In this incomplete trap layout (Borchers and Efford 2008), trapping points were scored 1 if operational and 0 if not. Thus, any capture history is composed of a combination of structural and sampling zeroes that are accounted for in the models (Royle et al. 2009b). We calculated traditional ad hoc density estimates using closed population abundance estimates adjusted by ETA. To calculate abundance, we chose the Jackknife estimator (M h ; Burnham and Overton 1978) and the two-class finite mixture model (Pledger 2000), which allow for individual variation in capture probabilities, following the recommendation of Karanth and Nichols (1998). Due to small sample sizes and low encounter rates, we did not consider more complex heterogeneity models. To estimate ETA and variance, we used the full mean maximum distance moved method (MMDM; Parmenter et al. 2003, O Brien 2011) for each species. We estimated density as ^D ¼ ˆN/ETA and variance in ^D density using the delta method (Wilson and Anderson 1985). To develop maximum-likelihood density estimates for each species, we fit a homogeneous Poisson density by maximizing the full likelihood using the software package DENSITY 4.4 (Efford 2009). For numerical integration, we evaluated the function at 2304 points evenly distributed in an area extending m beyond the trapping grid (area ¼ km 2, point spacing ¼ km). We tested half-normal (HN), negative exponential (NE), and hazard (HZ) detection functions. For each detection function, we considered three models: (1) All individuals share the same detection function [g 0 (.)r(.)], (2) individual heterogeneity in detection for the estimation of g 0 [g 0 (h 2 )r(.)], and (3) a response to first capture for the estimation of g 0 and g 0 0 [g 0 (b)r(.)]. We evaluated each model using the simultaneous and incomplete trap layouts. For model selection for each species, we used minimum AIC criteria (Burnham and Anderson 2002), as well as visual inspection of the estimated parameters and standard errors for evidence of overparameterization and model nonidentifiability. We looked for three kinds of suspicious parameters. First, we eliminated hazard models with unreasonably large estimates of the shape parameter z, or its standard error (SE(z)). We believed unreasonably large estimates of z and SE(z) were indicative of extrinsic redundancy due to sparse data sets (Giminez et al. 2004). Second, we eliminated g 0 (h 2 )r(.) models that assigned all members to the first or second group (w ¼ 0 or 1). Third, we eliminated g 0 (b)r(.) models in which the profile likelihood intervals (PLI) for g 0 (b) included 0. For model sets with AIC weights.0.2, we used model averaging (Burnham and Anderson 2002) to calculate the final parameter estimates. All densities are expressed as the number of individuals per 100 km 2. RESULTS The use of a standard sampling grid appeared to work well for multispecies sampling. We successfully photographed 16 carnivore species, but we restricted our analysis to those species whose individuals were (1) recognizable as individuals (10 species), (2) capture events of individuals in a species could be considered independent events (8 species), and (3) sample sizes were large enough to permit estimation of abundance (5 species) and density (4 species). This limited the analysis to cheetah, leopard, aardwolf, striped hyena, and spotted hyena. We captured 3 cheetahs on 4 occasions, 18 individual aardwolves on 30 occasions, 22 leopards on 38 occasions, 24 spotted hyenas on 47 occasions, and 26 striped hyenas on 69 occasions (Table 1). Leopards moved an average of 2022 m between recaptures (Table 1, Fig. 1a), aardwolves moved 1645 m between recaptures (Table 1, Fig. 1b), spotted hyenas moved 4071 m (Table 1, Fig. 1c), and striped hyenas moved 3800 m (Table 1, Fig. 1d). Although the number of cheetahs captured was small for reliable estimates, we

4 December 2011 DENSITY ESTIMATION OF CARNIVORES 2911 Number of captures, number of individuals captured [M(t þ 1)], number of individuals in each category of recapture, and mean and standard deviation of the mean maximum distance moved between recaptures for five carnivores at the Mpala Ranch, Kenya. TABLE 1. Number of recaptures Maximum distance moved (m) Species Captures M(t þ 1) Mean SD Leopard Aardwolf Spotted hyena Striped hyena Cheetah calculated an estimate of abundance and an ad hoc density estimate using the size of the study area as the ETA (Table 2). We had insufficient movement between camera trap points to develop spatial maximumlikelihood density estimates for cheetahs. Ad hoc density estimation Our estimates of ˆp based on M h models indicate that detection probabilities are low ( ˆp, 0.1) for most species (Table 2). Despite this, the jackknife estimator and twoclass finite mixture model produced similar abundance and density estimates for each species. The two-class finite mixture model was less robust to small detection probabilities and produced very wide profile likelihood intervals whenever detection probabilities fell below Density estimates based on the MMDM method ranged from 2.46 for cheetahs to 8.43 for leopards (Table 2). ETA estimates ranged from km 2 for cheetahs to km 2 for spotted hyenas. Because density estimates were similar, we restricted further comparisons between ad hoc density estimates and maximum-likelihood density estimates to the jackknife estimator. Maximum-likelihood density estimation Model selection tended to favor the simplest models, g 0 (.)r(.), most likely due to the small number of individuals in each data set. All models that considered individual heterogeneity g 0 (h 2 )r(.) placed all individuals in a single group (w ¼ 1 or 0). All models that considered behavioral response to first capture, g 0 (b)r(.), included 0 in the profile likelihood of g 0 (b). These models were, therefore, dropped from further considerations. Model selection results from the simultaneous and incomplete FIG. 1. Map of Mpala Ranch, Kenya, and road system with locations of individual detections for (a) leopard, (b) aardwolf, (c) spotted hyena, and (d) striped hyena on Mpala Ranch between 8 January and 12 April Heavy black horizontal lines separate the sampling blocks. Squares indicate trap locations, solid circles indicate the individuals detected at a trap, and straight lines indicate movements between traps by individuals.

5 2912 TIMOTHY G. O BRIEN AND MARGARET F. KINNAIRD Ecological Applications Vol. 21, No. 8 Estimated trapping area (ETA), detection probability ( ˆp), abundance ( ˆN), and 95% confidence intervals for jackknife estimator (95% profile likelihood interval [PLI] for two-class finite mixture estimator), and density estimates (D MMDM expressed as individuals/100km 2 6 SE) for five carnivore species using traditional capture recapture individual heterogeneity models and mean maximum distance moved (MMDM) as an hoc density estimation method. TABLE 2. Species ETA Jackknife Two-class finite mixture ˆp ˆN 95% CI D MMDM ˆp ˆN 95% PLI D MMDM Leopard Aardwolf Spotted hyena Striped hyena Cheetah trap layout did not differ, most likely because there were no conflicting captures where an individual was captured on the same trapping interval at different points in different blocks. Both data treatments resulted in similar model selection, model weights, and density estimates for a species. Density estimates using the simultaneous trap layout were slightly lower (1.9% on average) than estimates using the incomplete trap layout (Fig. 2). In each case, the models based on a simultaneous trap layout resulted in detection curves characterized by slightly higher estimates of g(0) and slightly lower estimates of r. Because of the similar results, we report on the model selection results (Table 3) and density estimates (Table 4) for the more realistic incomplete trap layout only. AIC model selection for leopards with an incomplete trap layout (Table 3) indicated strongest support for the negative exponential model NEg 0 (.)r(.) (weight ¼ ), but considerable support for the alternative models HNg 0 (.)r(.) (weight ¼ ) and HZg 0 (.)r(.) (weight ¼ ). All models gave similar estimates of density and profile likelihood intervals (PLI; Fig. 2). The model averaged density estimate was (95% PLI ¼ ; Table 4). Maximum-likelihood density estimate for leopards was higher than the ad hoc estimates based on MMDM (12.03 vs. 8.43) in part because the estimated sampling area (ESA ¼ km 2 ) was much smaller than the estimated trapping area (ETA ¼ km 2 ). AIC model selection for the aardwolf strongly favored the HZg 0 (.)r(.) model (weight ¼ 0.995; Table 3) over all other models with a density estimate of (95% PLI ¼ ; Table 4). The NEg 0 (.)r(.) produced a similar density estimate (^D NE ¼ ; Fig. 2), but was poorly supported. The ESA was km 2 and substantially smaller than the ETA, leading to a maximum-likelihood estimate for aardwolves higher than the ad hoc density estimate. The spotted hyena model selection strongly supported ahzg 0 (.)r(.) model (weight ¼ ; Table 3), there was some support for model NEg 0 (.)r(.) (weight ¼ 0.263) but little support for the HNg 0 (.)r(.). Density estimates for the HZ and NE models varied considerably (^D HZ ¼ vs. ^D NE ¼ ; Fig. 2). FIG. 2. Density estimates 6 95% profile likelihood intervals for leopard, aardwolf, spotted hyena, and striped hyena using halfnormal (HN), negative exponential (NE), and hazard (HZ) detection functions with an incomplete (circles) and simultaneous (squares) trap layout.

6 December 2011 DENSITY ESTIMATION OF CARNIVORES 2913 Model selection results for density estimation for four carnivore species using an 84-day incomplete trap layout. TABLE 3. Species Model Log-likelihood No. parameters AIC DAIC Model likelihood AIC weight Leopard NEg 0 (.)r(.) HNg 0 (.)r(.) HZg 0 (.)r(.) Aardwolf HZg 0 (.)r(.) NEg 0 (.)r(.) HNg 0 (.)r(.) Spotted hyena HZg 0 (.)r(.) NEg 0 (.)r(.) HNg 0 (.)r(.) Striped hyena HNg 0 (.)r(.) NEg 0 (.)r(.) Notes: Abbreviations are: HN, half-normal detection function; HZ, hazard detection function; and NE, negative exponential detection function. Additionally, g 0 is the detection probability when the distance between the trap and an animal s home range center is 0, and r is a spatial scale relating to a species home range width. The model averaged density estimate was 4.93 (95% PLI ¼ ; Table 4). This estimate was lower than the ad hoc density estimate ( ; Table 2). The ESA was km 2. The striped hyena HZg 0 (.)r(.) model produced an unreasonable estimate of the shape parameter (z ) and was dropped from further consideration. AIC weights for the HNg 0 (.)r(.) model and NEg 0 (.)r(.) model were nearly equal (Table 3), and the two models produced similar density estimates (^D HN ¼ vs. ^D NE ¼ ; Fig. 2). We chose a model averaged density of ^D MA ¼ 6.39 (95% PLI ¼ ). The ESA was km 2 and the maximum-likelihood density exceeded the ad hoc density estimate. DISCUSSION The use of a standardized trapping design for estimating density of sympatric carnivore species worked well in this study. In traditional capture recapture sampling, traps are placed at a density to ensure that all animals with home range centers within the trapping array have a nonzero probability of detection (no holes in the sampling array) and that nonzero detection probabilities are maximized. This has meant that species with different home ranges, movement patterns, and spatial distributions could not be sampled simultaneously unless their ranging patterns were similar. Furthermore, traps usually are clustered in relatively small areas to maximize detections such that the sample area may be unrepresentative of larger landscapes. In this study, holes in the trapping grid and edge effects were not a problem. Efford et al. (2005) point out that distances between sampling points should be on the scale of animal home ranges in order to sample movements. Our camera trap spacing was sufficiently close (1265 m) relative to animal movements ( m) to include more than one camera in most home ranges for range centers within the sampling grid. Estimates of the scale parameter r ranged from 518 m to 2853 m. Use of a standardized trapping grid required subjective compromises between best camera location for photographing a particular species and the optimal camera location for photographing several sympatric species. Use of a systematic trap layout may have reduced the number of captures/species and, consequently, the precision of estimates for some species. Small sample sizes are a recurrent problem with capture recapture studies of large carnivores due to their large home ranges and tendencies to avoid one another. In the largest camera trap study published to date, Karanth et al. (2004) surveyed 11 sites using trap points per site and targeted placement, and identified 5 26 individual tigers (Panthera tigris) per site. In this study, we attained above average sample sizes (18 26 individuals per species) without targeting a particular species. Coefficients of variation for density also are comparable to those of a number of recent, species-specific, capture recapture studies (Table 5). We believe that the advantage of being able to study several sympatric species simultaneously under one sampling TABLE 4. Maximum-likelihood density estimates ( ^D), effective sampling area (ESA), and model parameter estimates. Species Model ^D (no./100 km 2 ) Profile likelihood ESA (km 2 ) g 0 r z Leopard averaged Aardwolf HZ[g0(.)r(.)] Spotted hyena averaged Striped hyena averaged Notes: See Table 3 for descriptions of the model abbreviations. Estimates are shown 6SE. In the rightmost column, z is a shape parameter for the hazard detection function.

7 2914 TIMOTHY G. O BRIEN AND MARGARET F. KINNAIRD Ecological Applications Vol. 21, No. 8 PLATE 1. Camera trap image of leopard on Mpala Ranch in Laikipia County, northern Kenya. Photo credit: M. F. Kinnaird and T. G. O Brien. design and a single deployment of traps or cameras yields considerable savings in cost and effort compared to multiple deployments targeting single species, but at a potential cost of loss of precision. Precision can be increased in a standardized multispecies sampling design by increasing the number of sampling points over a larger sampling area, increasing the density of trapping points within a sampling area, by increasing the number of trapping days or by some combination of these methods. Trapping designs that rotate traps among sampling blocks are common in abundance and density estimation studies (Karanth and Nichols 2002), and consideration of use of a simultaneous or incomplete trap layout depends, in part, on the details of the capture histories. This study demonstrates that the use of a simultaneous trap layout or incomplete trap layout for analysis does not affect results when there are no conflicts in which one or more individuals are captured in the same interval but in different blocks. In situations where conflicts do arise, combining multiple captures at a single trapping point during a single sampling interval into single binary events is a sensible approach (Royle et al. 2009a). When multiple captures of an individual occur on the same sampling interval in different blocks, a decision must be made which observation to drop. The choice results in loss of data that may affect the density estimate depending on the location of the dropped trap event, and often leads to some loss of precision. An incomplete trap layout gives a more realistic representation of the temporal trapping process and avoids loss of data, which is especially important when sample sizes are small. Use of an incomplete layout, however, requires a careful consideration of the temporal closure assumption. The simultaneous trap layout implies the temporal closure assumption applies to the length of trapping at a single block, whereas the incomplete layout extends the closure to the length of the study defined by the total number of trapping days. In this study, we assumed that the population remained closed to change for 84 days, which may be appropriate for long-lived carnivores in areas with long seasons, but too long for other species. An alternative approach would be to explicitly incorporate the starting date for a sampling TABLE 5. Comparison of mean coefficient of variation (CV) ^ from for population estimates (N ) and density estimates (D) recent capture recapture studies. Species CV N (%) ^ CV D (%) Reference Leopard Aardwolf Spotted hyena Striped hyena Jaguar Jaguar Jaguar Ocelot our findings our findings our findings our findings Karanth and Nichols (2000) Karanth et al. (2004) Royle et al. (2009a) Royle et al. (2009a) O Brien et al. (2003) Linkie et al. (2008) Simcharoen et al. (2007) Silver et al. (2004) Wallace et al. (2003) Maffei et al. (2004) Maffei et al. (2005) Note: Daggers ( ) indicate a spatially explicit density estimate, and ellipses ( ) indicate that no data are available.

8 December 2011 DENSITY ESTIMATION OF CARNIVORES 2915 block and perhaps other environmental parameters likely to change over time (e.g., rainfall) as covariates describing the trap sites in a block and calculate detection probability using covariate models (Borchers and Efford 2008). Maximum-likelihood density estimation rests on assumptions similar to conventional capture recapture population estimation. The population is temporally closed (no additions or subtractions of animals) for each species, identification of animals is accurate (no tag loss or misidentification), and detections of individuals are independent events (Williams et al. 2002). Additional assumptions are that capture does not affect the patterns of movements within a trapping session, traps are set at known localities for a fixed time, trap placement is random with respect to animal ranges, animal ranges are oriented at random with respect to traps, animal ranges do not change during a trapping session, and the home range centers follow a Poisson distribution within the study area (Efford 2009). Since home range centers are unknown, it is difficult to verify whether trap placement is random relative to home range centers. Studies that attempt to maximize the probability of detection, however, are more likely to violate this assumption since trap placement targets home range centers, whereas a systematic deployment is more likely to meet the assumption. It is also difficult to verify assumptions about home range orientation. Stability of home ranges of carnivores is probably not a problem because of the short duration of sampling efforts. We have assumed a homogeneous Poisson distribution of home range centers for our study. Our study was analogous to Efford et al. (2005), in which they found that a pooled density estimate over five sampling grids produced unbiased results. Borchers and Efford (2008) suggest that a homogeneous point process may be justified when using multiple sets of traps to infer density over a larger area. When trap grids are randomized over a large area, variation in expected density within sets will tend to average out, making a homogeneous model plausible across sets. We believe similar arguments apply to systematic coverage of a large area in multiple trapping blocks, and that systematic designs are a reasonable alternative to randomized block locations on a large landscape. An important aspect of maximum-likelihood density estimation is proper specification of the detection function, especially when sample sizes are relatively small. In this study, the more complex heterogeneity and trap response models failed, most likely due to small sample sizes of individuals and recaptures that resulted in overparameterization of models (Dorazio and Royle 2003, Gimenez et al. 2004). Overly complex models applied to small data sets are very sensitive to model choice and distinguishing between competing models can be difficult. Eliminating the complex models, we used DAIC to compute model weights that reflect the evidence that a model is best among the models being considered. In the case of leopards and two hyenas, the weight of evidence supported more than one model, suggesting that if repeated samples were taken, the best model might vary from data set to data set. In this case, multi-model averaging may improve the stability of estimates and can incorporate model selection uncertainty into the estimates of variance (Burnham and Anderson 2002). Model selection uncertainty was most evident in the spotted hyena, where the best model estimated density at 4.68/100 km 2, while the other two models estimates were 6.39/100 km 2 and 6.41/100 km 2. One of the basic motivations for undertaking a camera trap study is to estimate the density of study populations. The nuances of closed population estimation have required that we follow strict trap-spacing protocols that restricted the application of multispecies studies. Traditional trapping studies provide information on the size of the sampled population, but not on the area sampled, making inferences about density difficult. Spatially explicit capture recapture models offer powerful tools for estimating densities of individually identifiable species using individual-based models of the capture process (Efford 2004). By treating the population size N as essentially infinite, using capture locations to infer animal locations, and spatially referenced capture probabilities, we treated density as a parameter to be estimated using maximumlikelihood and Bayesian methods. The maximumlikelihood estimation procedure of Borchers and Efford (2008) is essentially equivalent to the Bayesian solution of Royle et al. (2009b). Royle et al. (2009b) argues that Bayesian solutions may be preferable when sample sizes are small, but Marques et al. (2011) warn that this may not be the case. Although we have chosen to focus on a comparison of maximum-likelihood methods compared to traditional methods in this study, we believe that both maximum-likelihood and Bayesian methods have merits in studies of density among sympatric species. ACKNOWLEDGMENTS We thank the Office of the President of the Republic of Kenya and the National Museums of Kenya for their permission to conduct of this research (Permit MOST 13/001/ 38C238). F. Lomojo, C. Tenai, and C. Cheatham provided support in the field. We warmly thank those who provided financial support: L. Scott, Cleveland Metropolitan Zoo, Mpala Research Trust, Mpala Wildlife Foundation, Panthera, and the Wildlife Conservation Society. We also thank M. Efford, S. Strindberg, and two anonymous reviewers for their valuable comments on the manuscript. LITERATURE CITED Borchers, D. L., and M. G. Efford Spatially explicit maximum likelihood methods for capture-recapture studies. Biometrics 64: Buckland, S. T., D. R. Anderson, K. P. Burnham, J. L. Laake, D. L. Borchers, and L. Thomas Introduction to distance sampling. Oxford University Press, Oxford, UK. Burnham, K. P., and D. R. Anderson Model selection and multimodal inference: a practical information theoretic

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