Toward reliable population density estimates of partially marked populations using spatially explicit mark–resight methods

Abstract Camera traps are used increasingly to estimate population density for elusive and difficult to observe species. A standard practice for mammalian surveys is to place cameras on roads, trails, and paths to maximize detections and/or increase efficiency in the field. However, for many species it is unclear whether track‐based camera surveys provide reliable estimates of population density. Understanding how the spatial arrangement of camera traps affects population density estimates is of key interest to contemporary conservationists and managers given the rapid increase in camera‐based wildlife surveys. We evaluated the effect of camera‐trap placement, using several survey designs, on density estimates of a widespread mesopredator, the red fox Vulpes vulpes, over a two‐year period in a semi‐arid conservation reserve in south‐eastern Australia. Further, we used the certainty in the identity and whereabouts of individuals (via GPS collars) to assess how resighting rates of marked foxes affect density estimates using maximum likelihood spatially explicit mark–resight methods. Fox detection rates were much higher at cameras placed on tracks compared with off‐track cameras, yet in the majority of sessions, camera placement had relatively little effect on point estimates of density. However, for each survey design, the precision of density estimates varied considerably across sessions, influenced heavily by the absolute number of marked foxes detected, the number of times marked foxes was resighted, and the number of detection events of unmarked foxes. Our research demonstrates that the precision of population density estimates using spatially explicit mark–resight models is sensitive to resighting rates of identifiable individuals. Nonetheless, camera surveys based either on‐ or off‐track can provide reliable estimates of population density using spatially explicit mark–resight models. This underscores the importance of incorporating information on the spatial behavior of the subject species when planning camera‐trap surveys.

2. Understanding how the spatial arrangement of camera traps affects population density estimates is of key interest to contemporary conservationists and managers given the rapid increase in camera-based wildlife surveys.
3. We evaluated the effect of camera-trap placement, using several survey designs, on density estimates of a widespread mesopredator, the red fox Vulpes vulpes, over a two-year period in a semi-arid conservation reserve in south-eastern Australia. Further, we used the certainty in the identity and whereabouts of individuals (via GPS collars) to assess how resighting rates of marked foxes affect density estimates using maximum likelihood spatially explicit mark-resight methods.
4. Fox detection rates were much higher at cameras placed on tracks compared with off-track cameras, yet in the majority of sessions, camera placement had relatively little effect on point estimates of density. However, for each survey design, the precision of density estimates varied considerably across sessions, influenced heavily by the absolute number of marked foxes detected, the number of times marked foxes was resighted, and the number of detection events of unmarked foxes.
5. Our research demonstrates that the precision of population density estimates using spatially explicit mark-resight models is sensitive to resighting rates of identifiable individuals. Nonetheless, camera surveys based either on-or off-track can provide reliable estimates of population density using spatially explicit mark-resight models. This underscores the importance of incorporating information on the spatial behavior of the subject species when planning camera-trap surveys.

| INTRODUC TI ON
The reliable estimation of population densities is a key element of any conservation management strategy, whether the species of interest is a conservation asset or threat (Soisalo & Cavalcanti, 2006).
Many species are elusive and difficult to observe due to behaviors such as nocturnality or because they occur at low densities. In such circumstances, camera traps are used increasingly to detect species presence and estimate density (Ordeñana et al., 2010;Sollmann, Gardner, Parsons et al., 2013;Towerton, Penman, Kavanagh, & Dickman, 2011). The most reliable methods for estimating population density use models that incorporate spatial attributes (geographic coordinates) of both the camera traps and where animals are recorded. Selecting the most appropriate method depends on whether animals are identifiable individually. If no individuals are identifiable, options include random encounter modeling (Rowcliffe, Field, Turvey, & Carbone, 2008), spatial presence-absence (Ramsey, Caley, & Robley, 2015), and N-Mixture models (Jiménez et al., 2017;Royle, 2004). If a proportion of the population is identified individually, spatially explicit mark-resight (SEMR) methods are suitable (Rich et al., 2014;Sollmann, Gardner, Chandler et al., 2013;Sollmann, Gardner, Parsons et al., 2013), while spatially explicit capture-recapture (SECR) is appropriate if all animals recorded are identifiable (Alexander, Gopalaswamy, Shi, & Riordan, 2015;Bahaa-el-din et al., 2016;Borchers & Efford, 2008;Hearn et al., 2016;Royle & Young, 2008). Models are also available that combine data collection methods, for example, when animals cannot be identified uniquely (i.e., providing an encounter rate) but telemetry movement data are available for a portion of the population (e.g., Potts, Buckland, Thomas, & Savage, 2012;White & Shenk, 2001).
Regardless of the analytical method selected, the reliability of density estimates depends on appropriate survey design-an issue that has generally been undervalued in camera-trap studies (Meek, Ballard, & Fleming, 2015). Camera placement is a fundamental design decision that affects detection probability, and some designs will introduce biases into density estimates. The only truly unbiased design is to position all cameras randomly within the study area, although this strategy can reduce detectability for some species as frequently used locations are not targeted, typically increasing the uncertainty of density estimates. Nonetheless, placing cameras on roads, trails, and paths is standard practice for surveying carnivores (e.g., Anile, Ragni, Randi, Mattucci, & Rovero, 2014;Meek, Ballard, Fleming, & Falzon, 2016;Sollmann et al., 2011); either for logistic reasons (e.g., to more efficiently survey large areas) or to maximize detections of elusive species that frequently utilize trails (Karanth & Nichols, 1998;Sollmann et al., 2011). Here, we examine the trade-offs between camera placement and density estimation for a common mesopredator with non-distinctive pelage, the red fox Vulpes vulpes, in a semi-arid conservation reserve in south-eastern Australia.
In Australia, introduced mesopredators (foxes and feral cats Felis catus) have driven the decline or extinction of one-third of the island continent's endemic terrestrial mammals (Doherty, Glen, Nimmo, Ritchie, & Dickman, 2016;Fleming et al., 2014;Woinarski, Burbidge, & Harrison, 2015). Where mesopredators threaten the survival of native species, reliable density estimates are important to formulate appropriate management strategies (e.g., population control vs. eradication) and evaluate efficacy of different management interventions (e.g., trapping vs. baiting vs. shooting). In this study, we assess the effect of camera-trap placement on density estimates. Specifically, we compared maximum likelihood SEMR density estimates from three different spatial arrays of camera traps, including on-track grid, on-track transect, and off-track grid (plus all cameras combined), to determine how the spatial arrangement of camera traps affects the precision of population density estimates.
Moreover, we used the certainty in the identity and whereabouts of individuals (via GPS collars) to determine the rate of detection and non-detection of marked foxes. The results inform future camera-trap survey designs for mesopredators and other wildlife, and provide insight into how resighting rates of identifiable individuals affect populations density estimates using SEMR models.

| Study area
Our study occurred at Scotia Sanctuary, a 64,659-ha private conservation reserve in south-western New South Wales, Australia (−33.15°S, 141.06°E; Figure 1) owned and managed by the Australian Wildlife Conservancy. The climate is semi-arid with low and highly variable rainfall (spatially and temporally) that averages ~230 mm per year with high evapotranspiration (~1,500 mm/year) and low relative humidity (ave. ~20%; Australian Wildlife Conservancy, unpublished data). Cool winters (ave. max. <17°C) and hot summers (ave. max. >30°C) characterize the site, with annual temperature extremes ranging from −6 to 48°C. The landscape features stable east-west sand dunes of red sand and sandy solonized brown soil over clay (Westbrooke, Miller, & Kerr, 1998 (Westbrooke et al., 1998). Red foxes are the largest predator present and their population in the study area was not subject to any form of population control during the project or in the six years prior.

K E Y W O R D S
camera trap, capture-recapture, fox, maximum likelihood, mesopredator, survey design,

| Data collection
To measure fox density, we used 107 camera traps with passiveinfrared sensors (HC600; Reconyx, Holmen, WI, USA) distributed in three different "arrays" across a 14,000-ha study area, namely  to provide information for a related study. Photographs of foxes recorded simultaneously by both paired cameras were recorded as one detection-event only; hence, paired cameras had a higher detection probability than non-paired cameras. Whether transect cameras were individual or paired was included as a covariate in the modeling process (see Section 2.4 below). The time spent in the field each month to keep cameras operational was recorded separately for each array.
We conducted 24 camera-trapping sessions at monthly intervals for the on-track grid array. The first session commenced October 1, 2015, and the final commenced September 1, 2017. Trapping to 08:59 hr) unless problems were noted with camera operability, whereby trap usage was accounted for in the analysis (see Section 2.4 below).
Cameras were attached to a galvanized steel post driven into the ground, with the sensor positioned 0.5 m above ground, aimed approximately 4.5 m away "down" the center of the track (i.e., ~22° relative to the track's edge). Cameras recorded five consecutive images when triggered, with no time delay, and high image quality and trigger sensitivity. Images were stamped with camera location, date, and time. Cameras recorded monochromatic images at night and color images during the day under ambient light. No baits or lures were used at cameras.

| Identification of individual foxes
Due to their uniform pelage, individual red foxes cannot be identified reliably from photographs unless marked artificially (Guthlin, Storch, & Kuchenhoff, 2014). To identify individuals on camera-trap images, we fitted 28 foxes with GPS collars ( Information Appendix S1).

| Data analysis
Spatially explicit mark-resight (SEMR) models were fitted to the camera-trap data using the "secr" library (v. 3. location at which identifiable animals were detected in each session. Here, marked foxes could move freely between camera traps and therefore be detected at multiple trap locations during each occasion. The identity of all marked foxes in photographs was determined with certainty by cross-checking with location data from GPS collars (see Appendix S1); and 4. number of detection events of unidentified individuals at each camera-trap location. Here, since all marked foxes were known and identifiable on photographs, all detection events of unmarked foxes were considered detection events of unidentified individuals.
We did not include the marking process in the models (i.e., the capturing of foxes to deploy GPS collars). Consequently, our data set contained some zero-only encounter histories for foxes that were marked but never detected at any of the camera traps on any of the sampling occasions. For SEMR analyses, it is assumed that tags are not lost, which was true for GPS collars in our study. It is also assumed animal home ranges are circular and that home-range centers are distributed in space according to a Poisson point process.
For SEMR analyses, a habitat mask is required to constrain the likelihood for computational purposes, defining a region around the trap locations beyond which the probability of detecting it is essentially zero. The mask also restricts home-range centers to occurring in true habitat only. If activity centers are assumed to occur in nonhabitat, density estimates are biased low (i.e., animals are believed to occur within a region larger than reality). In our study, a habitat mask was created using a 4,000 m buffer around the trap locations in each survey, with inaccessible habitat removed (i.e., an 8,000-ha fenced region that excludes foxes). The choice of a 4,000 m buffer was based on GPS location data that indicated foxes rarely moved beyond this distance.
With SEMR analyses, marked individuals are assumed to be a random sample of the larger population. Using the capture history of a marked individual, a capture function can be estimated that is conceptually consistent with a detection function in Distance Sampling approaches (Buckland et al., 2001), such that the probability of detecting an animal is assumed to be a radially declining function of the distance between an animal's (unknown) home-range center and the Currently, all SEMR models in "secr" are closed-population models, so we analyzed each session separately. Estimates of fox density for each session were selected from AIC model-averaged estimates for the nine models fitted to the data (or 10 or 11 models for on-track transect and all cameras combined arrays, respectively).

| RE SULTS
Across the duration of the 24-month study, foxes were widespread throughout the study area, being detected at all locations in the  Table S1 for capture information by session), coinciding with the fox mat-   (Figure 4). respectively (see Supporting Information Table S3 for capture information by session).
Data for all three arrays (plus nine supplementary cameras) combined are presented in Figure 3c (see also, Supporting Information Consequently, density estimates using SEMR models for that session were not obtained ( Figure 4).
In all analyses, a half-normal capture function was selected and density estimates were model averaged across all fitted models (ontrack grid, off-track grid = 9 models; on-track transect = 10 models; all cameras = 11 models). Model selection output for the all cameras array is provided in Supporting Information Table S5. Estimates of fox density for each camera array and session are presented in

| D ISCUSS I ON
Most camera-trap studies that generate density estimates using SECR-based methods report on species with distinctive spots or stripes (e.g., felids) that enable individual identification from photographs (Rowcliffe et al., 2008;Wearn & Glover-Kapfer, 2017).
For species lacking uniquely identifiable pelage such as red foxes (Guthlin et al., 2014), standard SECR methods cannot be applied readily. In our study, a subset of foxes had GPS collars fitted, which enabled detection events from photographs of marked foxes to be assigned to individual animals; hence, there was no ambiguity in the identity of marked-fox detection events. Consequently, we use this certainty in the identity and whereabouts of individuals to present an analysis based on maximum likelihood mark-resight SECR methods (i.e., SEMR), to investigate how the spatial configuration of camera-trap surveys influence estimates of population density.
During our two-year study, more than 100 camera traps were deployed in three spatial arrays and 28 foxes were captured and marked individually. In total, there were 2,773 detection events across 24 survey sessions and 37,137 trap nights. Despite our large survey effort, on average 26% of marked foxes were not detected in any given month even though GPS data indicated they were resident within the study area. In total, less than 20% of detection events were of marked foxes and point estimates of density were similar across the trapping arrays ( Figure 4). Regardless of the trapping array, the 95% confidence intervals were always wider  The all cameras combined array typically produced density estimates with greater precision than either of the on-track arrays individually (e.g., January, July-December 2016, June-September 2017). However, in some instances when marked foxes were not detected on either array (or by the supplementary cameras), the estimates from the all cameras combined array were less precise than the individual on-track arrays. This is because, despite greater survey effort being used across the all cameras array, the number of detection events of marked foxes did not increase (e.g., March 2016, March 2017; Figure 4).
During July-September 2017 (winter/spring) when three different survey designs operated concurrently, the median estimated density across the three sessions was 0.06 foxes per km 2 (CI range = 0.02-0.14) for on-track grid cameras, 0.07 foxes per km 2 (CI range = 0.02-0.56) for off-track grid cameras, 0.11 foxes per km 2 (CI range = 0.03-0.26) for on-track transect cameras, and 0.08 foxes per km 2 (CI range = 0.05-0.17) when data from all cameras were combined. We found that g0-the probability of being trapped if the animal's home range is centered on a trap-was higher when cameras were set on tracks but the magnitude of this difference was mostly small (<0.03) and varied by session (Supporting Information Table S5).
The spatial arrangement of camera traps was found to greatly influence the number of detection events of both marked and un- are only two published studies that use camera traps to derive density estimates for foxes in Australia. Moreover, both studies were based on substantially shorter survey periods and used different analytical approaches because no foxes were uniquely identifiable. First, Silvey, Hayward, and Gibb (2015) estimated density to be 3.0 foxes per km 2 , in the same area as the current study, using camera traps and random encounter models (Rowcliffe et al., 2008 been shown in studies of large felids (e.g., Cheyne, Stark, Limin, & Macdonald, 2013;Sollmann et al., 2011;Sollmann, Linkie, Haidir, & Macdonald, 2014). This underscores the importance of incorporating information on the spatial behavior and/or preferences of the subject species prior to commencing camera-trap surveys, to ensure camera placement maximizes exposure to the population. Our findings suggest that wherever populations exist at low densities, an appropriate survey design is that which maximizes the likelihood that uniquely identifiable individuals will be detected and resighted because the reduced uncertainty in the estimator that this delivers will likely outweigh biases associated with any particular survey design.
Presently, there is limited capacity to incorporate animal movement information obtained from telemetry into mark-resight models within a maximum likelihood framework (Efford, 2017b(Efford, , 2018Efford & Hunter, 2018). Also, all mark-resight models in "secr" are closed-population models. In future research, we will explore openpopulation models and compare how incorporating GPS movement data into mark-resight analyses influences estimates of density using both Bayesian methods (e.g., Sollmann, Gardner, Parsons et al., 2013) and by extending trapping point transects to include animal movement (Potts et al., 2012).

AUTH O R CO NTR I B UTI O N S
AC and DR conceived the ideas and designed the methodology; AC collected the data; JP managed the data analysis; AC and DR led the writing of the manuscript. All authors contributed critically to the drafts and gave final approval for publication.
Access to the data has been embargoed until 01/01/2020.

S U PP O RTI N G I N FO R M ATI O N
Additional supporting information may be found online in the Supporting Information section at the end of the article.

FigureS1
How to cite this article: Carter A, Potts JM, Roshier DA.