Assumptions about fence permeability influence density estimates for brown hyaenas across South Africa

Wildlife population density estimates provide information on the number of individuals in an area and influence conservation management decisions. Thus, accuracy is vital. A dominant feature in many landscapes globally is fencing, yet the implications of fence permeability on density estimation using spatial capture-recapture modelling are seldom considered. We used camera trap data from 15 fenced reserves across South Africa to examine the density of brown hyaenas (Parahyaena brunnea). We estimated density and modelled its relationship with a suite of covariates when fenced reserve boundaries were assumed to be permeable or impermeable to hyaena movements. The best performing models were those that included only the influence of study site on both hyaena density and detection probability, regardless of assumptions of fence permeability. When fences were considered impermeable, densities ranged from 2.55 to 15.06 animals per 100 km2, but when fences were considered permeable, density estimates were on average 9.52 times lower (from 0.17 to 1.59 animals per 100 km2). Fence permeability should therefore be an essential consideration when estimating density, especially since density results can considerably influence wildlife management decisions. In the absence of strong evidence to the contrary, future studies in fenced areas should assume some degree of permeability in order to avoid overestimating population density.


Results
At 15 survey sites across South Africa (Fig. 1, Table 1) we collected 2690 camera trapping capture events of brown hyaenas (Table S1). We discarded 298 (11.08%) brown hyaena captures because image quality was insufficient to allow identification of individuals (Table S1). The majority of discarded captures had only one photograph (n = 289); therefore, the hyaena was only visible from one side, making identification more difficult. A total of 362 identifiable brown hyaenas were captured on 2392 occasions (Table S1).
The top population density models relating to both assumptions of fence permeability included only the site covariate on both g0 (detection probability when the distance between the activity centre of an animal and the camera trap is zero) and on density ( Table 2, Table S2). Density estimates derived from the top model ranged from 2.55 to 15.06 animals per 100 km 2 at each site when fences were considered to be impermeable, and from 0.17 to 1.59 animals per 100 km 2 when fences were considered to be permeable to hyaena movement (Fig. 2, Table S3).
When fences were assumed to be permeable, hyaena density estimates were on average 9.5 times lower than when fences were assumed to be impermeable to hyaena movement. Furthermore, we found an inverse relationship between reserve size and the ratio of brown hyaena density estimates modelled using different assumptions about fence permeability (Fig. 3, Table 3). In contrast, population size estimates were 1.6 times greater for models that assumed fence permeability (see Table S4). The general patterns of activity centre location were relatively similar for both model permeable and impermeable formulations at most study sites (Fig. S1). Estimates in smaller reserves were more sensitive to assumptions regarding the permeability of reserve boundaries to brown hyaena movement.

Discussion
Our study represents the largest and widest-ranging collection of density estimates to date for brown hyaenas. Our density estimates for each site varied substantially depending on whether fences were considered to be permeable or impermeable to the movement of brown hyaenas. Hyaena population densities were approximately ten times greater among impermeable estimates than permeable estimates due to the state-space difference associated with this assumption.
The population density of brown hyaenas has been estimated at only a handful of sites that are fully enclosed by fencing 19,21,32,33 , despite fences encompassing a large proportion of protected and non-protected land throughout the species range 8,9,34 . Overall, our estimates fit within the ranges of most previous studies 20,21,35,36 . Our estimates for permeable fenced areas (0.17-1.59 animals per 100 km 2 ) were slightly lower than, but comparable In the legend NR refers to Nature Reserve, and GR refers to Game Reserve. Created using QGIS 3.10.10 30 , using hyaena range data from 28 and base map data from 31 .    www.nature.com/scientificreports/ Many studies do not restrict the state-space to fence lines and reserve boundaries, resulting in relatively low density estimates 22,[37][38][39] . Less commonly the state-space is restricted to fences, often resulting in record high densities 19,21,24 . Our results show that the corresponding change in the state-space buffer used in SCR analysis when fences are assumed to be permeable or impermeable to animal movements results in substantially different densities, even when using the same capture histories, which may have important repercussions with regard to carnivore management objectives.
We found that the implications of truncating the state-space to the fence line are area dependant, where smaller reserves are more sensitive to assumptions regarding fence permeability than larger reserves. In larger areas, the trapping grid is likely located further away from the fence line, and thus density estimates are less sensitive to the state-space defined because the individuals exposed to sampling in these areas should be mostly those that have their activity centres within the reserve. In contrast, in smaller areas the trapping grid is likely located closer to the fence line and thus the individuals exposed to sampling in these areas are more likely to hold activity centres outside of the reserve. Consequently, assuming fences are impermeable (i.e. truncating the state-space) in a small, enclosed reserve would likely yield highly over-estimated densities. This indicates that decisions regarding fence permeability should not be taken lightly when studying less extensive reserves or more fragmented habitats, which are relatively common in countries such as South Africa that make up a large proportion of the range of brown hyaenas 40,41 .
In addition, we suggest a more nuanced approach to defining habitat. Brown hyaenas are likely to be able to survive outside of protected areas across much of rural southern Africa. However, large carnivore densities are likely to be higher within protected areas 42 . This is not reflected in the estimates of population size, which assume equal habitat quality both within and outside of protected areas, and are thus likely to produce inflated population estimates when fences are assumed to be permeable. We suggest that future studies acknowledge this reality by including a measure of habitat quality into the state space mask used in SCR analyses 43,44 . This will allow researchers to account for the likely permeability of reserve fences, while simultaneously modelling the probable costs to individuals ranging outside of the reserve (lower habitat suitability, greater risk of persecution, etc.).
One of the main challenges of this study was the lack of reliable data on fence permeability and the extent of movement by brown hyaenas at each survey site. Due to the size of the reserves, the number of survey sites, and financial and temporal constraints, we were unable to accurately quantify the potential for brown hyaena movement through fences, thus leading us to examine two extremes of fence permeability. The assumption of complete permeability or impermeability is unlikely to be entirely accurate in the way predators use landscapes, and in reality, the permeability of many fences will likely lie somewhere between these extremes. For example African wild dogs (Lycaon pictus) can cross the "predator-proof " fence surrounding our Pilanesberg National Park study site 45 , so even predator-proof fencing often has some degree of permeability. Movement will be concentrated around holes in the fence line, thus creating spatial heterogeneity in fence permeability. Furthermore, as animals dig holes, fences are damaged or fall into disrepair, or fences are maintained, the degree of permeability will change dynamically over time, compounding the challenge of making objective and meaningful assessments of fence permeability. At present there is also no way of incorporating these data directly into available SCR models, but the development of such models would be one way to help calculate more accurate density estimates in these systems, should collection of fence quality data be possible. If fence holes are documented and remain persistent, they could be modelled using non-euclidean distance methods and integrated into SCR models (M. Efford, pers. comm.). The successful incorporation of permanent holes in density modelling will likely encourage methods to be devised that consider movement through ephemeral holes.
For both scenarios of fence permeability, the models with the most support included only the site covariate in models of both g0 and hyaena population density. This suggests that site-specific factors were stronger determinants of brown hyaena abundance and detection probability than the other covariates included in the models. It was interesting that no support was found for an association between the relative abundance index (RAI) of competitor species and brown hyaena density, as variables were predictors of brown hyaena occupancy 46 . It is also possible that RAI lacks the precision to tease out these effects, and covariates such as absolute leopard (Panthera pardus) density may perform differently to leopard RAI, although these data are not yet available. Although RAI can be biased by ecological factors and sampling design 47 , numerous camera trapping studies use RAI as a proxy for covariates, especially when density estimates are unavailable 39,46,48 .
One potential caveat of the study is that camera trap spacing is a key element of SCR study design, so care should be taken to ensure that bycatch data are used appropriately. Our results could therefore be biased by estimating brown hyaena density using data that were collected using a design optimised for the estimation of leopard density, if leopards had much larger home ranges than brown hyaenas. But since brown hyaenas tend to have similar or larger home ranges than leopards 49-51 , we would expect the results to be comparable to a survey dedicated to brown hyaenas, and we would design the camera trap arrays in a very similar pattern for both species. Such a wide-ranging study using such a large dataset would not have been possible without using bycatch data.

Conclusion
Assumptions regarding the permeability of fencing to the movement of brown hyaenas had a great influence on population density estimates in SCR models, with density estimates being approximately ten times greater in models assuming impermeable fences than in models assuming permeable fences. We recommend that researchers consider if the density estimates are appropriate to the definition of the state-space used and fence permeability assumptions. We also suggest that further exploration of the distribution of estimated activity centres within and outside reserves could help in providing recommendations for defining the state-space because our results show that density estimates are heavily influenced by these assumptions. How these density estimates www.nature.com/scientificreports/ are influenced by sampling a continuum across both sides of the fence is an important future avenue of research to properly evaluate permeability assumptions. Of the covariates we included in the models, the site was the only one that was associated with brown hyaena density. This assessment, the first on such a broad scale, will provide useful baseline information for brown hyaena population monitoring and conservation programmes.
Our results show that large carnivore population density estimates are vastly inflated when fences are assumed to be impermeable. These data may be misleading, resulting in poor management decisions. Consequently, we strongly recommend that future studies assume a degree of fence permeability unless there is compelling evidence to the contrary, ideally supported by additional sampling outside of the fenced area.

Methods
Study area. The study was conducted in 15 fenced reserves located in South Africa's Eastern Cape, Gauteng, KwaZulu-Natal, Limpopo, North West, and Mpumalanga provinces (Fig. 1) Human population density within 10 km of each reserve varied between provinces, ranging from a mean of 8 people per km 2 in Limpopo to 214 people per km 2 in Gauteng (data from 52 ). All camera trap surveys were enclosed within the fences of the reserve boundaries. Fence quality and the level of maintenance varied between sites. Despite most reserve fences being electrified (n = 11), communication with landowners and managers, personal observations of fence line quality, and previous research indicate brown hyaena movement through fences was thought to be theoretically possible at all sites with the exception of Kwandwe Private Game Reserve. Kwandwe's perimeter fence was checked for holes and maintained daily, and a camera trap survey on adjacent properties did not record brown hyaenas, while they are abundant within the reserve 53 .
Camera trap surveys. Camera trap surveys were established in each reserve to estimate the population density of leopards using SCR modelling. Camera trap stations were separated by a mean of 2.05 (SD 0.48) km. This spacing, based on the average home range size of female leopards, ensures that all leopards in the study area have the opportunity to be photographed 54 . We utilised camera trap images of brown hyaenas collected by these camera traps (bycatch data) to model the population density of brown hyaenas. Analysing bycatch data is an efficient use of resources in conservation, provided species-specific methodological discrepancies are considered and accounted for 46,55,56 . Bycatch data on brown hyaenas from camera traps initially set up to survey leopards were used to successfully conduct occupancy analysis 46 . Similarities between leopards and brown hyaenas in detectability on camera traps, height, use of roads and trails, home range size, and geographical overlap make them an ideal pairing for data sharing opportunities 46 . This is the first study to estimate brown hyaena density using bycatch data.
Brown hyaena home range size varies between habitats 21,32,36 . Home range estimates collected at our survey sites were only available for Kwandwe Private Game Reserve, Madikwe Game Reserve, and Pilanesberg National Park 21,51 . The smallest recorded brown hyaena home range is at Kwandwe (26.32 km 2 ), which relates to a maximum suggested camera spacing of 2.89 km 21 . Since Kwandwe is the second smallest reserve sampled and the only reserve likely to be impermeable, it is probable that brown hyaenas in Kwandwe have one of the smallest home range sizes of all survey sites. Since the spacing used in this study was smaller than the maximum suggested spacing, all brown hyaenas with home ranges overlapping camera trapping survey areas had the chance to be photographed, thus fulfilling key requirements of SCR modelling 57 .
Camera trap data were used to estimate brown hyaena density once at each reserve. Data collection for this analysis was completed between January 2015 and April 2017, with the majority of data collected in 2016 ( Table 1). The mean size of the reserves was 356 km 2 , which were surveyed using an average of 36 paired camera trap stations (72 camera traps), covering a minimum convex polygon of 224 km 2 for an average of 1702 trap nights. Sampling periods were between 37 and 56 days, which was sufficiently brief to avoid violating the assumption of a closed population 23,58 , yet long enough for individuals to be photographed on multiple occasions 59 .
We placed Panthera V-series digital camera traps (camera models V4, V5, and V6) in locations large carnivores were likely to frequent such as on roads or game trails. Cameras were mounted on trees or poles in opposing but slightly staggered pairs to avoid the camera flash negatively affecting the images recorded by the paired cameras. The paired setup ensured that both flanks of passing animals were photographed to aid identification. We downloaded images and maintained the cameras on a weekly or fortnightly basis. Data analysis. Citizen scientists identified species photographed in camera trap images to a species level using the Zooniverse platform (www.zooni verse .org). To ensure confidence in identification, five independent classifications were averaged per image. Brown hyaenas were then individually identified by two experienced assessors using unique features such as leg stripes, snare wounds, and ear notches 20 . Both assessors verified each image at least three times to ensure accurate identification. Any images that could not be accurately identified were excluded from the analysis 60 . Brown hyaenas do not exhibit significant sexual dimorphism 61  www.nature.com/scientificreports/ to avoid artificially inflating population estimates by counting an individual's left and right flanks as two separate individuals 62,63 . No images of immature individuals were collected, so this study relates to adults only. Sampling occasions for brown hyaenas were defined as a 24-h period from 12:00 pm to 11:59 am. By incorporating the full duration of the night, we avoided the 'midnight problem' whereby an animal photographed on both sides of midnight is recorded as separate captures 64 . This approach is recommended for species such as the brown hyaena that is almost exclusively nocturnal 27 .
To estimate hyaena population density we fitted SCR models to the data within a maximum likelihood framework using the package secr v. 3.2.1 65 in R 3.6.0 66 . We fitted a multi-session model to our data, in which each reserve was treated as a single session 67 . We fitted half-normal, hazard rate, and negative exponential detection functions to the data, and retained the function with the lowest Akaike information criterion corrected for small sample sizes (AICc) 68 . The best supported spatial detection function was hazard rate, and this was used in subsequent models (Table S5). The models of g0 with the AICc for both impermeable and permeable fences included only the site covariate (Table 2). We therefore included site as a covariate on g0 in all models of population density. We used the derived function in secr to compute estimates of g0 and density for each site within each model. We modelled three parameters -population density, g0, and σ (the spatial scale parameter). We also estimated population size using the region.N function in secr, and plotted activity centres from the fitted model objects using the fx.total function in secr, which produces a map showing the probability of each pixel in the habitat mask being the activity centre of both observed and unobserved individuals. This allowed us to visually compare the spatial distribution of activity centres between fence-permeable and impermeable models for each study site.
To investigate the relationship between brown hyaena density and a range of potential explanatory variables, we modelled the relationship between reserve size, and the RAI of prey, leopard, spotted hyaena (Crocuta crocuta), and humans (on foot) on brown hyaena population density and g0. We also modelled the relationship between site and g0, and we fitted a learned response model, in which the probability of detection at the home range centre was affected by previous captures. Covariates were selected based on brown hyaena occupancy 46 , and speculated, but previously untested, drivers of brown hyaena density 19,21 . We estimated human population density in the area surrounding each reserve by calculating the mean density (humans per km 2 ) within a 10 km radius of the reserve boundaries (data from 52 ). We calculated RAI as the number of captures per 100 camera-trap days 69,70 . Captures excluded consecutive photographs of the same species at the same location more than once in a 30 min interval 71 . Prey RAI included species with an average female weight of 15 kg or more, based on brown hyaena dietary studies showing a preference for medium and large sized prey [72][73][74] . RAI values were standardised as z-scores 75 . Covariates were included separately in each model, and models were compared using AIC c 68 . We retained all models with ΔAIC c < 2 76 . The final model used to estimate brown hyaena population densities included the best models on g0 and density.
State space buffers were used to estimate home range centres that extend beyond the camera trapping area 77 . To examine the role of the permeability of fences on reserve boundaries to the movement of study animals and the resulting population density we fitted two sets of SCR models; one set in which the state space was restricted to the fence line (impermeable), and one with the state space buffer extending beyond the fence line (permeable). We used the suggest.buffer function in secr and applied the largest buffer suggested (31 km) to all sites in order to be conservative 78 . A home range centre spacing of 500 m was used in both sets of models. Areas of human infrastructure uninhabitable to brown hyaenas were excluded from the habitat masks. Model fitting was conducted using the Durham University High Performance Computing service. We tested the relationship between reserve size and the ratio of hyaena population densities estimated using the two assumptions of fence permeability (impermeable:permeable to hyaena movement) using a generalised linear model with an inverse gaussian distribution. This approach was the best fit to our data, which did not have a normal distribution. Data and code to reproduce the analyses are publicly available 79 . www.nature.com/scientificreports/