Camera-based badger density estimation using the REM, CT-DS, and SMR

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.

Methods
Data collection

Data were collected from six camera trap surveys at five sites in Cornwall, UK, in 2019 and 2021. 

Data Analysis

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.

REM Density Estimation

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.

CT-DS Density Estimation

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.

SEMR Density Estimation

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).