DOI: 10.5061/dryad.gb5mkkwwk
title: Camera-based badger density estimation using the REM, CT-DS, and SMR

description: Accurate and precise assessment of population density plays a critical
 role in effective wildlife management, but reliable estimates are often
 difficult to obtain. Camera traps have emerged as valuable non-invasive
 tools for studying elusive species, offering cost-effective solutions for
 both marked and unmarked populations. We evaluated the
 consistency of badger (Meles meles) density estimates obtained from the
 random encounter model (REM) and camera trap distance sampling (CT-DS)
 with independent estimates from spatial mark-resight (SMR) models and
 quantified the bias in CT-DS arising from animals reacting to camera
 traps. Six camera trap surveys were conducted in Cornwall, UK, in 2019 and
 2021, and data were used to estimate badger density using the REM and
 CT-DS. Four sites were included in a badger vaccination research project,
 providing an opportunity to mark badgers with uniquely identifiable fur
 clips to facilitate resighting within an SMR framework. We found
 consistency in the density estimates across all methods, but the results
 had wide confidence intervals. Density estimates derived from CT-DS tended
 to be higher than those from the REM and were sensitive to the exclusion
 of reactive sequences, resulting in a two-fold decrease in the estimated
 density in one case. The REM tended to be the most precise method;
 however, where badger density was low, precision was low using all
 methods. Our findings suggest animal density can be assessed from camera
 traps in the absence of individual identification; however, it is
 important to account for reactive behaviours, especially where such
 behaviour is prevalent. In these circumstances, we recommend utilising the
 REM which offers a clear methodology for addressing bias arising from
 reactive sequences. In addition, we emphasise the need for improved
 precision to ensure the effectiveness of these methods in the context of
 wildlife management. We offer practical considerations to facilitate the
 broader application of these methods, drawing upon the example of disease
 control through badger vaccination.
description: <strong>Data collection</strong>
 Data were collected from six camera trap surveys at five sites in
 Cornwall, UK, in 2019 and 2021.  <strong>Data
 Analysis</strong> Badger density was estimated
 using three methods: The Random Encounter Model (REM), Camera trap
 Distance Sampling (CT-DS), and Spatially Explicit Mark Resight (SEMR).
 Details of each method are given below.
 <strong>REM Density Estimation</strong>
 Density estimates were calculated from encounter
 rates using an equation involving variables like the number of independent
 badger encounters (y), temporal survey effort (t), and camera detection
 zone parameters (r and θ). Model parameters were
 estimated from camera images, including badger position data, speed,
 activity level, and detection zone dimensions.
 Density estimates were obtained using the 'camtools'
 package, including a nonparametric bootstrap of trap rate
 errors. Where badgers showed reactive behaviour,
 'reactive' sequences were removed from the estimation of animal
 speed and the camera detection zone. 
 <strong>CT-DS Density Estimation</strong>
 Point transect distance sampling methods adapted for
 still images were used. Temporal and spatial effort
 calculations were adapted for continuous camera trapping.
 Density was estimated using the number of badger observations,
 truncation distance, probability of detection, and activity level. We
 estimated density under two scenarios, where 'reactive'
 sequences were included or excluded from total badger
 observations.  Detection distances were determined
 through exploratory analysis and model selection.
 Left truncation was applied to control bias arising from animals
 passing under the camera undetected. 
 <strong>SEMR Density Estimation</strong>
 Individual badgers were identified by comparing marks
 in camera images with those taken during trapping and marking.
 Retrospective capture histories of identifiable badgers were
 constructed. SEMR models were fitted to the data
 using the 'secr' package in R. Effective
 sampled area and buffer widths were determined based on the distance
 between capture and resighting locations. Models with
 variable detection probability between marking and sighting occasions were
 considered. Overdispersion was accounted for in
 models and standard errors. All data
 analysis was performed in R (R Core Team, 2021).
description: # **Camera-based badger density estimation using the REM, CT-DS, and SMR**
 The data and code are provided for three methods used to estimate badger
 density - the Random Encounter Model (REM), Camera-Trap Distance Sampling
 (CT-DS), and Spatially-Explicit Mark Resight (SMR). ## **Description of
 the data and file structure** For each method, data are organised into
 separate files representing the different sites (numbered 1-5). Any data
 containing location information has been omitted in line with
 privacy-sharing agreements so that participating landholders remain
 anonymous. As such, we have not included the shapefiles to generate the
 habitat mask for SMR or the coordinates of camera locations. We have also
 included the code for the simulation of animal density using SMR across a
 range of *pID* values, reflecting the proportion of identifiable
 individuals. The values provided are similar to the observed detection
 conditions of the full dataset.   Below we have outlined the methodology
 for obtaining the density estimates and provided references for further
 details of the methods.  ### **REM - methods, data, and code** We obtained
 badger density estimates from all five sites using the REM following the
 methods and equation detailed in Rowcliffe* et al.* (2008). Data files
 used for the REM are: exifdata, deptable, deployment models, and cmods.
 Below is a description of each of these files. Exifdata: contains all of
 the image metadata, including species, count, contact, and calibration
 tags. Exifdata is used to construct the animdat and postdat data files,
 which are used to estimate animal speed and the dimensions of the camera
 detection zone, respectively. The ‘contact’ data within exifdat is used to
 fit activity models and estimate trap rate. A ‘contact’ is defined as the
 first image of an animal sequence when an individual enters the field of
 view for the first time. Cmods: camera calibration models built using an
 object of known size (a calibration pole), to estimate radius and angles
 in images. A separate camera model was built for each camera model and
 image size. Deployment models: models for each camera deployment fitted
 using cmods to estimate real-world radius and angles in images. Deptable:
 details of start and stop times of each camera placement. Used to build
 deployment calibration models and generate an estimate of temporal effort
 and trap rate. Badger density estimates can be replicated using these
 files and the code provided. For further details on packages and code
 please see the CTtracking and camtools repositories at
 [https://github.com/MarcusRowcliffe](https://github.com/MarcusRowcliffe)
 ### **CT-DS - methods, data, and code** Badger density estimates were
 obtained for all five sites using CT-DS following the methods and equation
 detailed in Howe* et al.* (2017). Data files used for CT-DS are: DS_data,
 DS_effort, and DS_radiantime. Below is a description of each of these
 files. DS_data: the data file that follows the distance sampling data
 structure specified for use with the ‘Distance’ package in R. Each line
 represents a badger detection with distance and location (camera
 placement) recorded. Where no badgers were recorded, an ‘empty’ line for
 that camera trap is present in the data. These data are used to fit
 distance sampling models, following the code provided. DS_effort: details
 of start and stop times of each camera placement. Used to estimate
 temporal effort. DS_radiantime: file containing contact data with radian
 time of day to fit activity models. Dimensions of the camera trapping zone
 (the angle of detection) are estimated as above for the REM and snapshot
 moments are estimated using the speed data from the REM. ### **SMR -
 methods, data, and code** Badger density estimates were obtained using SMR
 for three of the five sites where there were sufficient re-captures. Data
 files used for SMR are: Capdat_marked, Capdat_Tu, Capdat_Tm, Capdat_Tn,
 Decdat. Density estimates can be obtained using these files and the code
 provided, but please note that the location data (camera coordinates and
 shape file habitat masks) have been removed following landholder privacy
 agreements. Below is a description of each of these files. For
 comprehensive instructions on how to use this data and code to generate
 SMR density estimates using the ‘secr’ package, please see Efford (2023).
 Capdat_marked: capture histories of marked identifiable individuals.
 Capdat_Tu: capture records of unmarked individuals. Capdat_Tm: capture
 records of marked unidentifiable individuals. Capdat_Tn: capture records
 of individuals with an unknown marking status. These data are not used for
 density analyses but can be provided to the model. Decdat: detector
 information for badger traps and camera traps; location coordinates
 removed.   **References** Efford, M. (2023). Vignette: Mark–resight in
 secr 4.6. Howe, E.J., Buckland, S.T., Després-Einspenner, M.-L. &
 Kühl, H.S. (2017). Distance sampling with camera traps. *Methods in
 Ecology and Evolution*, 8, 1558-1565. Rowcliffe, J.M., Field, J., Turvey,
 S.T. & Carbone, C. (2008). Estimating animal density using camera
 traps without the need for individual recognition. *Journal of Applied
 Ecology*, 45, 1228-1236.