PAWS for thought.

Density estimation is vitally important in the conservation of endangered species. One non-invasive way of observing animals in the wild is camera trapping, a technique that has increased dramatically over the last 20 years. Models applied to the results from camera trapping can produce estimates for density. These techniques are now widespread, so it is now extremely important that the methodology is correctly and consistently used. This thesis reviews the current guidelines for camera trap capture-recapture survey design, and shows that few surveys currently meet these guidelines, thus, many density estimates published in the literature may be systematically biased. However, the guidelines themselves may not be appropriate under realistic movement conditions. A simulation model was developed using a statistically derived movement model for snow leopards, and this was used to explore the effect of survey design on the reliability of camera trap data used in Spatially Explicit Capture Recapture (SECR) analyses. I present evidence that basic assumptions about the movement patterns of the target species affect the accuracy and precision of SECR. As a result, SECR is less accurate when large survey area are used than was previously assumed. In addition, minimum capture numbers are currently used as a guide to the accuracy of density estimates. However, based on the simulation results, other measures such as distance between recaptures, and number of the individuals captured are better guides as to the accuracy of a density estimate. Finally, a possible new method for monitoring animals is introduced, a generalisation of the Random Encounter Model (REM) of density estimation. Whilst this methodology is not precise enough to study snow leopards, it opens up the possibility of applying the model to a wider range of sensors. Acknowledgements I would like to thank my supervisors Prof. Steve Hailes, Dr. Marcus Rowcliffe and Dr. Chris Carbone for all their help, and guidance for the duration of my PhD. As well as Prof. Kate Jones and Tim Lucas for co-authoring our paper together, their insight and experience was invaluable. My sincere thanks goes to Prof. Tom McCarthy and Orjan Johansson for use of their snow leopard data without which parts of this thesis would not have been possible. Last, but not least, I would like to thank my parents for their continued love and support. List of Figures 1.1 Comfortable snow leopard cub . . . . . . . . . . . . . . . . . . . . 17 1.2 Estimated range of snow leopards . . . . . . . . . . . . . . . . . . 18 2.1 Diagrams of optimal camera placement . . . . . . . . . . . . . . . 42 2.2 The area of survey compared to the average home range area when CMR was the method of analysis . . . . . . . . . . . . . . . . . . 47 2.3 The area of survey compared to the average home range area when SECR was the method of analysis . . . . . . . . . . . . . . . . . . 48 2.4 The inter trap distance compared to the average home range area when CMR was the method of analysis . . . . . . . . . . . . . . . 49 2.5 The inter trap distance compared to the average home range area when SECR was the method of analysis . . . . . . . . . . . . . . . 50 2.6 The estimated capture probability plotted against the number of individuals surveys used in CMR analyses . . . . . . . . . . . . . . . 51 2.7 The estimated density plotted against the number of captures in surveys using the SECR analyses . . . . . . . . . . . . . . . . . . . . 52 2.8 Number of individual males compared to the number of individual females . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 2.9 The number of male captures compared to the number of female captures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.1 Diagram of GPS compared to real movement . . . . . . . . . . . . 67 3.2 Example locations from one animal showing the convex hull of the animal home range, and the occupancy level . . . . . . . . . . . . 75 List of Figures 6 3.3 The convex hull of GPS locations with the percentage area from the centre marked . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 3.4 The density of the logged displacement for locations 5 hours apart . 82 3.5 The density of the turn angle for locations 5 hours apart . . . . . . . 83 3.6 The density distribution of the logged area of the convex hull . . . . 84 3.7 Number of locations plotted against the distance from the centre of the home range . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 3.8 The occupation levels of home ranges . . . . . . . . . . . . . . . . 86 3.9 The clusters of movement found in the male movement . . . . . . . 86 3.10 The clusters of movement found in the female movement . . . . . . 87 3.11 The distribution of displacement after 5 hours for males . . . . . . . 88 3.12 The distribution of displacement after 5 hours for females. Green lines and orange lines representing simulations and validation data respectively . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 3.13 The distribution of displacement after 10 hours and 25 hours for males and females . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 3.14 The distribution of turn angle after 5 hours for males. . . . . . . . . 91 3.15 The distribution of turn angle after 5 hours for females. . . . . . . . 92 3.16 The distribution of number of number of grid squares entered for males . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 3.17 The distribution of number of number of grid squares entered for females . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 3.18 The distribution of the logged home range area for males . . . . . . 94 3.19 The distribution of the logged home range area for females . . . . . 95 3.20 The home range use distribution for males . . . . . . . . . . . . . . 96 3.21 The home range use distribution for females . . . . . . . . . . . . . 97 4.1 The distribution of density estimates found in the snow leopard literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 4.2 The distribution of capture rate for snow leopard when using camera traps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 List of Figures 7 4.3 The distribution of capture rate for a range of camera radii within the simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 4.4 Diagram showing the distance calculations for variables . . . . . . . 117 4.5 The percentage error of densities estimated using SECR, when 10,000 cameras are used. Where the black line represents the median percentage error across all simulations, boxes represent the middle 50% of the data, whiskers represent variability outside the upper and lower quartiles with outliers plotted as individual points. . 119 4.6 The percentage error of densities estimated using SECR, when 25 cameras were used, with inter-trap distances ranging from 1 km to 15 km . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 4.7 The accuracy and precision given the amount of effort included in the survey, showing the percentage error and the coefficient of variation of densities estimated using SECR . . . . . . . . . . . . . . . 121 4.8 The internal parameters from the SECR model, when 25 cameras were used, with inter-trap distances ranging from 1 km to 15 km . . 123 4.9 The change in collected data when 25 cameras were used in different survey designs, with inter-trap distances ranging from 1 km to 15 km . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 4.10 The change in collected data when 25 cameras were used in different survey designs, with inter-trap distances ranging from 1 km to 15 km . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 4.11 The change in collected data when 25 cameras were used in different survey designs, with inter-trap distances ranging from 1 km to 15 km . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 4.12 The change in collected data when 25 cameras were used in different survey designs, with inter-trap distances ranging from 1 km to 15 km . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 4.13 The percentage error for simulation when they pass given guidelines 128 List of Figures 8 4.14 The accuracy and precision of the SECR density estimate when 25 were used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 5.1 Representation of sensor detection width and animal signal width . . 141 5.2 Simulation model results of the accuracy and precision for gREM submodels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 5.3 Simulation model results of the accuracy and precision of four gREM submodels given different numbers of captures . . . . . . . . 148 5.4 Simulation model results of the accuracy and precision of four gREM submodels given different movement models where the average amount of time spent stationary varies . . . . . . . . . . . . . 149 5.5 Simulation model results of the accuracy and precision of four gREM submodels given different movement models where the maximum change in direction at each step . . . . . . . . . . . . . . 150 5.6 Percentage error of the density estimate when incorrect signal width is used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 5.7 Percentage error of the density estimate when incorrect detection width is used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 5.8 Percentage error of the density estimate when incorrect radius is used152 5.9 Percentage error of the density estimate when incorrect speed estimate is used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 5.10 The percentage error for 26 cameras, when the original REM model is applied to a simulation of snow leopard movement . . . . . . . . 154 5.11 The percentage error for 43 cameras, when the original REM model is applied to a simulation of snow leopard movement . . . . . . . . 155 A.1 The length of surveys completed shown in the number of camera site, average length of time per site and total survey effort . . . . . . 197 B.6 The distribution of distance and turn angle for females . . . . . . . 211 List of Figures 9 C.1 The percentage error of densities estimated using SECR, when 26 cameras were used, with a range of inter trap distances . . . . . . . 213 C.2 The percentage error of densities estimated using SECR, when 30 cameras and 36 cameras were used, with a range of inter-trap distances214 C.3 The percentage error of densities estimated using SECR, when 42 cameras and 100 cameras were used, with a range of inter-trap distances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215 C.4 The accuracy and precision of the SECR density estimate when 42 were used, with a range of inter-trap distances . . . . . . . . . . . . 215 C.5 The change in number of cameras and percentage of animals when 100 cameras were used in different survey designs, with a range of inter trap distances . . . . . . . . . . . . . . . . . . . . . . . . . . 221 C.6 The change in maximum number of cameras, and percentage number of recaptures when 100 cameras were used in different survey designs, with a range of inter trap distances . . . . . . . . . . . . . 222 C.7 The change in the distance between recaptures when 100 cameras were used in different survey designs, with a range of inter trap distances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 D.1 Expressions for the average profile width, p̄, given a range of sensor and signal widths . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 List of Tables 2.1 Variables collected in the literature review . . . . . . . . . . . . . . 38 2.2 Effect on estimation of density using CMR when inter-trap distance is varied relative to home range size . . . . . . . . . . . . . . . . . 41 2.3 Effect on estimation of density using SECR when inter-trap distance is varied relative to home range size . . . . . . . . . . . . . . . . . 43 2.4 Effect on estimation of density using SECR when inter-trap distance is varied relative to home range size . . . . . . . . . . . . . . . . . 44 2.5 Number of papers and sites per species . . . . . . . . . . . . . . . . 45 2.6 Reporting of survey design variables for all species . . . . . . . . . 46 2.7 Percentage of the sites using the three main methods of density estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.8 Reporting of the camera trap results for all species . . . . . . . . . . 50 3.1 Criteria for cleaning GPS data . . . . . . . . . . . . . . . . . . . . 72 3.2 Description of the validation metrics used to assess movement models 81 3.3 Number of animals and locations after data cleaning . . . . . . . . . 81 6.1 Changes to the simulation that would increase it’s value . . . . . . . 165 A.1 Table of search terms use in Web of Science . . . . . . . . . . . . . 196 A.2 Summary statistics of the survey setup . . . . . . . . . . . . . . . . 198 B.1 Variables that have been calculated with their formulae . . . . . . . 199 B.2 Details of selected blocks of movement data during the summer season201 B.3 Selected blocks of winter data . . . . . . . . . . . . . . . . . . . . 201 List of Tables 11 B.4 Tests for differences between activity measures when made up of 1km grids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 B.5 Tests for differences between displacement between individual females during the summer season . . . . . . . . . . . . . . . . . . . 202 B.6 Tests for differences between displacement between individual females during the summer season . . . . . . . . . . . . . . . . . . . 203 B.7 Tests for differences between displacement between individual males during the summer season . . . . . . . . . . . . . . . . . . . 204 B.8 Tests for differences between displacement between individual females during the winter season . . . . . . . . . . . . . . . . . . . . 205 B.9 Tests for differences between displacement between individual males during the winter season . . . . . . . . . . . . . . . . . . . . 206 B.10 Random walk parameters . . . . . . . . . . . . . . . . . . . . . . . 207 B.11 The cluster number and the centre for each cluster for male clusters 207 B.12 The covariance matrix for the clusters for male clusters . . . . . . . 207 B.13 The markov matrix of transitions for male clusters . . . . . . . . . . 207 B.14 The average home range size in square meters for males in the training sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208 B.15 The cluster number and the centre for each cluster for female clusters 208 B.16 The covariance matrix for the clusters for female clusters . . . . . . 208 B.17 The markov matrix of transitions for female clusters . . . . . . . . . 208 B.18 The average home range size in square meters for females in the training sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208 C.1 The capture rate for snow leopards from multiple sources. Where capture rate is the number of captures per 100 days . . . . . . . . . 212 C.2 Correlation between the number of captures and the estimated value g0, σ , and density, for different levels of survey areas when 25 cameras are used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 List of Tables 12 C.3 Correlation between the number of captures and the estimated value g0, σ , and density, for different levels of survey areas when 42 cameras are used . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216 C.4 Correlation between the mean number of cameras an animal is captured and the estimated value g0, σ , and density, for different levels of survey areas when 25 cameras are used . . . . . . . . . . . . . . 217 C.5 Correlation between the mean number of cameras an animal is captured and the estimated value g0, σ , and density, for different levels of survey areas when 42 cameras are used . . . . . . . . . . . . . . 217 C.6 Correlation between the maximum number of cameras an animal is captured and the estimated value g0, σ , and density, for different levels of survey areas when 25 cameras are used . . . . . . . . . . . 217 C.7 Correlation between the maximum number of cameras an animal is captured and the estimated value g0, σ , and density, for different levels of survey areas when 42 cameras are used . . . . . . . . . . . 218 C.8 Correlation between the percentage of recaptures and the estimated value g0, σ , and density, for different levels of survey areas when 25 cameras are used . . . . . . . . . . . . . . . . . . . . . . . . . . 218 C.9 Correlation between the percentage of recaptures and the estimated value g0, σ , and density, for different levels of survey areas when 42 cameras are used . . . . . . . . . . . . . . . . . . . . . . . . . . 218 C.10 Correlation between the percentage of animals and the estimated value g0, σ , and density, for different levels of survey areas when 25 cameras are used . . . . . . . . . . . . . . . . . . . . . . . . . . 219 C.11 Correlation between the percentage of animals and the estimated value g0, σ , and density, for different levels of survey areas when 42 cameras are used . . . . . . . . . . . . . . . . . . . . . . . . . . 219 C.12 Correlation between the mean distance moved and the estimated value g0, σ , and density, for different levels of survey areas when 25 cameras are used . . . . . . . . . . . . . . . . . . . . . . . . . . 219 List of Tables 13 C.13 Correlation between the mean distance moved and the estimated value g0, σ , and density, for different levels of survey areas when 42 cameras are used . . . . . . . . . . . . . . . . . . . . . . . . . . 220 C.14 Correlation between the maximum distance moved and the estimated value g0, σ , and density, for different levels of survey areas when 25 cameras are used . . . . . . . . . . . . . . . . . . . . . . 220 C.15 Correlation between the maximum distance moved and the estimated value g0, σ , and density, for different levels of survey areas when 42 cameras are used . . . . . . . . . . . . . . . . . . . . . . 220 D.1 List of symbols used to describe the gREM and simulations. ‘-’ means the quantity has no units. . . . . . . . . . . . . . . . . . . . 225