Empirical comparison of density estimators for large carnivores

Transcription

1 Journal of Applied Ecology 2010, 47, Empirical comparison of density estimators for large carnivores Martyn E. Obbard 1, *, Eric J. Howe 1 and Christopher J. Kyle 2 doi: /j x 1 Wildlife Research and Development Section, Ontario Ministry of Natural Resources, DNA Building, Trent University, 2140 East Bank Dr., Peterborough, ON, Canada K9J 7B8; and 2 Natural Resources DNA Profiling and Forensics Centre, Forensic Science Department, DNA Building, Trent University, 2140 East Bank Dr., Peterborough, ON, Canada K9J 7B8 Summary 1. Population density is a critical ecological parameter informing effective wildlife management and conservation decisions. Density is often estimated by dividing capture recapture (C R) estimates of abundance ( ^N) by size of the study area, but this relies on the assumption of geographic closure a situation rarely achieved in studies of large carnivores. For geographically open populations ^N is overestimated relative to the size of the study area because animals with only part of their home range on the study area are available for capture. This bias ( edge effect ) is more severe when animals such as large carnivores range widely. To compensate for edge effect, a boundary strip around the trap array is commonly included when estimating the effective trap area ( ^A). Various methods for estimating the width of the boundary strip are proposed, but ^N ^A estimates of large carnivore density are generally mistrusted unless concurrent telemetry data are available to define ^A. Remote sampling by cameras or hair snags may reduce study costs and duration, yet without telemetry data inflated density estimates remain problematic. 2. We evaluated recently developed spatially explicit capture recapture (SECR) models using data from a common large carnivore, the American black bear Ursus americanus, obtained by remote sampling of 11 geographically open populations. These models permit direct estimation of population density from C R data without assuming geographic closure. We compared estimates derived using this approach to those derived using conventional approaches that estimate density as ^N ^A. 3. Spatially explicit C R estimates were % lower than densities estimated as ^N ^A.AIC c supported individual heterogeneity in capture probabilities and home range sizes. Variable home range size could not be accounted for when estimating density as ^N ^A. 4. Synthesis and applications. We conclude that the higher densities estimated as ^N ^A compared to estimates from SECR models are consistent with positive bias due to edge effects in the former. Inflated density estimates could lead to management decisions placing threatened or endangered large carnivores at greater risk. Such decisions could be avoided by estimating density by SECR when bias due to geographic closure violation cannot be minimized by study design. Key-words: American black bear, carnivore, density estimation, edge effect, geographic closure, spatially explicit capture recapture, Ursus americanus Introduction Effective conservation and management of wildlife populations requires reliable estimates of population density, but the available estimators rely on assumptions that are seldom met in studies of wild populations. Densities of large carnivores are frequently estimated by dividing capture recapture (C R) *Correspondence author. martyn.obbard@ontario.ca estimates of abundance by the area sampled. The conversion from abundance to density relies on an assumption that is especially troublesome: that the area occupied by the sampled population is well-defined and known. Large carnivores are difficult to enumerate because they range widely, occur at low densities, exhibit heterogeneous capture probabilities, and are often secretive or elusive (Garshelis 1992; Karanth 1995; Boulanger et al. 2004). This situation has improved through advances in remote identification from photographs or genetic samples (Karanth 1995; Ó 2009 The Authors. Journal compilation Ó 2009 British Ecological Society

2 Comparing density estimators for large carnivores 77 Woods et al. 1999) that enable researchers to obtain C R data quickly while avoiding some of the problems associated with live-capture. However, conventional C R estimators provide estimates of abundance ( ^N), not population density ( ^D), and N is a biologically relevant parameter only when the sampled population occupies a known, discrete area (Parmenter et al. 2003). ^N must be divided by the area sampled to obtain the biologically relevant parameter ^D, but for geographically open populations ^N is overestimated relative to the area of the trap array because animals with only part of their home range within the array are available for capture (White et al. 1982). This form of positive bias, termed edge effect (Dice 1938), remains a major obstacle to enumeration of large carnivore populations (Karanth et al. 2006; Kendall et al. 2008). To correct for edge effect, a boundary strip of width W can be included in an estimate of the effective trap area ( ^A; Dice 1938). W should approximate the distance animals at risk of capture move from the trap array during normal movements (White et al. 1982; Parmenter et al. 2003). However, most trap-revealed movements are underestimates because they are truncated at trap locations. Accurate ^W can be obtained if telemetry data are available for marked animals in the study. Indeed, studies combining C R with telemetry data for large carnivores demonstrate that where populations are not geographically closed, densities estimated from capture data alone are positively biased (Garshelis 1992; Soisalo & Cavalcanti 2006; Dillon & Kelly 2008). However, the need to instrument large numbers of animals to obtain unbiased ^W from telemetry data prevents many researchers from realizing the benefits of remote sampling in terms of study duration and costs. Efford (2004) presented a method for estimating population density directly from capture data without assuming geographic closure or estimating the area sampled. His spatially explicit capture recapture (SECR) approach combines C R and distance sampling (Burnham, Anderson & Laake 1980) methods to estimate three model parameters: the magnitude of the capture probability function (h 0 ), the spatial extent over which capture probability declines (r), and population density, defined as the intensity of a spatial point process describing the locations of home range centres (Efford 2004). Model parameters were originally estimated by simulation and inverse prediction (Efford 2004); more flexible, maximum likelihood-based estimators have subsequently been developed (Borchers & Efford 2008). Another approach to SECR models was recently developed using a Bayesian hierarchical framework (Gardner, Royle & Wegan 2009; Royle et al. 2009), but we do not evaluate that approach in this paper. Here, we focus on the SECR approach outlined by Efford (2004) and Borchers & Efford (2008). As inflated density estimates are especially problematic for carnivores that are at risk, a method that reduces the probability of generating inflated estimates could be useful. We evaluated the utility of the SECR estimator for large carnivores compared to more traditional estimators using data from a common large carnivore, the American black bear Ursus americanus (Pallas 1780). We remotely sampled black bears in 11 geographically open populations using barbed-wire hair corrals (Woods et al. 1999), and identified individuals using molecular methods. Densities were estimated both as ^N ^A and by SECR. Our objective was to compare density estimators in the context of their assumptions, precision and ability to account for biologically relevant forms of capture heterogeneity to identify a defensible method for estimating large carnivore densities from capture data collected on geographically open populations. Materials and methods STUDY AREA AND SAMPLING We sampled black bears in 11 different Wildlife Management Units (WMU) within the Boreal Forest (Rowe 1972) of Ontario, Canada (Fig. 1). All study areas were comprised of forest stands of varied ages and were characterized by low levels of human disturbance (see Obbard & Howe 2008 for a description of black bear habitat in the boreal forest of Ontario). We sampled bears at barbed-wire corrals spaced 2 km apart along secondary roads in each study area in 2004 or Sampling routes had high edge: area ratios (Fig. 1 inset) so positive bias in ^D due to edge effect was potentially severe (White et al. 1982). We baited traps with three partially opened tins of sardines suspended from a board nailed 2Æ5 m up a tree >2 m from any point on the wire. Hair samples were collected on four occasions over 47 days from late May through mid-july. On each occasion traps were baited for 1 week, after which samples were collected and baits removed. Hair samples were air-dried in paper envelopes and stored at room temperature. Sampling occasions were separated by a 1-week interval with no bait present, after which any snagged hairs were burned off when traps were re-baited. We deemed our study areas too small to measure movements of male bears because the size of their home ranges could approach that of our trap arrays (Alt et al. 1980; Koehler & Pierce 2003), so we analysed data from females only. We assumed the height of the wire (50 cm) excluded cubs and yearlings from the sample. DNA ANALYSES We selected hairs with visible roots from each sample when possible (samples with <5 hairs were not analysed). Samples were suspended in 250 ll of1 lysis buffer, treated with 15 units of proteinasek(>600uml )1 ; Qiagen, Inc., Mississauga, ON, Canada), and incubated at 37 C for 12 h. A paramagnetic bead automated DNA extraction (Promega MagneSil ONE; Promega Corporation, Madison, WI, USA) protocol (Cullingham, Smeeton & White 2007) was implemented using an Evolution P3 (Perkin Elmer, Waltham, MA, USA) liquid handler, eluting in a final volume of 70 ll. We amplified 15 microsatellite loci using three multiplex polymerase chain reactions. Loci included G1A, G1D, G10B, G10L, G10C, G10J, G10P, G10X, G10U, G10M (Paetkau & Strobeck 1994; Paetkau et al. 1995); G10H, UarMU59, UarMU05, UarMU50 (Taberlet et al. 1997) and Msut-6 (Kitahara et al. 2000). To identify gender, we amplified a region of the Amelogenin gene (Ennis & Gallagher 1994). One primer of each pair was synthesized with a fluorescent dye group, HEX, 6-FAM, or NED for subsequent detection and analysis on a MegaBACE 1000 capillary sequencer (GE Healthcare, Baie d Urfe, QC, Canada). To identify individuals, we initially compared genetic profiles at five microsatellite loci and the Amelogenin locus. Samples that did not amplify at four of six loci were removed from subsequent

3 78 M. E. Obbard et al. 52 0'N Kilometers 50 0'N A 15A 15B 21A 'N 'N 0 10 Kilometers 'W 85 0'W 80 0'W Fig. 1. Wildlife Management Units in Ontario, Canada, as defined by the Ontario Ministry of Natural Resources. Numbered Wildlife Management Units are those where black bears were sampled in 2004 or Inset map shows the trap layout in Unit 15B with a 2Æ5-km concave buffer around traps. analyses; samples profiled to four loci were grouped using genecap software (Wilberg & Dreher 2004). Subsequently, when possible, two or three representative samples from each group of identical profiles were profiled with the remaining 10 loci. Samples with a mixture of more than one individual profile were removed from further analysis. genecap was then used to confirm unique individuals from the 15 microsatellite loci and the gender locus. We considered pairs of samples that could not be distinguished from one another after taking two potential allelic dropouts into account to have originated from one bear, and reanalysed samples at specific loci to verify profiles that differed by two alleles that could not be explained by allelic dropout. Finally, we considered that profiles were from unique individuals only when they differed from other profiles by at least two of 16 loci. Positive and negative controls were run at all stages (extraction, amplification and visualization on the genetic analyser), and unknown samples were evaluated in light of results of the two positive controls (2Æ5 ng and 250 pg of DNA). DATA ANALYSIS We tested the assumption of demographic closure in C R data using tests described by Stanley & Burnham (1999). We fit eight closed-capture models with all additive combinations of time variation (t), individual heterogeneity (h) and WMU (as a grouping variable) on capture probabilities in Program mark v. 5.1 (White 2008). Two-point mixture distributions were used to model h (Pledger 2000). Traps were baited, so we also fit a model with a behavioural response to previous capture (b) and compared capture and recapture probabilities to check for trap response. We assessed support for different forms of capture heterogeneity and selected models for abundance estimation using Akaike s Information Criterion adjusted for small sample size (AIC c ; Hurvitch & Tsai 1989). We estimated effective trap area as the area of concave buffers of width W around all traps on each study area, and estimated W as the mean of maximum distances moved by all individuals captured more than once (MMDM), and half of MMDM (MMDM 2), on each study area and from pooled data. We calculated ^D in each WMU by dividing ^N from the selected C R model by ^A calculated using each of the four boundary strip widths. Naı ve standard errors for ^D were calculated by dividing standard errors of ^Nby ^A. We also estimated density by maximizing the full SECR likelihood for proximity detectors (Efford, Borchers & Byrom 2009) using density software (v. 4.3; Efford 2008). For numerical integration, the likelihood function was evaluated at 4096 evenly distributed points within a rectangular area extending 10 km around traps. We assumed a half normal spatial capture probability function, and that home range centre locations were Poisson distributed. We initially fit nine candidate models with three forms of variation in h 0 (constant, with h, and varying among WMUs) crossed with the same forms of variation in r. We then fit three additional models with the best-supported model of r variation and additional forms of h 0 variation and compared AIC c values across all fitted models. Two-point mixture distributions were used to model h in h 0 and r. Results Molecular data indicated from 9 to 36 (x= 21) unique females from 69 to 335 (x= 155) accepted genotypes in different WMUs. Numbers of recaptures excluding and including within-occasion recaptures at different traps ranged from 3 to 17 and 4 to 31, and averaged 9Æ5and14Æ5 respectively. Demographic closure violation was indicated only in WMU 21A (v 2 =7Æ973, 3 d.f., P =0Æ047); results of component and

4 Comparing density estimators for large carnivores 79 subcomponent tests showed violation was due to additions and losses between occasions 3 and 4, so we excluded data from the fourth occasion in WMU 21A when estimating N, W and D. We fixed capture probabilities on the fourth occasion in WMU 21A at zero in the C R analysis, removed data from the fourth occasion in WMU 21A from the SECR analysis, and excluded distances moved between the third and fourth occasion and on the fourth occasion in WMU 21A from ^W. The top AIC c -ranked C R model included additive effects of t and h in capture probabilities and accounted for 63% of the total AIC c weight (Table 1). The second-ranked model included only h in capture probabilities and yielded similar ^N (Tables 1 and 2). Differences in capture probabilities among WMUs or in response to previous capture were not supported (Table 1). Probabilities of initial capture and recapture from the model with b were 0Æ28 and 0Æ24 respectively. The mean maximum distance moved across all animals captured more than once was 3152 m (SE 1576); WMU-specific MMDM varied considerably (Table 2). An SECR model with h affecting both h 0 and r ranked first with 99% of the total AIC c weight (Table 3). Estimates of h 0 under this model were 0Æ26 (mixture 1) and 0Æ06 (mixture 2), and of r were 1360 m (mixture 1) and 7339 m (mixture 2). ^D was higher and less precise when h in h 0 and r were included in the estimating model (Table 4). Densities calculated using MMDM 2 as the boundary strip width were more than double those using MMDM (Fig. 2). Calculating W from pooled rather than WMU-specific data reduced variation in ^D amongwmusbuthadonlyasmall effect on the central tendency (Fig. 2). ^D from the AIC c - selected SECR model was >200% lower, on average, than ^D estimated as ^N ^A with ^W equal to MMDM 2, and >20% lower than ^D estimated as ^N ^A with ^W equal to MMDM (Table 4; Fig. 2). Densities estimated by SECR were apparently less precise than those estimated as ^N ^A (Table 4), but standard errors around ^N ^A estimates underestimated the actual uncertainty in ^D. Discussion We advocate using SECR models to estimate densities of large carnivores from capture data collected on geographically open populations for three reasons: (1) they did not rely on the assumption of geographic closure (Efford 2004), (2) they accounted for biologically relevant forms of heterogeneity in both capture probabilities and home range sizes and (3) the variance of ^D included additional forms of uncertainty and process variation compared to where ^D was estimated as ^N ^A. For geographically open populations, ^A is poorly defined with respect to the sampled population (White et al. 1982). Studies combining C R and telemetry data showed that when ^D is estimated as ^N ^A from capture data alone, ^A is underestimated and ^D overestimated (Garshelis 1992; Soisalo & Cavalcanti 2006; Dillon & Kelly 2008). Estimating ^W and including its area in ^A to correct for edge effect constitutes an ad hoc correction for a violated assumption, which itself relies on additional assumptions about home range sizes, shapes, and degrees of overlap (White et al. 1982; Parmenter et al. 2003; Karanth et al. 2006). Furthermore, it does not account for negative bias in capture probabilities and positive bias in ^N that occur when geographic closure violation causes demographic closure violation because animals are unavailable for capture on a subset of the sampling occasions (Kendall 1999). Densities estimated by SECR here were % lower than ^N ^A estimates. We cannot infer bias directly because true densities were unknown; however, the direction of the observed difference is consistent with overestimation of densities estimated as ^N ^A due to edge effect. We expected severe positive bias due to edge effect in our ^N ^A estimates because our study areas had high edge: area ratios and were small relative to home ranges of bears. The difference in ^D between spatially explicit and conventional C R density estimates would probably be less in studies employing large grids of traps. Our trap layout was constrained by the need for vehicle access, and the size of our study areas reflected a trade-off between the size and number of study areas we could achieve with available resources. Elsewhere, trap layouts or study area size may be constrained by costs and logistics (Settlage et al. 2008), trade-offs between potential sources of bias (Boulanger et al. 2004), or the need to set traps along trails used by the study species to maximize capture probabilities (Karanth & Nichols 1998; Ríos-Uzeda, Go mez & Wallace 2007). It is preferable to design field studies to minimize violations of assumptions, but where logistical constraints or characteristics of animals or their habitat Table 1. Model selection results for closed capture recapture models fit to data for female American black bears on 11 study areas in different Wildlife Management Units (WMU) in Ontario, Canada, 2004 or In model names, t denotes time variation, h denotes individual heterogeneity, b denotes behavioural response to previous capture and WMU denotes study area effects Model No. parameters AIC c DAIC c w i Deviance t + h Æ19 0Æ00 0Æ Æ2 h Æ43 2Æ24 0Æ Æ7 t + h + WMU Æ97 3Æ78 0Æ Æ0 h + WMU Æ52 4Æ33 0Æ Æ0 t + WMU Æ01 12Æ82 0Æ Æ3 t Æ74 14Æ55 0Æ Æ9 WMU Æ77 14Æ58 0Æ Æ4 Null Æ57 16Æ38 0Æ Æ0 b Æ20 18Æ01 0Æ Æ5

5 80 M. E. Obbard et al. Table 2. Numbers of unique females aged >1 year identified by genotyping [M (t+1) ], estimates of abundance ( ^N) and their standard errors (SE), and mean and SE of maximum distances moved between captures for female American black bears in 11 study areas in different Wildlife Management Units (WMU) in Ontario, Canada, 2004 or 2005 Abundance 1st-ranked model 2nd-ranked model Maximum distance moved WMU M (t+1) ^N SE ^N SE Mean SE Æ Æ Æ Æ Æ0 30 7Æ A Æ Æ A Æ6 34 7Æ B Æ4 27 6Æ A Æ3 47 9Æ Æ Æ Æ4 27 6Æ Æ8 17 4Æ Æ3 32 7Æ Table 3. Model selection results for spatially explicit capture recapture models fit to data for female American black bears aged >1 year in study areas in different Wildlife Management Units (WMU) in Ontario, Canada, 2004 or In model names Æ indicates the parameter was held constant, h denotes individual heterogeneity, b denotes an effect of previous capture, and WMU denotes study area effects Model No. parameters AIC c DAIC c w i Deviance h 0 (h)r(h) Æ01 0 0Æ Æ9 h 0 (WMU)r(h) Æ14 10Æ13 0Æ Æ1 h 0 (Æ)r(h) Æ74 14Æ73 0Æ Æ9 h 0 (h+wmu)r(h) Æ66 29Æ65 0Æ Æ4 h 0 (h)r(wmu) Æ59 76Æ58 0Æ Æ5 h 0 (WMU)r(WMU) Æ88 80Æ87 0Æ Æ3 h 0 (h)r(æ) Æ18 82Æ17 0Æ Æ4 h 0 (Æ)r(Æ) Æ62 92Æ61 0Æ Æ4 h 0 (b)r(h) Æ86 93Æ85 0Æ Æ7 h 0 (Æ)r(WMU) Æ36 95Æ35 0Æ Æ3 h 0 (b+h)r(h) Æ97 97Æ96 0Æ Æ5 h 0 (WMU)r(Æ) Æ35 98Æ34 0Æ Æ3 preclude using large grids of traps, SECR models are appealing for density estimation because they allow the assumption of geographic closure to be relaxed (Efford 2004; Royle et al. 2009). Prior to the development of SECR models, bias due to geographic closure violation was avoidable only by live-capturing and radio-tagging animals and monitoring their movements (Parmenter et al. 2003; Karanth et al. 2006). Densities estimated by boundary strip methods were more similar to SECR estimates when ^W was set equal to MMDM. MMDM 2 should theoretically approximate W as half the maximum linear distance of the average home range as recommended by Dice (1938) and was used as the boundary strip width in recent studies of felids and bears (Karanth et al. 2006; Immell & Anthony 2008). However, MMDM, which has no theoretical basis, performed better as an estimator of W in several studies where actual densities or home range sizes were observed (Parmenter et al. 2003; Soisalo & Cavalcanti 2006; Dillon & Kelly 2008). We propose explanations for the apparent superior performance of MMDM as a boundary strip width estimator which nevertheless do not support its general applicability. Home range lengths of voles Microtus montebelli observed from recapture locations were underestimates unless individuals were captured at 5 traps (Tanaka 1972). Because large carnivores exist at low densities, researchers may maximize trap spacing to sample more animals over a larger area, exacerbating the underestimation of ^W by truncating measured movements compared to the small mammal studies for which the approach was developed. Further, as defined, MMDM includes zero values when animals are recaptured only at their original capture location (Wilson & Anderson 1985; Karanth & Nichols 1998). When sampling occasions span several days, zero values are likely to reflect failure to detect movement due to imperfect detection and spatially discrete opportunities to detect animals, and contribute to negative bias in ^W. Hence, with wide trap spacing, few recaptures at different traps, and zeros in the data, MMDM may outperform MMDM 2 simply because the theoretically appropriate MMDM 2 more severely underestimates movements during

6 Comparing density estimators for large carnivores 81 Table 4. Densities ( ^D; bearskm )2 ) of female American black bears aged >1 year in 11 Wildlife Management Units (WMU) in Ontario, Canada, sampled in and derived from different estimators. Densities were estimated as ^N ^A where ^A was calculated using buffer strip widths estimated as half the mean maximum distance moved (MMDM 2) and the mean maximum distance moved between traps (MMDM) within each study area (WMU-specific), and across all animals. Densities were also estimated from null and AIC c -selected spatially explicit capture recapture (SECR) models. The mean coefficient of variation (CV) across WMUs appears in the bottom row ^N ^A (W MMDM 2 ) ^N ^A (W MMDM ) SECR WMU specific All animals WMU specific All animals h 0 (Æ)r(Æ) h 0 (h)r(h) WMU ^D SE ^D SE ^D SE ^D SE ^D SE ^D SE 5 0Æ467 0Æ093 0Æ357 0Æ071 0Æ207 0Æ041 0Æ162 0Æ032 0Æ071 0Æ015 0Æ127 0Æ Æ310 0Æ062 0Æ390 0Æ078 0Æ141 0Æ028 0Æ175 0Æ035 0Æ078 0Æ016 0Æ137 0Æ04 8 0Æ309 0Æ072 0Æ219 0Æ051 0Æ136 0Æ032 0Æ100 0Æ023 0Æ044 0Æ012 0Æ080 0Æ027 9A 0Æ341 0Æ066 0Æ439 0Æ085 0Æ156 0Æ030 0Æ197 0Æ038 0Æ088 0Æ017 0Æ152 0Æ043 15A 0Æ296 0Æ066 0Æ243 0Æ054 0Æ132 0Æ029 0Æ110 0Æ025 0Æ049 0Æ012 0Æ088 0Æ029 15B 0Æ149 0Æ037 0Æ224 0Æ055 0Æ068 0Æ017 0Æ100 0Æ025 0Æ047 0Æ013 0Æ084 0Æ030 21A 0Æ480 0Æ095 0Æ351 0Æ069 0Æ214 0Æ042 0Æ162 0Æ032 0Æ080 0Æ018 0Æ147 0Æ Æ331 0Æ066 0Æ420 0Æ084 0Æ149 0Æ030 0Æ187 0Æ037 0Æ084 0Æ018 0Æ147 0Æ Æ100 0Æ025 0Æ176 0Æ043 0Æ046 0Æ011 0Æ079 0Æ019 0Æ036 0Æ010 0Æ062 0Æ Æ266 0Æ075 0Æ126 0Æ036 0Æ101 0Æ029 0Æ056 0Æ016 0Æ025 0Æ009 0Æ044 0Æ Æ438 0Æ100 0Æ281 0Æ064 0Æ186 0Æ042 0Æ129 0Æ029 0Æ060 0Æ016 0Æ106 0Æ035 Mean CV 0Æ22 0Æ21 0Æ22 0Æ21 0Æ24 0Æ Median Min-Max MMDM/2 (WMU) MMDM (WMU) SECR (null) MMDM/2 (Pooled) MMDM (Pooled) SECR (selected) Fig. 2. Median and range of estimated densities of female American black bears aged >1 year across 11 Wildlife Management Units (WMU) in Ontario, Canada, 2004 or 2005, from different estimators. The different estimators were (from left to right): abundance divided by effective trap area with a boundary strip width equal to (1) half the mean maximum distance moved by individuals caught >1 time (MMDM 2) in each WMU, and (2) MMDM 2 across all animals (pooled); abundance divided by effective trap area with a boundary strip equal to (3) MMDM in each WMU, and (4) MMDM across all animals; (5) a null spatially explicit capture recapture (SECR) model, and (6) the AIC c -selected SECR model with individual heterogeneity in detection parameters. sampling. In our study, most individuals were recaptured at the same trap (27%) or at adjacent traps approximately 2-km apart (38%); only 6% of individuals were captured at traps >6 km apart. MMDM may therefore reflect trap spacing and sampling error rather than approximating mean home range length. Neither MMDM 2 nor MMDM should be expected to approximate ^W well in studies of large carnivores, many of which are characterized by wide trap spacing and few recaptures at different locations. Efford (2004) emphasized that parameter estimates from his SECR models did not depend on trap layout and specified that data from linear arrays were acceptable. Nevertheless, further investigation, including simulations, of effects of trap layout and spacing typical of studies of large carnivores on ^r are warranted. TheSECRmodelsweevaluatedavoidedtheassumptionof geographic closure but relied on other assumptions about home ranges, which previous work suggests may not severely bias ^D if violated. For example, SECR models assumed home ranges were circular, but violating this assumption probably affects only the variance of ^D (Efford 2004). Secondly, we assumed capture probabilities decreased with distance according to a half normal distribution and did not compare the fit of other detection functions. We considered this a reasonable assumption because occupied habitat extended well beyond the area of integration so capture probability would not have declined abruptly at any specific distance from the home range centre location. Further, sampling was complete before bears began summer foraging excursions outside their breeding ranges so bears outside the area of integration would have had negligible probabilities of capture. Other detection functions might be more appropriate for species with different movement patterns. For example, the negative exponential model could be used for animals that spend most of their time near a den or nest, or a threshold response applied to species with welldefined territories. In any case, densities estimated from SECR models were robust to the choice of detection function (Efford et al. 2009). Thirdly, we assumed that home range centre locations were randomly distributed. Home range locations are likely to be non-random in heterogeneous habitats like the boreal forest. However, because black bears exhibit mutual avoidance within overlapping home ranges (Schenk, Obbard & Kovacs 1998; Samson & Huot 2001) rather than spacing

7 82 M. E. Obbard et al. themselves evenly, randomly distributed home range centre locations may be a reasonable approximation. Finally, we assumed study populations were completely geographically open, and that all bears were able to traverse study area boundaries as there were no significant geographic barriers to movements within our areas of integration. However, where animal movements are constrained, for example by topography, water bodies, or fragmented habitat, areas of integration could include habitat not available to the sampled population, potentially causing underestimation of density. Because discrete approximations of areas of integration can be defined explicitly in SECR models, this assumption can be relaxed where necessary (Borchers & Efford 2008; Royle et al. 2009). The second reason we preferred SECR was that it accounted for relevant forms of detection heterogeneity. SECR models account for spatially induced individual heterogeneity due to variable exposure to traps, while allowing for additional h in both the magnitude and spatial extent of the detection function (Borchers & Efford 2008). Exposure to traps was probably variable among individuals in our study because most animals were exposed to few traps and had home ranges that included areas outside the trap array. By treating this source of h explicitly, SECR reduces reliance on statistical approaches to accounting for h in C R data (see Royle et al. 2009:125). We included models with additional h in detection parameters among candidate SECR models because bears exhibit heterogeneous probabilities of capture beyond what can be explained by variable exposure to traps (Noyce, Garshelis & Coy 2001; Boulanger et al. 2004), and home range sizes of female black bears may vary with local differences in habitat quality (Koehler & Pierce 2003), or with age and encumbrance status (Alt et al. 1980; Wooding & Hardisky 1994). Heterogeneous home range sizes cannot be accommodated by conventional density estimators. Generally, where density was estimated as ^N ^A, N estimators included h in capture probabilities, but ^W was calculated by averaging movements or home range sizes across all individuals (Karanth et al. 2006; Immell & Anthony 2008). Royle et al. (2009) and Gardner et al. (2009) presented density estimates for tigers Panthera tigris and American black bears, respectively, from Bayesian analyses of hierarchical SECR models, but did not evaluate models with h in detection parameters. In a reanalysis of their black bear data, Gardner et al. (in press) observed differences in r between sexes, but did not evaluate models with h within sexes. Our results, with individual heterogeneity in both h 0 and r strongly supported by AIC c, and higher density estimates from the SECR model with h, suggest that candidate models with h in detection parameters should be evaluated even when h induced by variable exposure to traps is treated explicitly using telemetry data or a spatial model. Behavioural responses to previous capture affected densities estimated by SECR (Borchers & Efford 2008; Gardner et al. in press), but were not supported by AIC c in our analyses. The small food reward and the 1-week interval between sampling occasions probably reduced behavioural responses to capture in our study. Time variation was apparent in our C R data, but had negligible effects on ^N. Local weather data had weak and inconsistent relationships with occasion-specific capture probabilities (M. E. Obbard, unpublished data), and models with sampling-occasion-specific detection parameters were not implemented in density, so we did not evaluate time variation in SECR detection parameters. Finally, we preferred SECR because the variance of ^D is estimated directly from the fitted spatial model (Efford et al. 2009) thereby reflecting all forms of uncertainty and process variation included in the model. Where density is estimated as ^N ^A, naïve standard errors for ^D are obtained by dividing the SE of ^N by a point estimate of ^A. This assumes ^A is measured without error and overstates the precision of ^D. Naı ve standard errors for ^D are currently presented only when the sampling variance of ^A is unknown (Kawanishi & Sunquist 2004; Dobey et al. 2005). More frequently, ^W is estimated from samples of individual movements so the variance of ^D may be calculated using the delta method to include uncertainty in both ^N and ^A (Seber 1982). However, published formulae for the variance of ^A are available only for grids (Wilson & Anderson 1985) and approximately circular study areas (Karanth & Nichols 1998). Approximating our sampled areas as grids or circles was inappropriate, so we presented naı ve standard errors for ^D estimated as ^N ^A. Furthermore, under the assumption of Poisson distributed home range centres the sampling variance of ^D is not conditional on the number of individuals within the area of integration, which is appropriate when sampled populations are geographically open. This variance is always larger than when home range centre locations are assumed to be binomially distributed because the variance of ^D is then conditional on the area of integration (Borchers & Efford 2008). This aspect of the sampling variance of ^D is ignored when density is estimated as ^N ^A under the assumption of geographic closure. The lower precision of our SECR estimates is therefore misleading, because sources of uncertainty included in the variance of SECR ^D did not contribute to the variance of ^D estimated as ^N ^A. Spatially explicit capture recapture is an emerging analytical tool that is theoretically superior to ^N ^A approaches to estimating animal densities when study populations are geographically open (Efford 2004; Royle et al. 2009). Our results are consistent with previous studies that showed densities estimated from capture data collected on geographically open populations using models that rely on the assumption of geographic closure were higher than where models allowed the assumption to be relaxed or telemetry data were available to correct for edge effect (Soisalo & Cavalcanti 2006; Kendall et al. 2008; Gardner et al. 2009). Although we cannot infer bias directly, we prefer SECR estimates over ^N ^A estimates because the latter were subject to biases associated with violation of the assumption of geographic closure, which were likely to be severe with our sampling design. Our results also highlight the need to evaluate SECR models with different forms of detection heterogeneity, as has become standard practice in C R analyses. Specifically, models with non-spatial individual heterogeneity in detection parameters should be evaluated. The improving availability of free, open-source software for fitting SECR models (Efford 2009; Royle et al. 2009) will allow

8 Comparing density estimators for large carnivores 83 a wider range of models to be explored, further enhancing the utility of the method to wildlife managers. For black bears in Ontario, the higher density estimates obtained where geographic closure was assumed could translate into higher, potentially unsustainable harvest levels. Harvest levels could be reduced if population declines were observed or other data indicated that mortality rates were unsustainable, although populations could take many years to recover from overharvest (Miller 1990). The consequences of management decisions based on inflated density estimates for large carnivore populations in other systems could be even more severe. Negative consequences could include local extirpation or underestimation of the minimum reserve size necessary to support a viable population. We recommend using the SECR approach to estimate densities of large carnivores when bias due to the violation of geographic closure cannot be minimized by study design because inflated estimates could lead to management decisions that place threatened or endangered populations at greater risk. Acknowledgements We thank the many biologists, technicians and field assistants with the Ontario Ministry of Natural Resources who conducted hair sampling, and K. Wozney, S. Coulson, and D. Abdelhakim for assistance with DNA analyses. The Applied Research and Development Branch, Ontario Ministry of Natural Resources provided funding. M. Efford provided advice on the theory and implementation of SECR. J. Laake provided advice and supplemental code for processing data and fitting C R models using RMark, and E. Cooch provided advice about closed-population models on the Program MARK online forum ( Comments from J. Bowman, J. Nocera, J. Boulanger, B. Gardner, and an anonymous reviewer helped us improve upon earlier drafts. References Alt, G.L., Matula, G.J. Jr, Alt, F.W. & Lindzey, J.S. (1980) Dynamics of home range and movements of adult black bears in northeastern Pennsylvania. International Conference on Bear Research and Management, 4, Borchers, D.L. & Efford, M.G. (2008) Spatially explicit maximum likelihood methods for capture recapture studies. Biometrics, 64, Boulanger, J., McLellan, B.N., Woods, J.G., Proctor, M.F. & Strobeck, C. (2004) Sampling design and bias in DNA-based capture-mark-recapture population and density estimates of grizzly bears. Journal of Wildlife Management, 68, Burnham, K.P., Anderson, D.R. & Laake, J.L. (1980) Estimation of density from line transect sampling of biological populations. Wildlife Monographs, 72, Cullingham, C.I., Smeeton, C. & White, B.N. (2007) Isolation and characterization of swift fox tetranucleotide microsatellite loci. Molecular Ecology Notes, 7, Dice, L.R. (1938) Some census methods for mammals. Journal of Wildlife Management, 2, Dillon, A. & Kelly, M.J. (2008) Ocelot home range, overlap and density: comparing radio telemetry with camera trapping. Journal of Zoology, 275, Dobey, S., Masters, D.V., Scheick, B.K., Clark, J.D., Pelton, M.R. & Sunquist, M.E. (2005) Ecology of Florida black bears in the Okefenokee-Osceola ecosystem. Wildlife Monographs, 158, Efford, M.G. (2004) Density estimation in live-trapping studies. Oikos, 106, Efford, M.G. (2008). Density 4.3: software for spatially explicit capture recapture Available at: Accessed 15 March Efford, M.G. (2009) SECR: Spatially Explicit Capture-Recapture Models. R Package Version Accessed 15 March Efford, M.G., Borchers, D.L. & Byrom, A.E. (2009) Density estimation by spatially explicit capture recapture: likelihood-based methods. Modeling Demographic Processes in Marked Populations (eds D.L. Thompson, E.G. Cooch & M.J. Conroy), pp Springer, New York, NY, USA. Ennis, S. & Gallagher, T.F. (1994) A PCR-based sex-determination assay in cattle based on the bovine amelogenin locus. Animal Genetics, 25, Gardner, B., Royle, J.A. & Wegan, M.T. (2009) Hierarchical models for estimating density from DNA mark recapture studies. Ecology, 90, Gardner, B., Royle, J.A., Wegan, M.T., Rainbolt, R.E. & Curtis, P.D. (2010) Spatial models for estimating density from DNA mark recapture studies. Journal of Wildlife Management, 74. Garshelis, D.L. (1992) Mark-recapture density estimation for animals with large home ranges. Wildlife 2001: Populations (eds D.R. McCullough & R.H. Barret), pp Elsevier Applied Science, London, UK. Hurvitch, C.M. & Tsai, C.-L. (1989) Regression and time series model selection in small samples. Biometrika, 76, Immell, D. & Anthony, R.G. (2008) Estimation of black bear abundance using a discrete DNA sampling device. Journal of Wildlife Management, 72, Karanth, K.U. (1995) Estimating tiger (Panthera tigris) populations from camera trap data using capture recapture models. Biological Conservation, 71, Karanth, K.U. & Nichols, J.D. (1998) Estimation of tiger densities in India using photographic captures and recaptures. Ecology, 79, Karanth, K.U., Nichols, J.D., Kumar, N.S. & Hines, J.E. (2006) Assessing tiger population dynamics using photographic capture recapture sampling. Ecology, 87, Kawanishi, K. & Sunquist, M.E. (2004) Conservation status of tigers in a primary rainforest of Peninsular Malaysia. Biological Conservation, 120, Kendall, W.L. (1999) Robustness of closed capture recapture methods to violations of the closure assumption. Ecology, 80, Kendall, K.C., Stetz, J.B., Roon, D.A., Waits, L.P., Boulanger, J.B. & Paetkau, D. (2008) Grizzly bear density in Glacier National Park, Montana. Journal of Wildlife Management, 72, Kitahara, E., Isagi, Y., Ishibashi, Y. & Saitoh, T. (2000) Polymorphic microsatellite DNA markers in the Asiatic black bear Ursus thibetanus. Molecular Ecology, 9, Koehler, G.M. & Pierce, D.J. (2003) Black bear home range sizes in Washington: climatic, vegetative, and social influences. Journal of Mammalogy, 84, Miller, S.D. (1990) Population management of bears in North America. International Conference on Bear Research and Management, 8, Noyce, K.V., Garshelis, D.L. & Coy, P.L. (2001) Differential vulnerability of black bears to trap and camera sampling and resulting biases in mark-recapture estimates. Ursus, 12, Obbard, M.E. & Howe, E.J. (2008) Demography of black bears in hunted and unhunted areas of the boreal forest of Ontario. Journal of Wildlife Management, 72, Paetkau, D. & Strobeck, C. (1994) Microsatellite analysis of genetic variation in black bear populations. Molecular Ecology, 3, Paetkau, D., Calvert, W., Stirling, I. & Strobeck, C. (1995) Microsatellite analysis of population structure in Canadian polar bears. Molecular Ecology, 4, Parmenter, R.R., Yates, T.L., Anderson, D.R., Burnham, K.P., Dunnum, J.L., Franklin, A.B., Friggens, M.T., Lubow, B.C., Miller, M., Olson, G.S., Parmenter, C.A., Pollard, J., Rextad, E., Shenk, T.M., Stanley, T.R. & White, G.C. (2003) Small-mammal density estimation: a field comparison of grid-based vs. web-based density estimators. Ecological Monographs, 73, Pledger, S. (2000) Unified maximum likelihood estimates for closed capture recapture models using mixtures. Biometrics, 56, Ríos-Uzeda, B., Gómez, H. & Wallace, R.B. (2007) A preliminary density estimate for Andean bear using camera-trapping methods. Ursus, 18, Rowe, J.S. (1972) Forest Regions of Canada. Canadian Forestry Service Publication No Environment Canada, Ottawa, ON. Royle, J.A., Nichols, J.D., Karanth, K.U. & Gopalaswamy, A.M. (2009) A hierarchical model for estimating density in camera-trap studies. Journal of Applied Ecology, 46, Samson, C. & Huot, J. (2001) Spatial and temporal interactions between female American black bears in mixed forests of eastern Canada. Canadian Journal of Zoology, 79, Schenk, A., Obbard, M.E. & Kovacs, K.M. (1998) Genetic relatedness and home range overlap among female black bears (Ursus americanus) in northern Ontario, Canada. Canadian Journal of Zoology, 76,

9 84 M. E. Obbard et al. Seber, G.A.F. (1982) The Estimation of Animal Abundance and Related Parameters. MacMillan, New York, NY, USA. Settlage, K.E., Van Manen, F.T., Clark, J.D. & King, T.L. (2008) Challenges of DNA-based mark recapture studies of American black bears. Journal of Wildlife Management, 72, Soisalo, M.K. & Cavalcanti, S.M.C. (2006) Estimating the density of a jaguar population in the Brazilian Pantanal using camera-traps and capture recapture sampling in combination with GPS radio-telemetry. Biological Conservation, 129, Stanley, T.R. & Burnham, K.P. (1999) A closure test for time-specific capture recapture data. Environmental and Ecological Statistics, 6, Taberlet, P., Camarra, J.-J., Griffin, S., Hanotte, O., Waits, L.P., Dubois-Paganon, C., Burke, T. & Bouvet, J. (1997) Noninvasive genetic tracking of the endangered Pyrenean brown bear population. Molecular Ecology, 6, Tanaka, R. (1972) Investigation into the edge effect by use of capture recapture data in a vole population. Researches on Population Ecology, 13, White, G.C. (2008) Closed population estimation models and their extensions in Program MARK. Environmental and Ecological Statistics, 15, White, G.C., Anderson, D.R., Burnham, K.P. & Otis, D.L. (1982) Capture Recapture and Removal Methods for Sampling Closed Populations. Los Alamos National Laboratory Rep. LA-8787-NERP, Los Alamos, NM, USA. Wilberg, M.J. & Dreher, B.P. (2004) genecap: a program for analysis of multilocus genotype data for non-invasive sampling and capture recapture population estimation. Molecular Ecology Notes, 4, Wilson, K.R. & Anderson, D.R. (1985) Evaluation of two density estimators of small mammal population size. Journal of Mammalogy, 66, Wooding, J.B. & Hardisky, T.S. (1994) Home range, habitat use, and mortality of black bears in North-Central Florida. International Conference on Bear Research and Management, 9, Woods, J.G., Paetkau, D., Lewis, D., McLellan, B.N., Proctor, M. & Strobeck, C. (1999) Genetic tagging of free-ranging black and brown bears. Wildlife Society Bulletin, 27, Received 22 June 2009; accepted 30 November 2009 Handling Editor: Ullas Karanth