Arts, Faculty of
Geography, Department of
DSpace
UBCV
Wall, Jacob C
Doctor of Philosophy - PhD
University of British Columbia
African elephants (Loxodonta africana and L. cyclotis) are important species for geospatial study given their ecological role as megaherbivores, their large home ranges which pose challenges for conservation, and the ongoing ivory crisis. Using GPS tracking data, I address five research topics that contribute new information to the geospatial analysis of tracking data, to elephant movement ecology, and conservation : 1. What is an appropriate method to collect, store, disseminate, visualize and analyze elephant tracking data? I present a system (Loxobase) designed to provide an efficient and scientific basis for the treatment of wildlife tracking data. I demonstrate its utility by analyzing tracking datasets collected from 247 elephants (Chapter 2). 2. Can we leverage real-time tracking data for management and conservation? I present a monitoring system that implements continuous analysis of elephant GPS tracking data streams to identify positional and movement-based geospatial alert conditions. Four algorithms identify when wildlife slow or stop moving or cross into or near to spatial objects (Chapter 3). 3. Can we estimate wildlife space-use from tracking data? I develop the Elliptical Time-Density model to estimate an animal's utilization distribution from tracking data where parameters are directly linked to species biology. I demonstrate its performance in relation to other space-use estimators (Chapter 4). 4. What does tracking data tell us about the movement patterns of the Sahelian elephants in Mali? I use GPS tracking to study elephants in the Gourma, Mali to understand this unique and important population. The Gourma elephant's range was found to exceed those reported elsewhere in Africa and movements were correlated with patterns of rainfall and vegetation phenology. I also identified corridors and core areas of conservation priority (Chapter 5). 5. What does tracking data tell us about the factors influencing elephant range size across Africa? I present a comparative analysis of elephant range area measured in West, Central, East and Southern Africa. Using mixed effects models, I test hypotheses about elephant range size in relation to sex, species, region, vegetation phenology and quantity, protected areas, human footprint and terrain (Chapter 6).
Geospatial analysis ofAfrican elephant movement(Loxodonta africana and L. cyclotis)byJacob C WallB.Sc.H, Queen’s University, 2000M.Sc., Queen’s University, 2005A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinFaculty of Graduate and Postdoctoral Studies(Geography)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)January 2015© Jacob C Wall 2015AbstractAfrican elephants (Loxodonta africana and L. cyclotis) are important species forgeospatial study given their ecological role as megaherbivores, their large homeranges which pose challenges for conservation, and the ongoing ivory crisis. UsingGPS tracking data, I address five research topics that contribute new informationto the geospatial analysis of tracking data, to elephant movement ecology, andconservation:1. What is an appropriate method to collect, store, disseminate, visualizeand analyze elephant tracking data? I present a system (Loxobase) de-signed to provide an efficient and scientific basis for the treatment of wildlifetracking data. I demonstrate its utility by analyzing tracking datasets col-lected from 247 elephants (Chapter 2).2. Can we leverage real-time tracking data for management and conser-vation? I present a monitoring system that implements continuous analysisof elephant GPS tracking data streams to identify positional and movement-based geospatial alert conditions. Four algorithms identify when wildlifeslow or stop moving or cross into or near to spatial objects (Chapter 3).3. Can we estimate wildlife space-use from tracking data? I develop the El-liptical Time-Density model to estimate an animal’s utilization distributionfrom tracking data where parameters are directly linked to species biology. Idemonstrate its performance in relation to other space-use estimators (Chap-ter 4).4. What does tracking data tell us about the movement patterns of the Sa-helian elephants in Mali? I use GPS tracking to study elephants in theGourma, Mali to understand this unique and important population. TheiiGourma elephant’s range was found to exceed those reported elsewhere inAfrica and movements were correlated with patterns of rainfall and vege-tation phenology. I also identified corridors and core areas of conservationpriority (Chapter 5).5. What does tracking data tell us about the factors influencing elephantrange size across Africa? I present a comparative analysis of elephant rangearea measured in West, Central, East and Southern Africa. Using mixedeffects models, I test hypotheses about elephant range size in relation to sex,species, region, vegetation phenology and quantity, protected areas, humanfootprint and terrain (Chapter 6).iiiPrefaceThe following tables provide a break-down of the contributions from myself andfrom my supervisory committee to my doctoral research. All elephant trackingdata used in this doctoral research was collected and made available by Save theElephants, Kenya.Chapter 2JakeWallGeorgeWittemyerValerieLeMayBrianKlinkenbergIainDouglas-HamiltonProblemidentification &research design75% 5% 5% 5% 10%Performing theresearch85% 5% 5% 5% 0%Data analyses 80% 0% 10% 10% 0%Manuscriptpreparation85% 0% 5% 10% 0%Chapter 3 (Novel Opportunities for Wildlife Conservation and Research withReal-Time Monitoring) was published in the journal Ecological Applications inearly 2014. Sections from Chapter 2 (Movement Data Download, Storage & Re-trieval) were also published in the supplementary information of Wall et al. (2014a).ivChapter 3JakeWallGeorgeWittemyerValerieLeMayBrianKlinkenbergIainDouglas-HamiltonProblemidentification &research design85% 5% 0% 0% 10%Performing theresearch85% 5% 0% 10% 0%Data analyses 85% 0% 10% 5% 0%Manuscriptpreparation75% 15% 0% 10% 0%Chapter 4 (Elliptical Time-Density model to estimate wildlife utilization distri-butions) was published in the journal Methods in Ecology and Evolution in 2014.Chapter 4JakeWallGeorgeWittemyerValerieLeMayBrianKlinkenbergIainDouglas-HamiltonProblemidentification &research design75% 10% 5% 5% 5%Performing theresearch80% 0% 10% 10% 0%Data analyses 75% 5% 10% 10% 0%Manuscriptpreparation65% 15% 10% 10% 0%Chapter 5 (Characterizing Properties and Drivers of Long Distance Move-ments by Elephants (Loxodonta africana) in the Gourma, Mali) was published inthe journal Biological Conservation in 2013 (Wall et al., 2013). I was also coauthoron a paper (Drought Threatens Mali Elephants) published in Pachyderm in 2009documenting a severe drought affecting the Mali elephants.vChapter 5JakeWallGeorgeWittemyerValerieLeMayBrianKlinkenbergIainDouglas-HamiltonProblemidentification &research design70% 5% 5% 5% 15%Performing theresearch80% 5% 5% 5% 5%Data analyses 75% 5% 10% 10% 0%Manuscriptpreparation75% 10% 5% 5% 5%Chapter 6 is now being prepared for publication.Chapter 6JakeWallGeorgeWittemyerValerieLeMayBrianKlinkenbergIainDouglas-HamiltonProblemidentification &research design70% 10% 5% 5% 10%Performing theresearch80% 5% 5% 10% 0%Data analyses 75% 5% 10% 10% 0%Manuscriptpreparation70% 10% 10% 10% 0%viTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Objectives & Overview . . . . . . . . . . . . . . . . . . . . . . . 32 Loxobase: An African Elephant Tracking System . . . . . . . . . . 72.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 Loxobase Description . . . . . . . . . . . . . . . . . . . . . . . 102.2.1 Tracking Unit Attachment . . . . . . . . . . . . . . . . . 102.2.2 Tracking Unit Description & Types . . . . . . . . . . . . 102.2.3 Collar Deployment Locations . . . . . . . . . . . . . . . 102.2.4 Movement Data Download . . . . . . . . . . . . . . . . 122.2.5 Movement Data Storage . . . . . . . . . . . . . . . . . . 142.2.6 Movement Data Retrieval . . . . . . . . . . . . . . . . . 152.3 Loxobase Synoptic Analysis . . . . . . . . . . . . . . . . . . . . 172.3.1 Data Retrieval . . . . . . . . . . . . . . . . . . . . . . . 18vii2.3.2 Travel Distance, Speeds & Home Range . . . . . . . . . 182.3.3 Statistical Model . . . . . . . . . . . . . . . . . . . . . . 202.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262.5.1 Loxobase . . . . . . . . . . . . . . . . . . . . . . . . . . 262.5.2 Elephant Movement Data . . . . . . . . . . . . . . . . . 302.5.3 Elephant Range & Travel Distance . . . . . . . . . . . . 302.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313 Novel Opportunities For Wildlife Conservation And Research WithReal-Time Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . 333.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.2 Positional Analyses . . . . . . . . . . . . . . . . . . . . . . . . . 353.2.1 Proximity . . . . . . . . . . . . . . . . . . . . . . . . . 353.2.2 Geographic Intersection . . . . . . . . . . . . . . . . . . 363.3 Movement Behavior Analyses . . . . . . . . . . . . . . . . . . . 363.3.1 Movement Rate . . . . . . . . . . . . . . . . . . . . . . 373.3.2 Immobility . . . . . . . . . . . . . . . . . . . . . . . . . 373.4 Application Of RTM To African Elephants . . . . . . . . . . . . 383.4.1 Proximity Example . . . . . . . . . . . . . . . . . . . . 403.4.2 Geofencing Example . . . . . . . . . . . . . . . . . . . . 423.4.3 Movement Rate Example . . . . . . . . . . . . . . . . . 443.4.4 Immobility Example . . . . . . . . . . . . . . . . . . . . 463.5 Alert Dissemination . . . . . . . . . . . . . . . . . . . . . . . . 483.6 Future Directions . . . . . . . . . . . . . . . . . . . . . . . . . . 493.6.1 Physiological Data . . . . . . . . . . . . . . . . . . . . . 513.6.2 Environmental Data . . . . . . . . . . . . . . . . . . . . 523.6.3 Acoustic Data . . . . . . . . . . . . . . . . . . . . . . . 523.6.4 Accelerometry . . . . . . . . . . . . . . . . . . . . . . . 533.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53viii4 Elliptical Time-Density Model To Estimate Wildlife Utilization Distri-butions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554.2 Elliptical Time-Density Model Development . . . . . . . . . . . 574.3 Weibull Probability Density Function . . . . . . . . . . . . . . . 604.3.1 Multi-Temporal Data . . . . . . . . . . . . . . . . . . . 614.3.2 Maximum Speed Parameter . . . . . . . . . . . . . . . . 614.4 Elliptical Time-Density Model Application . . . . . . . . . . . . 624.4.1 ETD Model Software . . . . . . . . . . . . . . . . . . . 634.4.2 Speed Parameter Selection . . . . . . . . . . . . . . . . . 644.4.3 ETD Model Accuracy Assessment . . . . . . . . . . . . 644.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 654.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 744.6.1 Trajectory-Based Model . . . . . . . . . . . . . . . . . . 744.6.2 Parametrization . . . . . . . . . . . . . . . . . . . . . . 764.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 785 Characterizing Properties And Drivers Of Long Distance MovementsBy Elephants (Loxodonta africana) In The Gourma, Mali . . . . . . 795.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 795.2 Materials And Methods . . . . . . . . . . . . . . . . . . . . . . 815.2.1 Study Area . . . . . . . . . . . . . . . . . . . . . . . . . 815.2.2 Elephant Position Data . . . . . . . . . . . . . . . . . . 825.2.3 Home Range Metrics: MCP, Kernel, aLoCoH & Time-Density . . . . . . . . . . . . . . . . . . . . . . . . . . . 835.2.4 Linear Movements & Velocity-Grids . . . . . . . . . . . 855.2.5 Movement Pattern . . . . . . . . . . . . . . . . . . . . . 875.2.6 NDVI . . . . . . . . . . . . . . . . . . . . . . . . . . . . 875.2.7 Statistical Analyses . . . . . . . . . . . . . . . . . . . . 885.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 895.3.1 Movement Pattern . . . . . . . . . . . . . . . . . . . . . 895.3.2 NDVI Selection . . . . . . . . . . . . . . . . . . . . . . 895.3.3 Home Range . . . . . . . . . . . . . . . . . . . . . . . . 90ix5.3.4 Linear Movements . . . . . . . . . . . . . . . . . . . . 935.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 975.4.1 Circular Movement Patterns . . . . . . . . . . . . . . . . 975.4.2 Spatio-Temporal Partitioning Of Movement Behavior . . 985.4.3 Spatial Utilization Heterogeneity . . . . . . . . . . . . . 995.4.4 Conservation Priorities . . . . . . . . . . . . . . . . . . 1006 A Pan-African Analysis Of Fine-Scale Elephant Ranging Behaviour 1026.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1026.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1076.2.1 GPS Tracking . . . . . . . . . . . . . . . . . . . . . . . 1076.2.2 Range Area . . . . . . . . . . . . . . . . . . . . . . . . . 1076.2.3 Covariates . . . . . . . . . . . . . . . . . . . . . . . . . 1086.2.4 Statistical Modeling . . . . . . . . . . . . . . . . . . . . 1136.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1166.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1236.4.1 Model Interpretation . . . . . . . . . . . . . . . . . . . . 1236.4.2 Future Directions . . . . . . . . . . . . . . . . . . . . . 1266.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1277 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140AppendicesA ETD Chapter Supplementary Information . . . . . . . . . . . . . . 165A.1 Dataset D1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165A.2 Dataset D2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168A.3 Dataset D3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170A.4 Ellipse Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . 173B Mali Chapter Supplementary Information . . . . . . . . . . . . . . 176B.1 Meteorological Data And NDVI . . . . . . . . . . . . . . . . . . 176xB.2 Tracking Dataset Summary . . . . . . . . . . . . . . . . . . . . 178B.3 La Porte Des Éléphants . . . . . . . . . . . . . . . . . . . . . . . 179C PanAfEl Chapter Supplementary Information . . . . . . . . . . . . 180C.1 Temporal Granularity Index . . . . . . . . . . . . . . . . . . . . 180C.2 Covariate Information . . . . . . . . . . . . . . . . . . . . . . . 182C.3 LME & GAMM Model Diagnostics . . . . . . . . . . . . . . . . 184C.4 LME Model Parameters . . . . . . . . . . . . . . . . . . . . . . 186C.5 GAMM Model Parameters . . . . . . . . . . . . . . . . . . . . . 190C.6 LME Model Predictions . . . . . . . . . . . . . . . . . . . . . . 191C.7 GEE Python Script . . . . . . . . . . . . . . . . . . . . . . . . . 197xiList of Tables2.1 Loxobase Tracking Unit Summary . . . . . . . . . . . . . . . . . 112.2 Dataset regional summary . . . . . . . . . . . . . . . . . . . . . 182.3 Regional & Sexual median values of home range areas, path dis-tances, and maximum displacements . . . . . . . . . . . . . . . . 253.1 Immobility algorithm critical radius values . . . . . . . . . . . . . 485.1 Mali path & home range metrics statistical summary . . . . . . . 915.2 Summary of Mali home range metrics . . . . . . . . . . . . . . . 925.3 Mali linear path metrics summary . . . . . . . . . . . . . . . . . 955.4 Mali-Kenya path distance & home range comparison . . . . . . . 956.1 PanAfEl covariates . . . . . . . . . . . . . . . . . . . . . . . . . 1126.2 Covariate summary statistics . . . . . . . . . . . . . . . . . . . . 119A.1 Dataset D1 Weibull parameters . . . . . . . . . . . . . . . . . . . 167A.2 Dataset D2 Weibull parameters . . . . . . . . . . . . . . . . . . . 170A.3 Dataset D3 Weibull parameters . . . . . . . . . . . . . . . . . . . 173B.1 Tracking data summary . . . . . . . . . . . . . . . . . . . . . . . 178C.1 Covariate centering values . . . . . . . . . . . . . . . . . . . . . 183C.2 LME model parameters . . . . . . . . . . . . . . . . . . . . . . . 186C.3 GAMM model parameters . . . . . . . . . . . . . . . . . . . . . 190C.4 GAMM model smoother parameters . . . . . . . . . . . . . . . . 190xiiList of Figures2.1 Elephant collaring operation . . . . . . . . . . . . . . . . . . . . 122.2 Data Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162.3 First valid fix locations & total 100% MCP home ranges. . . . . . 192.4 Regional, Species & Sexual variation in yearly MCP home rangearea and path distance . . . . . . . . . . . . . . . . . . . . . . . 232.5 Continental elephant speed map . . . . . . . . . . . . . . . . . . 242.6 Multi-year variation in annual MCP home ranges . . . . . . . . . 273.1 System Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . 403.2 System Data Model . . . . . . . . . . . . . . . . . . . . . . . . . 413.3 System overview . . . . . . . . . . . . . . . . . . . . . . . . . . 443.4 Movement Rate algorithm example . . . . . . . . . . . . . . . . . 463.5 Immobility algorithm example alert . . . . . . . . . . . . . . . . . 503.6 Conceptual framework . . . . . . . . . . . . . . . . . . . . . . . 514.1 Path and ellipse geometry . . . . . . . . . . . . . . . . . . . . . . 594.2 ETD function morphologies . . . . . . . . . . . . . . . . . . . . 674.3 ETD models for three different sampling regimes . . . . . . . . . 694.4 ETD model percentile area comparison . . . . . . . . . . . . . . 704.5 ETD model spatial variation at 50%, 95% and 99% Weibull speeddistribution values . . . . . . . . . . . . . . . . . . . . . . . . . . 714.6 ETD model percentile areas at 50%, 95% and 99% Weibull speeddistribution values . . . . . . . . . . . . . . . . . . . . . . . . . . 724.7 Accuracy assessment . . . . . . . . . . . . . . . . . . . . . . . . 735.1 Gourma, Mali study area map and tracking data . . . . . . . . . . 84xiii5.2 Weekly centroid North-South & East-West movement . . . . . . . 895.3 Temporal NDVI selection . . . . . . . . . . . . . . . . . . . . . . 905.4 Mali time-density range hot-spots . . . . . . . . . . . . . . . . . 945.5 Male & Female velocity-grids . . . . . . . . . . . . . . . . . . . 966.1 16-day aLoCoH areas . . . . . . . . . . . . . . . . . . . . . . . . 1176.2 PanAfEl GAMM model smoothers . . . . . . . . . . . . . . . . . 122A.1 Dataset D1 speed distribution . . . . . . . . . . . . . . . . . . . . 168A.2 Dataset D3 speed distribution . . . . . . . . . . . . . . . . . . . . 173A.3 Ellipse geometry . . . . . . . . . . . . . . . . . . . . . . . . . . 175B.1 Meteorological data . . . . . . . . . . . . . . . . . . . . . . . . . 176B.2 NDVI north-south gradient . . . . . . . . . . . . . . . . . . . . . 177B.3 La Porte des Éléphants . . . . . . . . . . . . . . . . . . . . . . . 179C.1 TGI hypothetical time-line . . . . . . . . . . . . . . . . . . . . . 181C.2 TGI variation with time-span . . . . . . . . . . . . . . . . . . . . 181C.3 Covariate pair-plot . . . . . . . . . . . . . . . . . . . . . . . . . 182C.4 PanAfEl LME model diagnostic plot . . . . . . . . . . . . . . . . 184C.5 GAMM Model Diagnostic Plot . . . . . . . . . . . . . . . . . . . 185C.6 LME model predictions (NDVI) . . . . . . . . . . . . . . . . . . 191C.7 LME model predictions (Tree Cover) . . . . . . . . . . . . . . . . 192C.8 LME model predictions (Human Footprint) . . . . . . . . . . . . 193C.9 LME model predictions (Slope) . . . . . . . . . . . . . . . . . . 194C.10 LME model predictions (Protected Areas) . . . . . . . . . . . . . 195C.11 LME model predictions (Temporal Granularity Index) . . . . . . . 196xivAcknowledgmentsFirstly, I thank Dr. Iain Douglas-Hamilton (Save the Elephants) for my introduc-tion to the GPS tracking of elephants in 2003, provision of the tracking data used inthis research, financial support and for ongoing collaboration. I’d also like to espe-cially thank Dr. George Wittemyer (Save the Elephants/Colorado State University)for his tireless feedback and support, Dr. Valerie LeMay for patiently answeringquestions about mixed-effects modeling and her ongoing support, and to Dr. BrianKlinkenberg for acceptance into the lab for Advanced Spatial Analysis and all hissupport as my direct supervisor.At the University of British Columbia, I’d like to thank Dr. Anthony Sinclairfor his feedback on the Mali elephant chapter and to Dr. Lang Wu, Dr. CindyGreenwood and Ed Kroc for discussions surrounding the elliptical time-densitychapter. I also thank Dr. Dan Moore and Dr. Peter Arcese for their valuablefeedback and participation on my defense committee.In Kenya, I’d like to thank the Office of the President of the Republic of Kenyafor permission to conduct elephant research and to Patrick Omondi and the KenyaWildlife Service (KWS) for ongoing collaboration in tracking elephants acrossKenya. I’d like to thank Samburu and Buffalo Springs County Councils for per-mission to work in the adjoining reserves. I also thank David Daballen, GilbertSabinga, Barnerd Lesowapir, Chris Leadismo, Jerenimo Leperei, and the rest ofSave the Elephants, both in Nairobi and Samburu, for their years of hard work andcontributions to this research. Thanks to Henrik Rasmussen and Ivy Mutiso at Sa-vannah Tracking and Place du Chaos. I thank the Mara Elephant Project (MarcGoss, Maddy Goss, Richard Roberts, Susie Feshenfeld), Ian Craig, Mike Watson,John Pameri, Geoffery Chege, Jamie Roberts and Susannah Rouse for all theircontributions to elephant tracking. I also thank David Gachuche and Tom Kioko atRivercross Technologies and the Safaricom Foundation, Kenya.xvIn Mali, I thank the Government of Mali (Ministry of Eaux et Forêts) for sup-porting and facilitating this research, the US Embassy in Bamako (especially Mr.Oumar Konipo) for logistical support, and especially Mr. El Mehdi Doumbia (Chefd’Antenne, Eaux et Forêts, I-n-adiatafane) for local elephant knowledge, field workand community liaison. I thank Mike Deutsch his field work and the human foot-print project. I also thank the Mali collaring team for the difficult operation in2008.In South Africa, I especially thank Dr. Michelle Henley and Marlene Mc-Cay for their ongoing support. At the Wildlife Conservation Society, I thank Dr.Samantha Strindberg and Dr. Steve Blake for their contributions to the Pan-Africanelephant dataset and discussions and ideas.At Esri, I thank Charles Convis and Sasha Yumakaev for provision of ArcGIS®software through the Esri Conservation Program and to Bob Meyering and RichieCarmichael for helping me get started with the ArcMET extension.At Google, I thank Rebecca Moore, Tanya Birch and the Earth Outreach andEarth Engine teams for their ongoing support.My research was supported financially by the Natural Sciences and Engineer-ing Research Council of Canada (PGSD3 #348450), Save the Elephants, Universityof British Columbia, my family and Evelyn Voigt.Finally, and very importantly, I extend a special thank-you to my parents, toChristina Toms and all my friends and family for their years of support.xviChapter 1Introduction1.1 IntroductionMovement is the ambulatory process that links terrestrial wildlife with resourcesin the surrounding environment. Geospatial analysis of movement is, therefore,an important area of research for furthering our understanding of the ecology andconservation of free-ranging terrestrial wildlife and their habitats. The science ofanimal tracking1 is advancing rapidly and can provide insight into the spatial be-haviour of diverse and sometimes difficult-to-monitor species. Along with evolvingtracking technologies, there is a growing list of analytical methodologies being ap-plied in the study of animal movement and the field of movement ecology — whichaddresses such topics as resource selection, home range, dispersal, migration andwildlife corridors — has recently claimed its own specialty field status (Holden,2006; Nathan et al., 2008).African elephants (Loxodonta africana and L. cyclotis) are a particularly im-portant species for geospatial study. From an ecological perspective, they are thelargest extant terrestrial mammals and capable of consuming 6% of their bodyweight in vegetation per day (e.g., 600 Kg for a large bull), placing them at the topof the class of megaherbivores2 (Owen-Smith, 1988). Elephants have also beendescribed as megagardeners and landscape engineers who are capable of directlyshaping their surrounding environment by felling trees (Western, 1989; Campbell,1992), growing them (Blake et al., 2009; Campos-Arceiz & Blake, 2011; Beauneet al., 2013), or creating water points used by other species (Haynes, 2012).1Animal tracking by early human hunters was proposed as the origin of all science (Liebenberg,2001)2Megaherbivores are defined as any animal weighing over 1000 Kg and there are currently nineextant species1Chapter 1: IntroductionElephant movements and home ranges are extensive and among the largestof terrestrial mammals in Africa (Lindeque & Lindeque, 1991; Thouless, 1995).Their need for space is a characteristic largely at odds with the rapidly expandinghuman footprint in Africa (Sanderson et al., 2002). The building of roads, thesprawl of urban areas and construction of fences can destroy and fragment elephanthabitat (Blake et al., 2008) and incidences of human-elephant conflict (HEC) areon the rise (Thouless, 1994; Hoare & Du Toit, 1999; Jackson et al., 2008; Grahamet al., 2009). Most recently, a resurgence in the illegal killing of elephants for theirivory tusks has resulted in an estimated 100,000 animals killed between 2010-2012 (Wittemyer et al., 2014). The study of elephant range and spatial behaviouris, therefore, a key component of conservation and management efforts as well ascontributing to scientific knowledge about elephants as a species.Chief among techniques for recording animal movement is the U.S. Govern-ment NAVSTAR Global Positioning System (GPS) (Rodgers, 2001; Hebblewhite& Haydon, 2010). Introduced commercially in 1989, GPS was quickly adopted bythe wildlife community after the development of receivers integrated with a bat-tery, solid state storage and a micro-controller encased in a weatherproof housing,which were then attached to an animal, generally on a collar affixed around an ani-mal’s neck (Rempel et al., 1995; Rodgers et al., 1996). GPS positioning can recordthe position of a tracked animal at regular intervals and in almost all conditions(e.g., at night) – a characteristic particularly useful with cryptic or otherwise dif-ficult to follow species (Hebblewhite & Haydon, 2010; Tomkiewicz et al., 2010).Despite the cost of units (Hebblewhite & Haydon, 2010), and the associated track-ing data management and analysis issues (Millspaugh & Marzluff, 2001; Cagnacci& Urbano, 2008), GPS tracking is a useful lens through which we can observe ani-mal spatial behaviour in terrestrial ecosystems. African elephants were among thefirst species of wildlife tracked globally using GPS technology (Douglas-Hamilton,1998; Blake et al., 2001). Their ability to carry relatively heavy payloads and ap-parent behavioural ambivalence to the presence of a collar (Horback et al., 2012)also make them well suited to GPS tracking.2Chapter 1: Introduction1.2 Objectives & OverviewThe objectives of my doctoral research are to: i) develop an efficient, scientificframework for managing elephant GPS tracking data collected in real-time, a frame-work that could also be applicable to a variety of other species, ii) to developnew geospatial methods for analysis of complex tracking data and; iii) to use GPStracking to further our understanding of elephant movement ecology and conser-vation. This third objective is particularly timely in light of the rapidly changinganthropogenic landscape in Africa, and the acute threat to elephant populationsnow posed from the illegal ivory trade (Wittemyer et al., 2014). Prevailing themesthroughout this research include tracking data management, along with geospatialanalysis methods and software critically important for GPS tracking data spatio-temporal correlations at variable scales. To meet the objectives, I worked in part-nership with the organization Save the Elephants (STE) in Kenya, who generouslyprovided access to the most comprehensive dataset on elephant movement in theworld (approximately 3.2 million recorded locations from 247 elephants acrossAfrica). In this introductory chapter, I briefly outline my research chapters; rele-vant literature and background are presented within each chapter.What is an appropriate method to collect, store, disseminate, visualize andanalyze elephant tracking data? In Chapter 2 I explore the problem of man-aging data collected by modern GPS tracking devices. The large volumes of datagenerated, and the temporality of tracking data, create challenges to data manage-ment and analysis. To meet these challenges I developed a custom tracking system(Loxobase) built around a centralized cloud database to automate ingestion andstorage of GPS tracking data. I also developed software for the rapid retrieval ofdata, including a system for geovisualization using Google Earth (Google, 2013)and for analysis using Esri ArcMap (Esri, 2013) software. In order to demonstratethe utility of the centralized system I perform an exploratory movement analysis bycalculating statistics and metrics for elephants across Africa. The analysis providesthe first comprehensive quantitative summary of Save the Elephants’ movementdataset and demonstrates the utility of the Loxobase tracking system approach, anapproach that is also applicable within the wider context of multi-species tracking.3Chapter 1: IntroductionCan we leverage real-time tracking data for management and conservation?In Chapter 3 I seek to address two fundamental questions related to the conserva-tion and management of target species: ‘what is the current location of an animal?’and ‘what is the animal doing?’. I explore how data being collected from collarscapable of transmitting positional data over GSM or Satellite networks can be usedto answer these important questions through both visualization and continuous,algorithmic analysis. I developed four routines to monitor elephant movement be-haviour in real-time and issue alerts in the event that certain conditions are metwith regards to: i) proximity, ii) geofencing, iii) immobility, and iv) movement rate.The real-time monitoring system is a novel approach to the geospatial analysis oftracking data and has provided a new tool in the efforts to protect elephants andwildlife in general. It has since been adopted for operational use in Kenya andSouth Africa for anti-poaching efforts.Can we estimate wildlife space-use from tracking data? In Chapter 4 I ad-dress the intrinsic problem of how to estimate wildlife space-use from discrete-time tracking data – an important component for resource selection analyses – es-pecially when analyzing data acquired under different temporal sampling regimes.Many widely used methods (e.g., Kernel Density Estimator) are not well-suitedto estimate fine-grained spatial use from time-series data. I therefore developeda new technique for estimating an animal’s space-use distribution called the El-liptical Time-Density (ETD) model. The method begins by identifying ellipticalconstraining regions related to an animal’s speed distribution between successivepoints and calculates the expected value of a time-density function across each re-alizable ellipse area. The time-density function used within the ETD model is anovel approach compared with other previous time-geographic methods. The ETDmethod has biologically interpretable parameters and makes no assumptions aboutthe form of movement undertaken by an animal. I show that it out-performs severalother methods in its ability to characterize space-use from discrete spatio-temporalsampling. I also present software to calculate ETD and detail use of a Bayesianapproach for determining the Weibull distribution parameters used to model thespeed distribution of an animal. Although developed and applied to elephant track-ing data, the method is easily generalized to other species.4Chapter 1: IntroductionWhat do tracking data tell us about the movement patterns of the Sahelianelephants in Mali? In Chapter 5 I address the question of what tracking datacan tell us about the ecology and conservation of a small but special populationof elephants living in the Gourma region of Mali. Based on data from nine col-lars deployed in 2008 I characterize the unique circular movement pattern of thesenorthernmost elephants in Africa. I also developed a novel velocity-grid methodas an approach for spatially summarizing landscape-wide velocity characteristicsover multiple individuals and use this method to identify travel corridors. I foundthat the Gourma elephants have the largest range of elephants in Africa and theirmovements are closely correlated to vegetation phenology and precipitation. Basedon the tracking data I identify core range areas and conservation targets, and showthat males and females have different movement strategies.What do tracking data tell us about the factors influencing elephant rangeacross Africa? In Chapter 6 I address the questions of i) can we identify popula-tion level endogenous/exogenous movement covariates by performing comparativeanalyses of tracking data across wide geographical gradients, and; ii) what does thisapproach tell us about continent-wide elephant ranging behaviour? I used shortduration (16-day) temporal windows to analyze ranging behaviour from trackingdata collected across Africa: desert (West), forests (Central), savannah (East) andbushveld (South). I examine the relationship between range size and concomitantvariables such as the Normalized Difference Vegetation Index (NDVI), percent treecover, human footprint, protected area intersection, slope, dataset quality, sex andregion. Using mixed-effects modeling I test five hypotheses about the continentalranging behaviour of elephants: H1: Elephant range size will decrease as vegeta-tion quality increases within the range area, H2: Elephant range size will decreaseas vegetation abundance increases within the range area, H3: Elephant range sizewill decrease in areas of high anthropogenic influence, H4: Elephant range size willdecrease inside of protected areas, and; H5: Elephant range size will decrease withincreasing hilliness (slope). The Pan-African elephant analysis synthesizes knowl-edge about the continental ranging behaviour of elephants for the first time andprovides a novel analytical and conceptual approach based on emergent geospatialtechnology and statistical techniques.5Chapter 1: IntroductionI conclude the thesis with a final chapter (Chapter 7) summarizing resultsof these five research chapters and suggest directions for future research. I alsopresent an extensive appendix that contains computer code, technical material andadditional figures for relevant chapters. Many of the analyses in this research wereperformed using custom software I developed for the analysis of movement data.The analysis package (Movement Ecology Tools for ArcGIS: ArcMET) extendsArcGIS Desktop software. ArcMET, and user manual, have been made freelyavailable at: www.movementecology.net.6Chapter 2Loxobase: An African ElephantTracking System2.1 IntroductionTracking animals using remotely attached tracking devices can provide great in-sight into wildlife spatial behaviour and has become an important methodology inthe field of movement ecology (Nathan et al., 2008; Hebblewhite & Haydon, 2010).Animal tracking is also being used for applied species monitoring programs as be-ing run by national parks and other private and public conservation infrastructures,in order to inform management and conservation efforts (Geremia et al., 2014).The Global Positioning System (GPS) has played a major role in furthering thescience of animal tracking by enabling the acquisition of animal positional data atfiner temporal and spatial scales than could be achieved using other methods (e.g.,Very High Frequency radio tracking) (Millspaugh & Marzluff, 2001; Hebblewhite& Haydon, 2010).African elephants are an important species to monitor spatially because of theirwide-ranging movements and needs for space, their interesting movement ecol-ogy, the potential impact they can have on vegetation and the environment (Gulde-mond & van Aarde, 2008), because of their proclivity to raid farm crops leadingto conflict with humans (Thouless, 1994; Graham et al., 2009) and because ofregional threats from poaching that are now severely threatening extant popula-tions (Wittemyer et al., 2014). The movements of elephants have been studiedacross Africa for decades, beginning first with deployment of radio telemetry col-lars (Douglas-Hamilton, 1971) and later in fine detail using GPS tracking collars(Douglas-Hamilton, 1998; Blake et al., 2001). Since 1998, the Kenya-based orga-7Chapter 2: Loxobase: An African Elephant Tracking Systemnization Save the Elephants (STE) has undertaken an intensive elephant trackingprogram that started in Samburu Reserve, Kenya, with the goal of characterizingelephant spatial movements and applied species management and conservation.The tracking program has now expanded to four distinct regions of Africa: i) theSahel of West Africa, ii) the forests of Central Africa, iii) the savannahs of EastAfrica, and; iv) the bushveld of Southern Africa. Initial results from this track-ing program have been reported in (Douglas-Hamilton et al., 2005; Cerling et al.,2006; Wall et al., 2006; Wittemyer et al., 2007b; Blake et al., 2007; Wittemyeret al., 2008; Blake et al., 2008; Ngene et al., 2009, 2010; Wall et al., 2013, 2014a,b;Bohrer et al., 2014).Continent-wide data such as these provide a unique opportunity to answerquestions about comparative movement characteristics and gain insight into themovement ecology of elephants as a species (Avgar et al., 2013), and inference isstrengthened when considering large sample sizes of individuals recorded across awide range of conditions (White & Garrott, 1990; Millspaugh & Marzluff, 2001;Avgar et al., 2013). Even broad questions about elephants, such as ’does move-ment behaviour vary depending on region, species or between sexes?’ remainlargely unanswered. Understanding the similarities and differences and the proba-ble drivers of broad scale movement patterns in African elephants is important fortheir future conservation and landscape planning (Croze & Moss, 2011).High-resolution GPS tracking data come at the cost of data management com-plexity. A necessity in any research program is establishment of a well-defineddata processing work flow that is scientifically reproducible, can scale to meetdata volume and security needs and also satisfy the needs of a diverse commu-nity of users (Rodgers, 2001; Cagnacci & Urbano, 2008; Hebblewhite & Hay-don, 2010; Urbano et al., 2010; Fiedler & Davidson, 2012). Urbano et al. (2010)specifically outline a set of 13 requirements for modern tracking systems (Datascalability, Long-term storage for data reuse, Periodic and automatic data acqui-sition, Efficient data retrieval, Management of spatial information, Global spatialand time references, Heterogeneity of applications, Easy implementation of newalgorithms, Integration of different data sources, Multi-user support, Data sharing,Data dissemination, Cost-effectiveness). At the start of this research there were noknown publicly available solutions that provided the holistic approach needed for8Chapter 2: Loxobase: An African Elephant Tracking Systemtracking elephants for both research and management/conservation objectives. Acritical first step in order to handle the voluminous data requirements from a pan-African tracking program was to develop a tailored tracking system meeting allnecessary requirements, and which I hereafter refer to as Loxobase, consisting of acentral database and constellation of programs for ingesting, storing and dissemi-nating data. Loxobase has several design similarities with other enterprise trackingsystems (i.e., multi-user and large-scale systems) such as Movebank (Kranstauberet al., 2011; Fiedler & Davidson, 2012) or ISAMUD (Cagnacci & Urbano, 2008;Urbano et al., 2010), systems that have undergone parallel development.Compounding the technical and analytical challenges in synthesizing continen-tal or global movement datasets are the associated computational challenges forefficient computing of ’big data’ (e.g., ’batch-mode’ execution of tools to iteratealgorithms over multiple datasets, facilities to segment datasets over fine-grainedspatial or temporal windows, book-keeping functionality to store parameter infor-mation and other algorithm results, facilities to take advantage of parallel process-ing in modern computer architecture, tools for linking movement data with envi-ronmental covariate information, and the need for a standardized movement datastorage format). In order to address these issues I first developed a dedicated ani-mal movement analysis package (ArcMET: Movement Ecology Tools for ArcGIS)to provide a framework for movement data analysis that I found lacking with otheranalytical tools.The objectives of this opening chapter are therefore to address: i) how to collectand synthesize data on African elephant movements from across the continent, ii)how to establish a framework for accessing and analyzing large volumes of move-ment data, and finally iii) how to use this framework to provide a broad quantitativesummary of available datasets. In order to demonstrate the utility of Loxobase, Ipresent a broad regional comparison of standard home range metrics and lineartravel distances calculated from Loxobase movement data collected between 1998and 2013.9Chapter 2: Loxobase: An African Elephant Tracking System2.2 Loxobase Description2.2.1 Tracking Unit AttachmentMovement data are collected from elephants by affixing a tracking unit using alength of belting around the neck of the animal (mean circumference: 260 cm(female), 330 cm (male)) following chemical immobilization by a veterinary doctor(Figure 2.1). The tracking unit is designed to rest at the crest of the shoulders onthe animal’s neck while a counter-weight at the opposite side of the belting loopensures the unit will remain facing skyward (Douglas-Hamilton, 1998; Soltis et al.,2012). Elephants are not as restricted when compared with some species such asbirds in the size and weight of the tracking payload, and there are no known effectson the behaviour or biology of individuals wearing collars (Horback et al., 2012).Either etorphine or carfentanil hydrochloride were used to chemically immo-bilize animals for collar fitting, administered using a high-velocity dart (e.g., DANInject or Teleinject) fired into the muscle of the animal (Kreeger & Arnemo, 2012).While immobilized, water is poured over the elephant’s ears in the absence of me-chanical cooling to prevent the animal from over-heating. The collar belting issecured with stainless steel hardware within a safety limit of 20 minutes. Chemicalimmobilization must be counter-acted by administering a reversal drug (e.g., nal-troxene or diprenophine). Elephants typically regain their feet in under 20 minutes.2.2.2 Tracking Unit Description & TypesA typical tracking unit used in this study contains a GPS receiver, non-volatilememory for on-board storage of data and a Very High Frequency (VHF) radio bea-con (Rodgers, 2001). A summary of collar models and manufacturers is provided(Table 2.1).2.2.3 Collar Deployment LocationsFrom 1998 to 2013 collars have been deployed onto elephants in Mali, Gabon,Congo, Central African Republic, South Africa and Kenya (Figure 2.3). Selectionof individuals was a mix between choosing individuals known to researchers in thestudy areas, and randomly selecting animals for collar deployment. Big bulls and10Chapter 2: Loxobase: An African Elephant Tracking SystemTable 2.1: A summary of tracking units used to track 247 elephants across Africabetween 1998 - 2013 by Save the Elephants: AWT (African Wildlife Tracking,Pretoria, South Africa), LOTEK (LOTEK Engineering Ltd., Newmarket, ON,Canada), ST (Savannah Tracking, Nairobi Kenya), TVP (Televilt Positioning AB,Lindesberg, Sweden).Manufacturer Model DataTransmissionMethodLoxobaseAcquisitionMethodUnits DeployedAWT A SMS / GSM AWT API 22AWT AM SMS / GSM AWT API 39AWT AG TCP/IP / GSM AWT API 25AWT MT2000 TCP/IP /SatelliteSky-Q API 134LOTEK 1000 UHF Modem Manual Upload 23LOTEK 2000 ManualInterfaceManual Upload 22ST GL100 TCP/IP / GSM Animal-LinkCOM Port10ST EPS8 TCP/IP / GSM ST API 2ST NHDS SMS / GSM GSM Modem 5ST RF UHF Modem Manual Upload 7TVP SIMPLEX VHF Modem Manual Upload 13TVP T5H SMS / GSM GSM Modem 4TVP GSL01 Satellite E-Mail 10TVP T5HS Satellite E-Mail 17TVP T10HS Satellite E-Mail 311Chapter 2: Loxobase: An African Elephant Tracking SystemFigure 2.1: An example elephant collaring operation with Dr. Ephantus of theKenya Wildlife Service changing a collar on ’Mountain Bull’ at Lewa WildlifeConservancy in Northern Kenyafemales with large tusks were increasingly favored from 2009 in response to theincrease in elephant poaching levels in Central and East Africa (Wittemyer et al.,2011, 2014). Other choices include individuals known to crop-raid frequently, orwho are believed to have interesting and far ranging movements.2.2.4 Movement Data DownloadPositional data are retrieved either via direct interface with a recovered collar orvia remote transmission by a collar unit (Table 2.1). LOTEK and TVP SimplexVHF and UHF transmission require positioning of a modem to within <3 km line-of-sight of a collar unit (elevated positions such as hilltops or using aircraft arepreferred). LOTEK 1000 models were programmed on a monthly duty cycle oftransmitting data one day per month in order to save on power consumption and aredescribed by Douglas-Hamilton (1998); Blake et al. (2001). Newer ST-RF modelshave a longer distance transmit range of up to 10 km and data can be downloadedat any time.12Chapter 2: Loxobase: An African Elephant Tracking SystemCertain collar models are also capable of transmitting data as they are collectedin real-time using either the Short Message Service (SMS) or via a data connec-tion using Transmission Control Protocol/Internet Protocol (TCP/IP) over eithersatellite-based or Global System for Mobile Communications (GSM) networks,making them especially useful for real-time monitoring applications (Wall et al.,2014a). The SMS format limits message content to 160 characters; therefore, re-cent collar models have adopted the use of data connections (TCP/IP) in preferenceto SMS since transmission is faster, cheaper and there is not a limit to the amountof data that can be sent. GSM coverage has increased dramatically in many parts ofAfrica since its first introduction, although there are many parts of the elephants’range throughout Africa where coverage does not yet exist.Dataset collation and storage are coordinated by custom built Animal-Link soft-ware running on a Microsoft Windows-based server hosted in the Amazon Elas-tic Compute Cloud (EC2) (http:// aws.amazon.com/) cloud-based environment.Animal-Link was developed using the Microsoft C# programming language, theMicrosoft .Net 4.0 framework, and the Environmental Systems Research Institute(Esri) Engine Runtime version 10.2 ArcObjects class library.Ingestion of data by Animal-Link occurs in a variety of ways: data from LOTEK1000 & 2000 series and Savannah Tracking RF units (i.e., collars that are manuallydownloaded) are ingested by Animal-Link by first manually uploading a format-ted csv file to a server folder being monitored by Animal-Link (e.g., using FileTransfer Protocol (FTP), or more recently, Dropbox (www.dropbox.com)). Track-ing data from AWT GSM collars is telemetered using one of three methods: ’A’and ’AM’ units transmit via a SMS message to a server located in South Africawhile AWT ’AG’ units telemeter data using a TCP/IP data connection. Data fromall three AWT GSM models are stored in a database operated by AWT and madeavailable for download using a Hyper Text Transport Protocol (HTTP) Applica-tion Programing Interface (API). Animal-Link is therefore set to query the AWTAPI on a frequent basis and request new positions. Data from AWT Satellite unitsare telemetered using a data connection via the Inmarsat satellite constellation toa data download center located in Australia. These data are made available via aSimple Object Access Protocol (SOAP) API called the Sky-Q API. Data from Sa-vannah Tracking GL-100 units are telemetered directly using a TCP/IP data con-13Chapter 2: Loxobase: An African Elephant Tracking Systemnection and are received on a communications port being continuously monitoredby Animal-Link. TVP GSM data is routed from a collar unit over a GSM networkand received by a modem located in Nairobi, Kenya. Custom built MessageServersoftware provides an API that can be used by Animal-Link to retrieve SMS recordreceived locally by the Kenya GSM modem. Data from TVP satellite-based collarsis transmitted and received remotely by TVP in Sweden. The data is then sent byE-mail to a POP3 account monitored by Animal-Link.2.2.5 Movement Data StorageOnce received by Animal-Link, data are stored in a ’AnimalTracking’ PostgreSQLdatabase. PostgreSQL is a high-performance, open-source and free database man-agement system (DBMS) that supports a relational table model and standard struc-tured query language (SQL) based queries.The basic unit of data structure is a movement dataset defined to be the time-ordered series of location estimates acquired at discrete times by a single trackingunit for a single animal (called a chronofile within the system) and uniquely iden-tified by a chronofile identification number. An animal, defined uniquely in thedatabase by its name identifier, may have multiple chronofiles if the animal wastracked over multiple periods with different tracking units (or could hypotheticallywear two devices simultaneously).The TrackingMaster table contains data relevant to each dataset and the integerchronofile value acts as the primary key for the table and specifies each uniquecombination of animal with a collar unit. The data_starts and data_stops columnsprovide important information when filtering data to remove fixes acquired beforea unit was put on an animal or after it was taken off. These data must be collectedand recorded in the field during collaring operations.GPS positional records are stored in the archive_loc table in their native lati-tude/longitude format with reference to the WGS84 datum. Time information isstored in Universal Coordinated Time (UTC) using a PostgreSQL timestamp datatype. A SQL outer join on the TrackingMaster using the chronofile number recov-ers information about the dataset such as the collar ID number, animal name, ani-mal sex, etc. A unique Recordserial integer uniquely identifies each record within14Chapter 2: Loxobase: An African Elephant Tracking Systemthe archive_loc table and incrementally increases with the addition of each new row(a PostgreSQL bigserial data type capable of storing values up to ~9E18). Indexingthe archive_loc table allows for fast chronological sorting within each chronofilefor record retrieval. A PostgreSQL UNIQUE policy applied to the archive_loc ta-ble specifies that no two entries for a given chronofile can have the same fixtimevalue, ensuring that data cannot be duplicated in a table (although spatial overlapof coordinates is allowed as long as the fixtimes are different, since an animal maybe found at the same position more than once). The ability for the database toenforce the unique fixtime policy is one of the primary advantages of storing datawithin a database system compared with other file-based options.The TrackingUsers table stores details about patrons of the tracking system in-cluding their contact information and chronofile access lists. The TrackingUserstable enables data sharing and security so that users may or may not access move-ment datasets owned by other users. Data can also be specified as time-delayed if auser should not have access to real-time information about an animal’s whereaboutsfor security reasons.The Display table stores information useful when drawing location data withina GIS client such as Google Earth or Esri ArcMap. Animals are typically assigneda unique colour and/or position icon that helps visually interpret the movementdata. The HTMLInfo table stores HTML code for drawing a web page with furtherinformation relevant to an animal, including photos and biography if available. TheRegions table extends the TrackingMaster table by providing information regardingthe study site where a dataset’s first valid fix occurred.2.2.6 Movement Data RetrievalEfficient data retrieval by a user was a key design component of the system. Thesimplest method is via a Key Hole Markup Language (KML) data service that isaccessed via an HTTP request to the tracking server. The server-side applicationthat handles incoming HTTP queries from remote clients was built using MicrosoftASP.Net technology and is hosted within the Microsoft Internet Information Ser-vices version 7 (IIS7) framework. KML data can be consumed by a variety ofclients, but primarily using the Google Earth geo-browser both for desktop clients15Chapter 2: Loxobase: An African Elephant Tracking SystemARCHIVE_LOCChrono le SMALLINTRecordserial BIGSERIALCollar_ID TEXTFixtime TIMESTAMPDLoadTime TIMESTAMPLon DOUBLELat DOUBLEHeight DOUBLEGSM_Coverage SMALLINTTemperature DOUBLESpeed DOUBLEHeading DOUBLEFixstatus SMALLINTSatIDs TEXTDISPLAYName TEXTColour SMALLINT[]MarkerIcon TEXTPointStyle TEXTTrackStyle TEXTLogo TEXTHTML INFOName TEXTUseHTMLHTMlContentRAW TCPRecordserial BIGSERIALReceiveTime TIMESTAMPTcpString TEXTSenderIP TEXTREGIONSChrono le SMALLINTRegion TEXTCountry TEXTTRACKING MASTERChrono le SMALLINTCollarType TEXTCollarID TEXTActive BOOLEANDatasource TEXTFrequency TEXTAnimalID TEXTName TEXTSpecies TEXTDataStarts TIMESTAMPDataStops TIMESTAMPDateO TEXTSex TEXTUTC FLOATComments TEXTTRACKING USERSUsername TEXTPassword TEXTFirstName TEXTLastName TEXTOrganization TEXTPhonenumbers TEXT[]Emails []ReceiveSystemReports BOOLEANExpiry TIMESTAMPFullDataAccess INTEGERDelay DOUBLENotes TEXTChrono les SMALLINT[]Figure 2.2: The AnimalTracking database model at the core of the Loxobase sys-tem. GPS locations are stored within the archive_loc table. Each movement datasetis defined by a unique chronofile number and signifies a single tracking unit as-signed to a unique individual animal for a period of time. The TrackingMastertable provides information specific to each movement dataset, most importantlywhen the first and last valid fix locations occurred (data_starts & data_ends). TheTrackingUsers table provides control over user access to datasets and can also time-delay data if needed. The Display, Region & HTMLInfo tables extend the infor-mation contained in the TrackingMaster table and store data about how to displaydata in Google Earth/Esri ArcMap GIS clients, how to draw an HTML web pagefor a given animal and which region/country contains the dataset’s first valid fix.16Chapter 2: Loxobase: An African Elephant Tracking Systemand for mobile devices (e.g., Apple iOS iPhones and iPads and Google Androidphones and tablets). The KML tracking data API provides a quick way of visual-izing data and accessing the latest coordinates and movement of an animal. TheAPI will by default return the most recent 16-days of filtered data. Filtering isaccomplished using a cut-off speed and rejecting any GPS points in the animal’smovement path that could not be reached using a speed under the threshold value(currently set to 7 km/hr for elephants). The API also has the option of turningfiltering off to look at all raw locations and for expanding the time window be-yond the 16-day period. Temporal replay of data is possible in Google Earth usingthe ’time-slider’ functionality; a program feature that was integrated based on aspecific request by Save the Elephants (Rebecca Moore: Pers Comm).Data is also made available using an API for Esri clients (e.g., ArcMap). Theserver-side application was built using Microsoft Windows Communication Foun-dation (WCF) technology and is hosted using IIS7. Desktop clients install theLoxobase Downloader client application which is built using Esri Engine Run-time 10.2 software components, the Microsoft .Net 4.0 class library and the C#programming language. The Downloader connects to the Esri service using theTCP/IP protocol and updates a locally-stored Esri geodatabase with tracking datafrom the server AnimalTracking database. Authentication with a username/pass-word limits access to only chronofiles listed within the TrackingUser table. Datatransfer speeds are generally only limited by user internet connection speeds. Stor-age of data within a local Esri file geodatabase located on the client machine pro-vides offline access to data as well as retrieval of complete record sets for scientificanalysis on a user’s desktop machine. A database interface tool accessible withinthe Downloader lets users conduct advanced selection and filtering operations onstored locations and extract data for further analyses.2.3 Loxobase Synoptic AnalysisTo demonstrate a practical application of the Loxobase system and ArcMET soft-ware I now present a synoptic analysis of the Loxobase movement datasets and per-form a comparative analysis of select movement metrics calculated for four ecore-gions of Africa: Sahel (West), Forest (Central), Savannah (East) and Bushveld17Chapter 2: Loxobase: An African Elephant Tracking SystemTable 2.2: Summary of Loxobase tracking datasets by regionRegionCountry ofcollardeploymentElephantCountChronofileCountDatapointcountWest Mali 12 12 125846CentralCAR /Congo /Gabon34 34 37211East Kenya 146 224 2328739South South Africa 55 88 714055Total 247 358 3205851(South). Data collection by STE is on-going and I only consider data that werecollected between 1998 and 2013.2.3.1 Data RetrievalData were first extracted and filtered by chronofile using the Downloader program.Each chronofile was then checked visually for errors and then chronofiles werepooled into individual datasets by animal and projected to the appropriate Uni-versal Transverse Mercator (UTM) projection zone (either 31N, 33N, 33S, 34N,36S, 37N, 37S or 38S) and finally stored (grouped by common projection zone)as feature classes in an Esri file geodatabase (totaling 3,205,851 positions). Ani-mals are separable within a feature class by their unique name value stored withina MovDataID column.2.3.2 Travel Distance, Speeds & Home RangeAnimal travel paths (trajectories) were approximated using straight line interpola-tion between recorded locations up to a maximum of 36 hours. Trajectory pathswere calculated with the ArcMET Trajectory Path tool and a speed value was esti-mated per segment (speed = length/time).I summarized segment speed values across the continent by first establishing18Chapter 2: Loxobase: An African Elephant Tracking SystemEEEEEEEEEEEEEEEEEEEEEEEEEE EEEEEEEEEEEEEEEEEEEEEEE EEEEEEEEEEEEEEEEEEEEEEEEEE EESources: Esri, DeLorme, NAVTEQ, USGS, NRCAN, METI, iPC,TomTom, Copyright:© 2013 EsriTanaK e n y aChyuluLaikipia Mt KenyaSeraSamburuMasai MaraMarsabitShabaEEE EEEEEE EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEESources: Esri, DeLorme, NAVTEQ,USGS, NRCAN, METI, iPC,TomTomAPNRS o u t hA f r i c aKrugerM o z a m -b i q u eEEE EEEEEEEEEEEEEEEEEEESources: Esri, DeLorme, NAVTEQ, USGS, NRCAN, METI, iPC,TomTomC A ROdzalaNouabalé-Ndoki-DzangaC o n g oG a b o nLoangoLopéMinkébéIvindoGambaC a m e r o o nEEEEEEEEEESources: Esri, DeLorme, NAVTEQ, USGS, NRCAN, METI, iPC,TomTomGourmaM a l iWESTCENTRALEASTSOUTHFigure 2.3: A map illustrating the collar deployment locations for (first valid fix lo-cation) for 358 elephant movement datasets (representing 247 individual animals)collected between 1998 and 2013. Range extent (combined yearly 100% MCPranges calculated for each individual) are shown as blue polygons, (Total Area =149,125 km2). Green polygons demarcate protected areas (source: World Databaseon Protected Areas (IUCN & UNEP-WCMC, 2013))). Elephant species in West,East and South regions are Loxodonta africana compared with Loxodonta cyclotisin the Central region.19Chapter 2: Loxobase: An African Elephant Tracking Systemlandscape wide grids with a relatively coarse grid resolution (5 x 5 km) for eachregion. Using Esri ArcMap software (Esri, 2013), I then calculated mean speedvalue for each grid cell based on a minimum of five intersecting trajectory segmentsper cell (otherwise the grid cell was assigned a ’NULL’ value).Annual total travel distances and maximum displacements were calculated us-ing the ArcMET Trajectory Metrics tool (using temporal window dates producedby the ArcMET MovWinDates tool). Annual periods for each animal starts withthe first valid location in an animal’s dataset up to the available number of full yearsof data. Straight-line movement between successive positions was assumed for alllinear metrics and therefore reported values are minimums.Selection of a range estimator is complicated by the variety of strengths andweaknesses of different methods (Horne & Garton, 2006; Powell & Mitchell, 2012;Fieberg & Börger, 2012). Although newer space-use estimators exist that are de-signed to handle the highly-correlated nature of GPS tracking data (e.g., the Brown-ian Bridge Movement Model (Horne et al., 2007) or Elliptical Time-Density (ETD)model (Chapter 4)), I chose the Minimum Convex Polygon (MCP) range estima-tor (Blair, 1940; Mohr, 1947; Odum & Kuenzler, 1955) to promote comparisonwith previous studies on African elephant movements (e.g., (Lindeque & Lind-eque, 1991; Thouless, 1996)). For further comparative opportunities I have alsocalculated both Local Convex Hulls (’adaptive’ parametrization (aLoCoH) (Getz& Wilmers, 2004; Getz et al., 2007)) and Kernel Density Estimators (KDE) (Wor-ton, 1989) characterized at the 50%, 90%, 95% and 100% (99% for KDE) isoplethlevels. All range estimators were calculated for the same annual periods as traveldistances.2.3.3 Statistical ModelI performed statistical analyses on yearly 100% MCP home range areas and yearlypath travel distances using the categorical explanatory variables Region (’West’,’Central’, ’East’, ’South’) (Figure 2.3) and Sex (’Male’, ’Female’) in order tocharacterize yearly movement metrics (note that all elephants in the ’Central’ re-gion are Loxodonta cyclotis species compared to Loxodonta africana in all otherregions and, therefore, Region is also a covariate for species). MCP range was20Chapter 2: Loxobase: An African Elephant Tracking Systemlog-normalized to meet residual normality assumptions (Zuur et al., 2009). Obser-vations over multi-year periods for some individuals meant that these observationswere not independent and therefore multilevel models were fit with the nlme pack-age (Pinheiro & Bates, 2013) using R statistical software (R Core Team, 2013) bygrouping observations by animal and treating animal as a random effect (Pinheiro& Bates, 2000). The varIdent structure within the nlme package permitted fittingseparate residual covariance parameters by both region and sex to account for resid-ual heterogeneity (Pinheiro & Bates, 2000). The generalized model specificationfor both linear mixed effects models is:log10 (MCPit) = Regioni +Sexi +RegioniSexi +αi + εit (2.1)PathDistit = Regioni +Sexi +RegioniSexi +αi + εit (2.2)whereαi is the random variation per animal and εit is the within-animal residualerror.Linear hypothesis testing of model parameters was made at the 0.05 confidencelevel using the generalized linear hypothesis test (glht) function in the multcomppackage in R (Hothorn et al., 2008) and correcting for multiple comparisons (Tukeycontrasts).2.4 ResultsThe Loxobase system is an enterprise-level centralized tracking system with 140currently active users capable of instantly accessing up-to-date elephant move-ment data using either of the custom KML or Downloader APIs and is comparablein morphology to other tracking systems since developed and specific to animalmovement (e.g., Movebank (Kranstauber et al., 2011; Fiedler & Davidson, 2012),ISAMUD (Cagnacci & Urbano, 2008; Urbano et al., 2010)).Loxobase houses data from a total of 247 elephants (358 movement datasets)that were tracked between 1998 and 2013, resulting in 3,205,851 total filteredpositions. An approximately even distribution of males (131) and females (116)are represented (Table 2.2). First valid-fix locations for each chronofile are seenin Figure 2.3. Positions were most frequently sampled at 1-hour intervals (24221Chapter 2: Loxobase: An African Elephant Tracking Systemchronofiles) ranging up to 24 hour intervals (12 chronofiles) with only one datasetsampled at longer intervals. The longest continuous dataset from a single collar was7.1 years (Chronofile 239) and the bull Morani in Kenya was the longest trackedindividual (9 years).The continental speed map (Figure 2.5) shows considerable variation in thetravel speeds of elephants across the continent as well as heterogeneity within re-gions. The Mali elephants show especially high travel speeds compared with otherregions. Localized areas of high-speed movement are possibly indicative of travelcorridors and streaking (Douglas-Hamilton et al., 2005).Yearly linear travel distances ranged from a minimum of 957 km by the malePfeffer in Ivindo, Gabon to 5120 km by the female Timurid in Samburu, Kenya.Median yearly travel distances are reported (Table 2.3). The multilevel model(Equation 2.2) found no significant differences in travel distance between the sexesin any of the four regions (South: p < 0.93, East: p < 1.00, Central: p < 1.00,West: p < 1.00). However, there were significant regional differences in lineartravel distances between all regions in the order West > East > South > Central.22Chapter 2: Loxobase: An African Elephant Tracking SystemllllllllllllllllllWestSouthEastCentral050001000015000200002500030000Yearly 100% MCP HR Area (Km2 )llllllllllllllllllllllllMaleFemale050001000015000200002500030000lllWestSouthEastCentral10002000300040005000Yearly Path Distance (Km)lMaleFemale10002000300040005000Figure 2.4: Regional, Species and Sexually based variation in home range size(100% MCP estimator) and yearly linear path distance. Box-widths are propor-tional to sample sizes. Elephants in the ’Central’ region are Loxodonta cyclotiscompared to Loxodonta africana in all other regions.23Chapter2:Loxobase:AnAfricanElephantTrackingSystemCopyright:© 2013 EsriCopyright:© 2013 EsriCopyright:© 2013 EsriCopyright:© 2013 EsriMean SpeedKm/Hr0.1040.105 - 0.3600.361 - 0.5250.526 - 0.7210.722 - 0.9770.978 - 1.261.27 - 1.591.60 - 2.072.08 - 2.692.70 - 3.343.35 - 4.60Figure 2.5: A continental elephant (Loxodonta africana and L. cyclotis) speed map summarizing mean travel speeds fromLow (Green) to High (Red). Data are summarized using 5 km x 5 km grid squares. A minimum of 5 intersecting tracks wasrequired before calculating statistics for a grid cell. Note that the scale of each map varies given the differing regional spatialextents.24Chapter2:Loxobase:AnAfricanElephantTrackingSystemTable 2.3: Median values of yearly home range areas, path distances, and maximum displacements according to region andsexRegionMCP Range Area(km2)LoCoH RangeArea (km2)KDE Range Area(km2)Path Distance(km)MaxDisplacement(km)50% 100% 50% 100% 50% 99%M F M F M F M F M F M F M F M FWest 5439 9335 16338 20860 137 325 3549 4979 2011 4770 17011 27773 3707 3597 191 212Central 41 30 575 119 10 10 363 84 34 44 703 283 1209 1227 38 31East 226 128 1204 670 39 34 559 408 135 80 912 654 2860 2804 59 43South 262 160 1809 899 66 59 983 572 186 140 1712 1010 2438 2349 67 5125Chapter 2: Loxobase: An African Elephant Tracking SystemElephant yearly 100% MCP home ranges ranged from a minimum of 40 km2for the female Malonge in Loango, Gabon (Figure 2.3) to 31,332 km2 for the fe-male Ramata located in the Gourma, Mali (although not assessed yearly, comparewith 33 km2 in Lake Manyara, Tanzania (Douglas-Hamilton, 1972); 72 – 4451 km2in Kruger National Park, SA (Grainger et al., 2005); 102 – 5527 km2 in Laikipia,Kenya (Thouless, 1996); 5800 – 8700 km2 in Namibia (Lindeque & Lindeque,1991)). Median home range values for MCP, aLoCoH and KDE at different iso-pleth levels are reported (Table 2.3).Male elephants had the greatest inter-quartile range (IQR) in yearly 100% MCPranges (1854 km2 IQR) compared to females (888 km2 IQR). Combining all 100%MCP polygon range areas (including animals with less than one-year of data) ledto a single overall range area of 149,125 km2 comprising 5% of the current totalcontinental range of African elephants (i.e. ’Known’ + ’Possible’ = 3,366,405 km(AfESG, 2013)). Year to year variation in 100% MCP home range areas werehighly variable and individualistic (Figure 2.6).A regional comparison of log transformed 100% MCP ranges based on themultilevel statistical model (Equation 2.1) showed male ranges were significantlygreater than female ranges in South Africa, and were generally larger than femaleranges overall (Figure 2.4 and Table 2.3) but not significantly in regions outsideof Southern Africa (South: p < 0.0161, East: p < 0.6079, Central: p < 0.8772,West: p < 0.6380). Significant inter-regional differences were discovered in theorder West > South > East > Central (Figure 2.4).2.5 Discussion2.5.1 LoxobaseLoxobase is a modern and powerful approach to wildlife tracking. Although thesystem supports over 15 collar models from different commercial manufacturers,the centralized and standardized data model (Figure 2.2) make data comparableacross regions, species and collar modalities allowing for multi-user collaborationsand continental/global level research. The Loxobase data model is built aroundboth tags (e.g., GPS tracking collars) and individual elephants as base level data26Chapter 2: Loxobase: An African Elephant Tracking SystemYearYearly 100% MCP HR Area Log10 (Km2 )2.53.03.54.02000 2010lllZingillllllYvonne2000 2010lllYalellWinston2000 2010lllllllWessalllWendy2000 2010l lllUmbabatllUkutalllllllTusslellTornEarlllTonyl llllTia MariallTauruslllSummerlllStriburus2.53.03.54.0llSouthern Cross2.53.03.54.0lll lSoshanganelllSorallSindiyollShadracklllSeralllSalif KeitallllRosemaryllRitallllllProudllPepperllOmondillOl PejetallllOl Ari NyirollllNwankwimbillNwambi2.53.03.54.0llNicky2.53.03.54.0lllNgeleshal lNgalatonillNeptunelllNamastellllMutarallllMpalalllllMountain BulllllllllllMoranil lMondlillllMellowlllMayal lllMauallllMatambulllMapimbilllMangala2.53.03.54.0llllMandy2.53.03.54.0llMaddylllMacl llLoldaigallllLenanalllllllLapajumallKuroollKukulllKimanillKenyattallKaurollllJocelynlllllllJoanlll lJerusalemllJacintallIvy2.53.03.54.0llIrving2.53.03.54.0llllIntwandamelalllllllGowerllGilfredllllllGenghis KhanllllllGeneralll lEsidailllllDrachmaell l llDineylllDiannellColleenllllllllClassicllCigarllllCaughleyllCarolinellllCaptain Hook2.53.03.54.0lllBonsai2.53.03.54.0lllBig Al2000 2010llBetsyllAnne2000 2010llllAnastasialllAmina2000 2010llAli Farka TourelllAgnes2000 2010llAchar − AliFigure 2.6: Multi-year variation in 100% MCP home range size for 88 elephantswith >1 full year of movement data.27Chapter 2: Loxobase: An African Elephant Tracking Systemobjects. Positional tags and elephants are conjoined when a tag is attached to anelephant and establish a chronofile (a chronological record of observed positions)of variable duration. Although designed originally for elephants, Loxobase is notspecies-specific and can be used to track multiple taxa. For example, the Loxobasesystem is also currently being used to track Grevy’s zebra (Equus grevyi), blackrhino (Diceros bicornis), white rhino (Ceratotherium simum), sable antelope (Hip-potragus niger), lion (Panthera leo), pastoralist cattle and vehicles.As mentioned above, Urbano et al. (2010) have outlined 13 requirements formodern animal tracking systems. It can be seen that Loxobase meets each of thesestated requirements:1. Data scalability: Loxobase uses the Postgres DBMS running in the AmazonEC2 cloud environment. I am unaware of limits using this infrastructure;Postgres can be replicated and partitioned across multiple EC2 instances3,making this system very scalable.2. Long-term storage for data reuse: Data from Loxobase are periodicallywritten to a Postgres dump file, downloaded and stored off-site on 3 separatestorage mediums as a means of backing-up data. Long-term storage is alsoprovided by the Postgres DBMS itself and each of the individual user’s Esrifile geodatabase stored on their local client machines.3. Periodic and automatic data acquisition: Data are updated by the Animal-Link software which coordinates collection and ingestion of new records intothe AnimalTracking database requiring very little user effort. Depending onthe collar unit and sampling regime, datasets are continuously updated innear real-time (Wall et al., 2014a).4. Efficient data retrieval: The Downloader software provides a very fastmethod for downloading new records from the central server and storingthem locally for further offline analysis. An interface for the client’s localdatabase provides the means to extract data as KML, Esri Feature Classesor CSV files depending on the client’s intended use (i.e., visualization using3The technique used by internet services such as Instagram and Netflix28Chapter 2: Loxobase: An African Elephant Tracking SystemGoogle Earth, spatial analysis using ArcGIS or statistical analysis using Ror other software).5. Management of spatial information: The Loxobase system uses an Ar-cGIS SDE spatial database hosted on a second Amazon EC2 instance to hostspatial data used for analysis in conjunction with movement data.6. Global spatial and time references: All movement data are stored in theGPS system’s native WGS84 geographic coordinate system (decimal de-grees) using Universal Time Coordinated (UTC).7. Heterogeneity of applications: Loxobase was designed to meet the needsof a wide range of user needs and is being used by researchers and students,wildlife managers (e.g., Kenya Wildlife Service and Northern RangelandsTrust (NRT) in Kenya, SAN Parks in South Africa), and conservationists(e.g., Elephant’s Alive in South Africa).8. Easy implementation of new algorithms: Because data on the central serveris also stored locally on a client’s machine, a user is free to analyze data andimplement algorithms of their design. Python scripts can be tested locallyand then set to run on the server if they require it. Algorithms can be setto run in isolation and on variable schedules. Unlike the ISAMUD system(Cagnacci & Urbano, 2008), we prefer to store only raw data collected di-rectly from tags in the AnimalTracking database and not derived metrics suchas MCP ranges. Calculation of metrics is often very specific to a certain an-alytical output, and given the diversity of potential uses of the tracking data,I prefer that users access data and compute derived metrics and store themseparately as needed to help reduce database storage complexity.9. Integration of different data sources: The Loxobase system supports morethan 15 collar types. Additional tag models can be easily incorporated byupdating the Animal-Link software.10. Multi-user support: Loxobase maintains a user table that identifies reg-istered users and their log-in information and supports concurrent calls toeither the Downloader API or Google API29Chapter 2: Loxobase: An African Elephant Tracking System11. Data sharing: Storing data belonging to multiple users within a commonsystem helps promote data sharing. Accessing data belonging to anotheruser is achieved by adding a chronofile index to a user’s chronofile accessstring in the user’s table.12. Data dissemination: Data dissemination is achieved in Loxobase via theDownloader API or Google API or by dumping data from the server to CSVfiles on a disc for manually dissemination.13. Cost-effectiveness: Loxobase is cost-effective to the extent that operatingan enterprise level tracking can be. Reliance on cloud-computing has certainassociated costs that are unavoidable. However, use of the free and open-source Postgres DBMS has reduced costs of the system considerably. Esrilicenses have been provided at no cost by the Esri Conservation Program andthe Google Earth program is also free to download and use.2.5.2 Elephant Movement DataLoxobase represents one of the highest-resolution, wide-ranging and long-termdatasets on the movement of African elephants currently available. Ultimately, in-dividual animals are the appropriate sampling unit in statistical tests and a greaternumber of tracked individuals provide greater statistical power than a large numberof readings on a smaller subset of animals (Otis & White, 1999). Even though 247elephants were tracked, only 53% of the animals had at least one full year of datathat could be analysed for yearly, regional comparisons, demonstrating why largedatasets such as Loxobase are so important and can provide the statistical powerneeded for research into elephant movement ecology and spatial behaviour.2.5.3 Elephant Range & Travel DistanceThe continental speed map provides the first spatial summary of African-wide ele-phant travel speeds (Figure 2.5). Regional differences and spatial heterogeneity intravel speeds are immediately apparent and are most likely related to behaviouralstates (Gurarie et al., 2009) and landscape energy expenditure budgets (Taylor30Chapter 2: Loxobase: An African Elephant Tracking Systemet al., 1982; Langman et al., 1995; Fryxell et al., 2004). There were no signif-icant differences in yearly travel distances between males and females, althoughthere was significant regional variation suggesting that travel distance is an im-portant factor for accessing resources equally required by both sexes, but that ithas a varying regional spatial distribution (e.g., the availability of water). Furtherinvestigation of spatial distribution of speeds is provided in Chapter 5.Despite its tendency to overestimate area by including regions never actuallyvisited by an animal (White & Garrott, 1990), the MCP range estimator is sim-ple to interpret and visualize (Harris et al., 1990). The MCP method also hashistorical inertia that makes it useful for comparison with other published values(Lindeque & Lindeque, 1991; Thouless, 1996; Grainger et al., 2005). Elephantranging behaviour and the areal size of the space used by an animal annually is theresult of potentially multitudes of factors (e.g., vegetation type and cover, water,climate, human-footprint (road density & human population presence), protectedarea size/morphology and terrain (slope & elevation)). The MCP range area mixedeffects model suggests significant regional and species-based differences in ele-phant ranging behaviour and a sexually-based difference in range area occurred inSouth Africa. Further investigation is needed in order to understand these differ-ences through measurement of specific regional covariates, and is the subject of theinvestigations presented in Chapters 5 & 6.2.6 ConclusionLoxobase represents a significant contribution to animal tracking research for eco-logical, conservation and management purposes. The current Loxobase datasetand analytical framework provide the means for unique discoveries about the spa-tial behaviour of African elephants. By housing data from across the continent,and with efficient tools to facilitate their analysis (e.g., ArcMET), inter-regionalcomparisons about elephant ranging behaviour have been made for the first time.I have also provided a raster representation of elephant travel speeds in order tovisualize and summarize movement characteristics at landscape scales. I have cal-culated yearly home range areas and travel distances for 247 elephants and shownthat significant regional differences exist across the continent. In Chapters 5 & 6 I31Chapter 2: Loxobase: An African Elephant Tracking Systeminvestigate these regional differences further and focus on understanding the move-ments in relation to environmental covariates. In the next chapter, I show how theLoxobase system can be extended and used for real-time monitoring by analyzingthe positional data collected from collar units that report in real-time.32Chapter 3Novel Opportunities For WildlifeConservation And Research WithReal-Time Monitoring3.1 IntroductionReal-time monitoring (RTM) of environmental data is increasingly common, ad-vanced by the expansion of communications networks and the improvement ofwireless sensor technologies. A vast number of environmental variables can nowbe measured, processed, disseminated and accessed in real-time and are being usedin diverse applications to improve public safety and for global monitoring, includ-ing the detection of earthquakes and extreme weather events, and monitoring ofclimatic variables. The unique opportunities afforded by RTM are changing aca-demic and public ability to access and interact with environmental data. RTMis also entering the fields of animal tracking and movement ecology, providingnovel research opportunities. Here I present a framework and examples by whichRTM of animal movement can help advance our understanding of animal move-ment ecology and behavior and also provide critical information for managerialand conservation action.The use of remote sensors to track movements of animals has evolved fromVery High Frequency (VHF) radio beacons to Global Navigation Satellite Sys-tems, such as the Global Positioning System (GPS), which can be used to pin-point, with high-accuracy, the location of an animal at a given time. Technologicaladvances, especially the miniaturization of electronics, reduced energy consump-tion, and extension of battery life, have greatly expanded the types of species that33Chapter 3: Novel Opportunities For Wildlife Conservation And Research With Real-Time Monitoringcan be tracked and the quantity and quality of data collected (Ropert-Coudert &Wilson, 2005; Wilson et al., 2008). Current analytical approaches of these highresolution data provide new insight into animal life history and behavior, includingdefinition of travel routes (Berger et al., 2006; Wall et al., 2013), spatially explicitdifferentiation of behaviors (Patterson et al., 2008), and novel information on en-ergy budgets (Fryxell et al., 2004). In addition, sensor units can be configured torecord covarying, exogenous environmental variables (e.g., ambient temperature,relative humidity, ambient light), and endogenous physiological information (e.g.,skin temperature, heart rate) collectively referred to here as ‘biospatial’ data.Communications technology, either satellite-based (e.g., the ’Argos’, ’Iridium’or ’Inmarsat’ constellations) or the ground-based System for Mobile Global Com-munications (GSM) technologies, can now be integrated into tracking units, mak-ing it possible to track animals and process data in near real-time (Dettki et al.,2004; Urbano et al., 2010). Here I define ‘real-time’ to refer to any data that areimmediately telemetered upon acquisition and readied for analysis within a periodof five minutes. RTM has enormous potential in the fields of wildlife ecology andconservation, especially for wildlife at-risk from poaching (Wittemyer et al., 2011),or wildlife prone to frequent interactions with humans (e.g., mountain lion incur-sion into residential areas (Kertson et al., 2011)), or for studies requiring immediatedata retrieval (e.g., prey/predation interactions (Knopff et al., 2009)).RTM analysis allows an analyst to visualize the position or movement trajec-tory of an animal within a Geographic Information System (GIS) as it unfolds.Such real-time interaction with animal movements can help alleviate the disassoci-ation between ecologists and their study subject when remotely collecting trackingdata, allowing development of a biological ’feel’ for the behaviors of tracked in-dividuals (Hebblewhite & Haydon, 2010). Desktop or mobile software programs,such as Environmental Systems Research Institute (Esri) software or Google Earth,can act as wildlife observatories in the absence of continuous field observation, in-cluding visualization of the topographic and ecological context in which the move-ments take place with the addition of layers of geographic information (e.g. high-spatial resolution satellite imagery or land-use coverage). Direct application ofreal-time visualization can greatly enhance patrolling focused on at-risk species oraccess to cryptic organisms. To augment such visualization and interpretation, I34Chapter 3: Novel Opportunities For Wildlife Conservation And Research With Real-Time Monitoringpropose several continuous algorithmic analyses that can serve to identify quantifi-able behaviors of interest across numerous individuals and different temporal andspatial scales.My goal in this chapter is to present approaches that leverage algorithmic spa-tial informatics with real-time tracking data in order to expand the applicationsand insight of animal remote sensing. In particular I look at how real-time accessand analysis of movement data can be used to answer questions relevant to bothwildlife management and conservation research, such as ‘what is the current loca-tion of an animal?’ and ‘what is the animal doing?’. Two geospatial approaches— position based and movement-behavior based analyses — can be used to answersuch questions. I give examples of application of these concepts by developing anRTM component for the Loxobase system. Finally, I discuss developing techniquesusing biospatial data that address the question ’what is the animal experiencing?’.In combination, these real-time approaches can provide a cohesive picture as to thecurrent spatial, behavioral and physiological state of an animal.3.2 Positional AnalysesDetermination of the current spatial relationship between an animal and geographicfeatures — points (e.g., water holes for arid-land wildlife), linear features (e.g.,roads, fence-lines, fishing nets), areal features (e.g., hunting concessions for tro-phy wildlife) or spatially-dynamic features (e.g., a mobile herd of livestock) —can provide valuable insight for conservation and management decision makingand insight into ecological processes. Within the real-time monitoring framework,I suggest two positional metrics useful to wildlife management and ecological re-search: proximity and geographic intersection.3.2.1 ProximityProximity refers to the Euclidean distance between an animal’s location and a spa-tial object and is a useful metric in a number of scenarios. For example, conspecificproximity and contact is of interest in epidemiological and evolutionary studiessuch as in the spread of disease (e.g., bovine brucellosis) from cattle to wildlife or35Chapter 3: Novel Opportunities For Wildlife Conservation And Research With Real-Time Monitoringvice versa (Geremia et al., 2011). Similarly, conspecific proximity could be used inmonitoring specific movement ecology processes such as inter-species proximityduring grazing succession (e.g., as occurs in the Serengeti migration (Gwynne &Bell, 1968)). RTM proximity analysis could also be applied to situations wherecertain geographic points or areas pose an immediate threat to a species but wherequick management action could help in protection (e.g. shutting down energy windturbines for migrating bats (Kunz et al., 2007; Willis et al., 2010)).3.2.2 Geographic IntersectionWhereas proximity can be used to assess approaches of an animal to areas of in-terest, geographic intersection identifies incursions into or across areas of interest.Analysis of geographic intersection is popularly termed Virtual Fencing (Ander-son, 2007) or Geofencing — the detection of the location and timing of an ani-mal’s path into, or across, geographic objects as represented within a GIS, such asa land-cover classification or buffers of point or linear features. Geofencing hasmyriad applications in wildlife conservation and management, including the alle-viation of human-wildlife conflict, alerting humans to the presence of susceptiblespecies, or alerts of animal presence in critical safety areas (e.g., whales enteringshipping lanes (Ward-Geiger et al., 2005)).3.3 Movement Behavior AnalysesMovement ecology theory (Nathan et al., 2008) posits that the track of an animalmay be considered a mixture of multiple, definable behaviors such as foraging,encampment, resting, fleeing predators, dispersal, which reflect both endogenousand exogenous factors influencing the animal over its life-history. A behavioralstate, provided it is statistically discernible, may be inferred by comparison withempirically derived movement signatures or from transitions in state (Fryxell et al.,2008). Movement rates can be used to determine the behavioral state of an animal(Gurarie et al., 2009) while sophisticated switching state-space models (SSSM)(Jonsen et al., 2007) and behavioral change point analysis (BCPA) (Gurarie et al.,2009) have also been used to identify shifts from one behavioral regime to the an-36Chapter 3: Novel Opportunities For Wildlife Conservation And Research With Real-Time Monitoringother (e.g, a shift from foraging to resting behavior). Several behavioral states areof potential interest to wildlife ecologists and managers, two of which I believe canbe highly beneficial to management and research within the real-time monitoringframework: movement rate change and immobility.3.3.1 Movement RateRate of movement and the underlying locomotive mechanical energy output canprovide fundamental insight into an animal’s physiological state and current be-havior. Significant movement rate reduction that results from injury, illness orother condition such as parturition (e.g., female mule deer (Long et al., 2009)),animals that are moving in a discernible pattern such as sustained increased move-ment demonstrated during migration, or dispersal (Singh et al., 2012), or specificmovement characteristics indicative of distinct behavior such as rutting (e.g., ele-phant ‘musth’ (Poole & Moss, 1981)) or hunting (Hansen et al., 2013a), may beof specific research or management interest. Using non-parametric approachesimplemented in real-time allows identification of such behaviors of interest. Forexample, reduced or increased movements can be identified by comparing real-time telemetered movements with a distribution of movement rates for an animalcollected and established when the animal was known to be operating normally(i.e., spanning a mix of different but acceptable behavioral modes). After the dis-tribution of normal movement rate statistics has been established, a movement ratealgorithm compares the cumulative distance traveled in the most recent availabletemporal window (e.g., 24 hours) to the cumulative distribution of normal activ-ity rates. If the value falls below or above the distribution value at a demarcatedpercentile for the defined time-scale then an alert can be raised.3.3.2 ImmobilityMovement immobility is defined in terms of the cessation of displacement by ananimal over a period of time and is a species-specific behavior. For predators,immobility over a certain period could signal a predation event and kill site (Knopffet al., 2010) or denning behavior (Ciarniello et al., 2005), whereas for herbivoresthe same may signal mortality or entrapment. The incapacitation or death of an37Chapter 3: Novel Opportunities For Wildlife Conservation And Research With Real-Time Monitoringanimal and the identification of kill sites are events of special importance to wildlifemanagement and localizing them quickly is an important objective in many speciesmonitoring projects (e.g., for security response to poaching or in studying predator-prey interactions). One approach to identifying immobility is to search for spatial-temporal clusters in recorded positions (Knopff et al., 2009). Any group of pointscan be quantified in terms of the mean distance of the points from their commoncenter of mass and the time spanned by the group. A particular grouping that hasa mean value less than a critical mean radius and spans a time-period greater thana minimum time threshold can then be classified as an immobility event and anappropriate species-specific alert issued.3.4 Application Of RTM To African ElephantsA subset of the tracking units within the previously described Loxobase systemare capable of reporting data in real-time (Table 2.1). Once ingested and stored inthe AnimalTracking database by the Animal-Link software, the data become avail-able for immediate analysis by a custom built MovementMonitor program. Similarto Animal-Link, the software was developed using the Microsoft C# programminglanguage, Microsoft .Net 4.0 framework, and the Esri Engine Runtime version 10.2software components. Each real-time monitoring algorithm is run by Movement-Monitor in continuous succession for each active chronofile found within the Track-ingMaster table. Spatial data used in the Proximity and Geofencing algorithms arestored in a separate Esri SDE-enabled PostgreSQL 8.4 database called STESpatial.The STESpatial database is hosted on a separate server from the AnimalTrackingsystem (Figure 3.1).Each MovementMonitor algorithm has a database table (e.g., ’GeofenceMas-ter’) that stores the algorithm-specific parameters for a particular chronofile (Fig-ure 3.2). In this way, algorithms are customizable to each animal being tracked andparameters can be varied as necessary. Below, I provide details and pseudo-codeon four algorithms: Proximity, Geofencing, Movement Rate and Immobility. Thealgorithms only search movement data within a specified recent temporal windowto ensure that any triggered alerts are within a time frame of interest (e.g., withinthe last 24 hours).38Chapter 3: Novel Opportunities For Wildlife Conservation And Research With Real-Time MonitoringThe African elephant RTM system has the marked advantage of focusing ona species able to support large hardware payloads, a practical limitation in otherspecies that may limit the current applicability of the concepts and ideas I present.While several of the algorithms are specific to elephant ecology and behavior, theprinciples presented are readily extendible to a multitude of species and questionscontingent on the availability of species-specific RTM hardware.39Chapter 3: Novel Opportunities For Wildlife Conservation And Research With Real-Time MonitoringKML Alerts ServiceESRI ServiceKML Tracking ServiceCloud ServerMovementMonitorAnimalLinkAnimalTracking DBAlertsDBAWTServerSouthAfricaAWTServerAustraliaSpatialDBGSM ModemSMS DBMessageServerKenya ServerSMS APIPOP3 (Gmail)SMS(WCF)African Wildlife TrackingGSMSavannah TrackingAfrican Wildlife TrackingSATAfrican Wildlife TrackingGSMTCP/IPSMSTCP/IPSkyQ API (SOAP)AWT API (HTTP)TCP/IPAlertEmailAlertSMSDesktopComputerKML API (HTTP)ESRI API (WCF)KML API (HTTP)MobileDeviceFigure 3.1: Real-time Monitoring (RTM) system to monitor the movement behav-ior of African elephants (Loxodonta africana). GPS tracking data is collected fromfour collar types deployed on 94 elephants and telemetered to a cloud-based server.Animal-Link software ingests the data and stores it in a PostgreSQL database (An-imalTracking). MovementMonitor software continuously monitors incoming dataand implements four algorithms (Proximity, Geofencing, Movement Rate, Immo-bility). If an alert condition is detected, both an SMS message and E-mail aregenerated and issued to subscribed users. Application Programming Interfaces(APIs) make both alert and tracking data instantly available to desktop and mobilebased clients including both Google (as Keyhole Markup Language — KML) andEnvironmental Systems Research Institute (Esri) Geographic Information System(GIS) software.3.4.1 Proximity ExampleThe Proximity algorithm uses a set of spatial features (represented as polygons)stored within the STESpatial database to assess the proximity of an animal witheach spatial feature of interest. A ProximityMaster table defines the subset of40Chapter 3: Novel Opportunities For Wildlife Conservation And Research With Real-Time MonitoringGEOFENCE GROUPSGeofenceGroupName TEXTGeofenceNames TEXT[]GEOFENCE MASTERChrono le SMALLINTUseGeofencing BOOLEANSearchtimeHrs DOUBLEFenceGroup TEXT REF*IMMOBILITY PROFILESChrono le SMALLINTUsePro le BOOLEANRadiusMeters DOUBLETimeThresholdHrs DOUBLEpValue DOUBLESearchTimeHrs DOUBLENotes TEXTPROXIMITY GROUPSProximityGroupName TEXTProximityNames TEXT[]PROXIMITY MASTERChrono le SMALLINTUseProximity BOOLEANSearchtimeHrs DOUBLEDistThreshold DOUBLEProximityGroup TEXT REF*MOVEMENT RATE PROFILESChrono le SMALLINTUsePro le BOOLEANPercentile DOUBLEPercentileVal DOUBLETimeWindowHrsTrainingStart TIMESTAMPTrainingEnd TIMESTAMPNotes TEXTREPORT DISPLAYName TEXTColour SMALLINT[]MarkerIcon TEXTLogo TEXTGEOFENCE REPORTChrono le SMALLINTName TEXTSpecies TEXTStartTime TIMESTAMPEndTime TIMESTAMPStartLat DOUBLEStartLon DOUBLEEndLat DOUBLEEndLon DOUBLEGeofenceName TEXTStartRegionName TEXTEndRegionName TEXTHeading DOUBLESpeed DOUBLEAlgorithmName TEXT RTM REPORTSenderUserName TEXTReceiptTime TIMESTAMPEstimatedTime TIMESTAMPReportType TEXTDisaplyGroup TEXTReportLocation TEXTLatitude DOUBLELongitude DOUBLESenderLatitude DOUBLESenderLongitude DOUBLESenderIP TEXTSendMethod TEXTReportNotes TEXTRelatedReports INTEGER[]IMMOBILITY REPORTChrono le SMALLINTName TEXTSpecies TEXTRadius DOUBLEProbability DOUBLESampleSize INTEGERAlgorithmName TEXTPROXIMITY REPORTChrono le SMALLINTName TEXTSpecies TEXTProximityObjectName TEXTDistance DOUBLEAlgorithmName TEXTMOVEMENT RATE REPORTChrono le SMALLINTName TEXTSpecies TEXTTestPercentile DOUBLETestPercentileValue DOUBLEActualPercentilaValue DOUBLEAlgorithmName TEXTRTM USERSUsername TEXTPassword TEXTFirstName TEXTLastName TEXTOrganization TEXTPhonenumbers TEXT[]Emails []Active BOOLEANCanSend BOOLEANPreferredReceiveMethod TEXTReceiveAlertTypesNotes TEXTSUBSCRIBED CHRONOFILESUsername TEXTChrono les SMALLINT[]REPORT TYPESName TEXTReal-Time Monitoring System Data ModelFigure 3.2: The RTM system extends the AnimalTracking database model (Figure2.2) by adding tables specific to the RTM algorithms, alerts and users.41Chapter 3: Novel Opportunities For Wildlife Conservation And Research With Real-Time Monitoringspatial features that are relevant to a particular animal and the proximity distancethreshold value configurable to a particular chronofile.Algorithm 3.1: Proximity algorithm pseudocodef o r e a c h ( a n i ma l ){S e l e c t an imal ’ s L a s t P o s i t i o nMaxSearchTime=Now−24 h o u r sT h r e s h o l d P r o x i m i t y =500 m e t e r sf o r e a c h ( S p a t i a l F e a t u r e ){P r o x i m i t y = S h o r t e s t D i s t a n c e ( L a s t P o s i t i o n , S p a t i a l F e a t u r e )i f ( P r o x i m i t y < T h r e s h o l d P r o x i m i t y ){S e n d A l e r t ( )}}}The Proximity algorithm is being implemented in Kenya to monitor the spatialproximity of elephants to several spatial objects of interest. One example is theA2 highway (part of the Cape-to-Cairo route) where crossing points and human-elephant interaction are of interest to wildlife managers. Alerts are issued in theevent that an elephant is detected within 1 km of delimited spatial features.3.4.2 Geofencing ExampleThe Geofence algorithm determines where an animal’s straight-line track (calcu-lated between the LastPosition and the PenultimatePosition) crosses a particulargeofence. Geofences are a set of line features stored in the STESpatial database. AGeofenceMaster table defines a subset of geofences that are relevant to a particularanimal. Linear interpolation of the break-point between the start time and end timeof the animal’s track is used to estimate the time of the geofence break.Geofencing was first implemented for use in problem animal control in Laikipia,Kenya. The target animal was a bull elephant, prone to breaking fences, that madealmost nightly forays (over a three week long period) through an expensive elec-tric fence into neighboring subsistence farming land in order to forage in fields ofmaize (Zea mays). A virtual fence-line was erected corresponding to the electrifiedperimeter fence of the conservancy (see inset in Figure 3.6 a) and alerts generated42Chapter 3: Novel Opportunities For Wildlife Conservation And Research With Real-Time Monitoringby our RTM system were disseminated to wildlife managers using short messageservice (SMS) each time the bull broke through the actual fence-line. After receiv-ing automated alerts from the Geofence algorithm, patrol teams responded to hisincursions forcefully and eventually curbed this behavior with aversive condition-ing.Algorithm 3.2: Geofence algorithm pseudocodef o r e a c h ( a n i ma l ){S e l e c t an imal ’ s L a s t P o s i t i o n and P e n u l t i m a t e P o s i t i o nMaxSearchTime=Now−24 h o u r sTrack = C r e a t e S t r a i g h t L i n e ( L a s t P o s i t i o n , P e n u l t i m a t e P o s i t i o n )f o r e a c h ( Geofence ){C r o s s e s = I n t e r s e c t i o n ( Geofence , Track )i f ( C r o s s e s == t r u e ){S e n d A l e r t ( )}}}43Chapter 3: Novel Opportunities For Wildlife Conservation And Research With Real-Time MonitoringDatabaseMultiple Species< 5 minProximity Geofencing MovementRate ImmobilityMovement MonitorResearchWildlife ManagementPublicFigure 3.3: Example of a RTM system for multiple wildlife species. Softwareis set to analyze these data with a suite of relevant algorithms for a given species(e.g., Proximity, Geofencing, Movement Rate, Immobility) and to produce resultswithin 5 minutes of collection. If certain conditions are met, alerts can be issuedin a number of ways (e.g., SMS, E-mail, etc.) to a large audience with differentneeds (e.g., researchers, wildlife managers and the public). Photo Credits: FranzKummeth (Tortoise), Orr Spiegel (Vulture)3.4.3 Movement Rate ExampleThe movement rate algorithm calculates the temporal sum of the distance traveledby an animal within a set temporal window and compares the value with a distri-bution of known ‘normal’ values (i.e., spanning a mix of different but acceptablebehavioral modes). An alert is generated if the value falls below what is expected(i.e. a chosen percentile value of the normal-behaviour distribution). A statisticallyviable sample of movement distances within a normal activity period (e.g., the firsttwo months of movement data) is chosen to establish the distribution of ‘normal’movement activity for a given individual. The percentile (e.g., 1%) is calculated44Chapter 3: Novel Opportunities For Wildlife Conservation And Research With Real-Time Monitoringby MovementMonitor software and this value is stored in a database table Move-mentRateProfiles. The period of normal activity can vary between animals andcan be re-calculated as more data becomes available. Results of application of thealgorithm to a wounded African elephant are provided (Figure 3.4).Algorithm 3.3: Movement Rate algorithm pseudocodef o r e a c h ( a n i ma l ){MaxSearchTime=Now−24 h o u r sL o c a t i o n D a t a A r r a y =GetGPSData ( MaxSearchTime , an im a l )C u m u l a t i v e D i s t a n c e =0f o r ( i n t i =1 ; i < L o c a t i o n D a t a A r r a y . Count ; i ++){TrackSegment= C r e a t e S t r a i g h t L i n e ( L o c a t i o n D a t a A r r a y [ i ] ,L o c a t i o n D a t a A r r a y [ i −1])D i s t = C a l c u l a t e D i s t a n c e ( TrackSegment )C u m u l a t i v e D i s t a n c e += D i s t}Below=Compare ( C u m u l a t i v e i s t a n c e < 1% p e r c e n t i l e Value ( NormalA c t i v i t y D i s t r i b u t i o n ) )i f ( below== t r u e ){S e n d A l e r t ( )}}The utility of movement rate analysis in the context of identifying an injuredanimal, to enable prompt veterinary treatment, is exemplified via an experiencewith a wounded elephant tracked in the Maasai Mara, Kenya. The cumulativemovement distances traveled within successive 24-hour periods were establishedduring a two month period when the animal was not physically injured (Figure3.4a). The algorithm then continuously monitored cumulative travel distanceswithin a 24-hour period and compared the percentile value to the distribution.I used the 1st percentile value of the normal movement rate distribution as thecut-off for determining below-normal movement rates. Once the threshold hadbeen reached, an alert was issued to subscribed users (Figure 3.4c). Followingtwo veterinary interventions, the animal recovered and movement returned to thepre-injury baseline (Figure 3.4b).45Chapter 3: Novel Opportunities For Wildlife Conservation And Research With Real-Time Monitoringa.a.b.c.d. e. f.Training PeriodCumulative 24-hr Distance (km)03.4815.00Figure 3.4: Analysis of the daily rate of movement of a bull elephant in the MaasaiMara, Kenya. [A] 24-hour cumulative distances traveled based on the GPS track-ing locations (9 months of data are shown). The first two months were used asa training period to develop a distribution of normal behavior. [B] Subset graphshowing when the bull elephant was likely injured (red vertical line), 1st treatmentand 2nd treatments (green & blue vertical lines). The maroon horizontal line indi-cates the 1st percentile cut-off value (3.48 km/day). Each orange dot signifies thatthe previous 24-hour cumulative distance traveled fell below the 1% level of thedistribution of daily cumulative distances traveled based on the first two months ofdata when the bull was known to be in good health. [C] Example SMS messagesent by the RTM system corresponding to each alert. [D] The injured bull be-fore treatment. [E] The bull being treated by a Kenya Wildlife Service Veterinarydoctor. [F] The bull after treatment and eventually making a full recovery. PhotoCredits: Madeleine Goss3.4.4 Immobility ExampleThe Immobility algorithm searches for clustering of data-points that fall within acritical radius and that extend beyond a biologically-relevant threshold time. Thealgorithm is based on agglomerative weighted centroid clustering (Legendre &46Chapter 3: Novel Opportunities For Wildlife Conservation And Research With Real-Time MonitoringLegendre, 1998) similar to that used by Knopff et al. (2009) and continuously up-dates a ‘Cluster’ through the addition of successively acquired positions (startingwith a seed cluster of two points). The cluster radius is calculated as the mean dis-tance of each point in the cluster from the cluster’s centroid. The MovementMon-itor software references a database table ImmobilityProfiles to look-up algorithmparameter values for a particular chronofile.Determining the critical radius value is a trade-off between missing actual clus-tering of data-points by making the radius too small, or setting the radius toolarge and triggering false positives (misidentifying a non-cluster as a cluster). Thethreshold time is species’ specific and depends greatly on how long one would rea-sonably expect an animal to remain stationary. For African elephants I estimate thisat 5 hours. A within-cluster percentage value is also defined to allow for the occa-sional positional error and therefore the calculation depends only on a percentageof points occurring within the critical radius.Algorithm 3.4: Immobility algorithm pseudocodef o r e a c h ( a n i ma l ){C r e a t e a new C l u s t e rS e t C l u s t e r . Time=NowS e t C l u s t e r . C r i t i c a l R a d i u s = C r i t i c a l R a d i u sS e t Thresho ldTime =Now−5 h o u r sS e t MaxSearchTime=Now−24 h o u r sL o c a t i o n D a t a A r r a y =GetGPSData ( MaxSearchTime , an im a l )f o r ( i n t i =0 ; i < L o c a t i o n D a t a A r r a y . Count ; i ++){C l u s t e r . AddLocat ion ( L o c a t i o n D a t a A r r a y [ i ] )C l u s t e r . ComputeCentrenumWithin= C l u s t e r . D e t e r m i n e N u m b e r P o i n t W i t h i n C r i t i c a l R a d i u snumTotal= C l u s t e r . T o t a l N u m b e r P o s i t i o n sp e r c e n t =numWithin / numTotali f ( p e r c e n t >= C r i t i c a l P e r c e n t a g e ){S e n d A l e r t ( )E x i t A lgo r i t hm}}}I tested the performance of the algorithm on six African elephant movementdatasets where the animal had been killed by poachers but where the tracking unitcontinued to function post-mortality. I ran a test using a month of positions preced-47Chapter 3: Novel Opportunities For Wildlife Conservation And Research With Real-Time Monitoringing the animal’s mortality and twenty-four hours of positions post-mortality. Theclustering algorithm was repeatedly run over each dataset by varying the clusterradius value between 1 meter up to 60 meters using a moving window tool andwhile keeping a threshold time of 5 hours and a within-cluster percentage of 80%.I found that a cluster radius of 13 meters successfully picked up on all mortalityevents (Table 3.1).Table 3.1: Critical radius values sufficient to detect mortality in movement datasetsof six African elephants killed by poachers. A month of data prior to, and 24hours after, the mortality were used for the analysis. The number of false positivestriggered by the algorithm is given for each of the critical radius values (e.g., forthe animal ‘Prunella’, the critical radius value needed to detect the true mortalityevent was 13 meters but the algorithm also generated two false immobility alarmsin the prior month when using that radius value).Elephant Sex Critical Radius(Meters)False Positives(Number)Chemi Chemi M 7 0Kijiji F 10 0Marania M 4 0Mercury F 4 0Prunella F 13 2Soboiga M 3 03.5 Alert DisseminationOnce a behavioral state of interest has been identified algorithmically, an alertis triggered and distributed using a number of dissemination methods that targetthe variety of users of the RTM system (Figures 3.1 and 3.3), including E-mail(e.g., Figure 3.5), SMS (the primary choice for most practitioners in the field) ora Google Keyhole Markup Language (KML) API for use with Google Earth. Thereal-time distribution of alerts allow analysis and visualization of the identifiedbehavior in central research stations, warden offices or visitor centers, as well as48Chapter 3: Novel Opportunities For Wildlife Conservation And Research With Real-Time Monitoringdirectly in the field by stakeholders and wildlife employees through portable inter-net linked devices.Once an algorithm has positively identified an alert condition, the Movement-Monitor software will query the RTMUsers table to determine the users who aresubscribed to a particular chronofile/algorithm combination and store details ofthe alert within the database (Figure 3.2). Users can choose to receive alerts viaSMS, E-mail or both. The RTM system currently uses a physical server located inNairobi, Kenya that has a GSM modem for sending SMS alerts. The Movement-Monitor software communicates to the Kenya modem using a custom built SMSAPI I developed using Microsoft Windows Communication Foundation (WCF)technology to disseminate alert SMS messages using custom-built software calledMessageServer. E-mail alerts are also issued by MovementMonitor using a C#POP3 class library that sends alerts using the Google Gmail E-mail system (Figure3.1). I provide an example alert report generated by the immobility algorithm andreceived over E-mail in Figure 3.5.3.6 Future DirectionsI have shown that algorithmic implementation of tracking data analyses can be usedto effectively monitor wildlife in real-time. However, measurement of variables —both physiological and environmental — concomitantly with movement data ex-pands the possibilities associated with real-time monitoring beyond location-basedinferences alone (Rodgers, 2001; Hebblewhite & Haydon, 2010). Covariate mea-surements can give information as to the internal state and health of an animal, andthe environmental conditions it is experiencing, providing rich ancillary data layersfrom which complex behavior patterns can be interpreted and the state of the ani-mal understood. Coupling the real-time algorithmic analysis of animal movementswith covariate information creates an exciting new frontier in applied ecological re-search and I briefly discuss here several currently available technologies that wouldbe of immediate practical application in theoretical and applied research.49Chapter 3: Novel Opportunities For Wildlife Conservation And Research With Real-Time MonitoringFigure 3.5: An example immobility alert received via E-mail. This particular reportcorresponds to an elephant having dropped its collar which subsequently triggeredthe alarm.50Chapter 3: Novel Opportunities For Wildlife Conservation And Research With Real-Time MonitoringA. Positional alerts B. Movement alerts Proximity GeofencingC. Environmental & Physiological alerts !! !!!! !! !!!!! !!!!!!!!!!ImmobilityMovement RatePulse & EKGLandscape CovariatesOl PejetaFigure 3.6: Examples of the RTM algorithms that can be applied to a given wildlifespecies (e.g., African elephant). [A] Positional: Proximity (e.g., the distance theelephant is from a farming area), and Geofencing (e.g., the time & position wherethe elephant crossed an electric fence-line) [B] Movement behavior: Movementrate (e.g., the time & position when the elephant’s 24-hour cumulative distancetraveled dropped below a threshold value) and Immobility (e.g., the time & positionwhere an elephant stopped moving for longer than 5 hours) [C] Physiological &Environmental: Heart-rate (e.g., the time & position when the heart beat of theelephant stops) and landscape environmental covariates of interest (e.g., the time& position when the localized Normalized Difference Vegetation Index (NDVI)value reaches a threshold of interest).3.6.1 Physiological DataRelatively simple physiological measurements, such as an animal’s heart-rate, canlead to a host of interesting analytical opportunities, such as spatially explicitmetabolism and energy expenditure partitioning (Cooke et al., 2004). When con-sidered in real-time, physiological information is applicable within a wildlife man-agement and conservation framework as a way of assessing animal mortality (e.g.,51Chapter 3: Novel Opportunities For Wildlife Conservation And Research With Real-Time Monitoringfrom poaching) or other physiological responses (e.g., stress) that would consid-erably improve movement based analyses such as the aforementioned immobilitydetection algorithm. For example, the ability to detect, in real-time, the absenceof a pulse in a wild animal would greatly increase the capacity for managementaction as in the case of illegal wildlife poaching. Telemetry of heart-rate and corebody temperature with movement data would mark a major research and manage-ment milestone opening avenues to remotely measure animal energetics, health anddisease spread based on physiological data.3.6.2 Environmental DataAnimal-attached sensors, at a point in time, can provide a spatially located datumof a host of environmental variables such as ambient temperature, humidity, light,background noise levels, etc. Great potential for understanding movement behaviorarises when these data are analyzed in real-time, such as triggers of dispersal andmigration (e.g., the movement trigger for the Mali elephant population (Wall et al.,2013)).Remotely sensed imagery products can provide a wealth of information aboutenvironmental conditions (e.g., weather, vegetation indices) but have traditionallybeen slower to acquire, process and analyze than animal movement data (althoughsee Urbano et al. (2010)). Recently, development of advanced cloud-based imageprocessing infrastructures, such as the new Google Earth Engine (GEE) technology(Hansen et al., 2013b), are able to provide near real-time access to satellite imagedata products and analyze them ’on-the-fly’ with an unprecedented scale of com-puting power. GEE technology promises many unique opportunities for ecologicalmonitoring of wildlife.3.6.3 Acoustic DataAcoustic monitoring systems are becoming more prevalent and have the poten-tial to provide data useful for a variety of behavioral or ecological research areas.Successful implementation of such devices include monitoring cattle foraging be-havior (Clapham et al., 2011), characterizing activity budgets of wildlife (Lynchet al., 2013), investigation of species communication (Payne et al., 2003) or to iden-52Chapter 3: Novel Opportunities For Wildlife Conservation And Research With Real-Time Monitoringtify the presence of marine mammals (Klinck et al., 2012). Real-time directionaltracking of sounds is also possible (Bergamo et al., 2004) and gunshot detection(e.g., ‘ShotSpotter’ http://www.shotspotter.com/) is an immediate application ofthe technology for animal conservation and management purposes where poachingis a problem.3.6.4 AccelerometryFinally, a rapidly developing approach in animal telemetered data are applicationsthat monitor animal activity through fine grained sampling of overall dynamic bodyaccelerations (ODBA) using tri-axial accelerometers (Wilson et al., 2006). Thehigh sample rate of current instruments (e.g., 32 Hz (Soltis et al., 2012)) can serveto derive nearly continuous movement paths and are analyzable into detailed seg-mentation of energy expenditure (Halsey et al., 2009). The high sample rate ofthese units creates significant data volume in comparison to traditional movementdata and has implications for real-time telemetry, given the limited memory/bat-tery life of current animal-attached tag systems. As a result, on-board processingof accelerometry signals or short recordings of ODBA will generally be requiredfor real-time applications.3.7 ConclusionAdvancement of technology and the continued expansion of communications net-works are allowing targeted, on-animal data collection and the expedient distri-bution of such data. As a result of these developments, opportunities available toresearchers and wildlife managers for studying and monitoring wildlife in real-timeare expanding rapidly. The reduction in costs of both tracking units and telecom-munications are also making RTM applications increasingly economically viable.The movements of an animal, as recorded and relayed with a remotely attachedtracking device, provide information about the animal’s current spatial behaviorfrom which inferences can be made as to its condition and physical state. Pro-cessing information as it is collected can help researchers collect context specificdata needed to understand drivers of behavioral change. For more applied objec-53Chapter 3: Novel Opportunities For Wildlife Conservation And Research With Real-Time Monitoringtives, such information allows managers to take timely and crucial managementaction and can complement existing wildlife monitoring programs such as rangerpatrols and other field-based monitoring techniques. . The real-time monitoring al-gorithms presented here for monitoring African elephants (Proximity, Geofencing,Movement Rate and Immobility) are widely adaptable and applicable to monitor avariety of behaviors across numerous species. Exciting new developments, both inattached and landscape sensor technology, as well as in acquisition and delivery ofremotely-sensed imagery products, will expand the types of real-time monitoringthat are possible.54Chapter 4Elliptical Time-Density Model ToEstimate Wildlife UtilizationDistributions4.1 IntroductionQuantifying the movement of an animal, its use of a landscape, and the resourcesavailable therein, is fundamental to wildlife ecology and conservation. Trackinganimals with technology such as Global Positioning System (GPS) tracking de-vices is a widely used methodology that can provide detailed positional informa-tion (Kie et al., 2010; Hebblewhite & Haydon, 2010). Although the technologyfor continuous-time monitoring of animals is fast approaching (e.g., using tri-axialaccelerometers (Wilson et al., 2006)), GPS and similar relocation technology (e.g.,Argos or Very High Frequency (VHF) collar-based information) only sample atdiscrete and relatively infrequent times. Models are therefore needed to predict ananimal’s spatial utilization when not being directly sampled and are generally re-ferred to as animal ’home range’ models (Laver & Kelly, 2008; Fieberg & Börger,2012).Home range models have started to emerge that explicitly incorporate the tem-porality of sampled positions into the model definition, thereby leveraging the in-herent movement structure of the sample to derive a more accurate statistical andbiological estimate: Brownian Bridge Movement Model (BBMM) (Horne et al.,2007), Time-Geographic Density Estimation (TGDE) (Downs, 2010; Downs et al.,2011), dynamic BBMM (dBBMM) (Kranstauber et al., 2012), Potential Path Area(PPA) (Miller, 2005; Long & Nelson, 2012), Time Localized Convex Hull (T-55Chapter 4: Elliptical Time-Density Model To Estimate Wildlife Utilization DistributionsLoCoH) (Lyons et al., 2013), and therefore, these home range models are bet-ter suited to handle the temporally and spatially autocorrelated nature of high-resolution datasets (Lyons et al., 2013).The BBMM and dBBMM models both estimate landscape utilization basedon mechanistic assumptions (i.e. Brownian motion) of the underlying movementbehavior between sampled positions. In contrast, the theory of ’time-geography’(Hägerstrand, 1970; Miller, 2005) uses elliptical areas to demarcate the bound-ing region that a moving object could have occupied between recorded positions,but does not make assumptions about the form of movement the object took be-tween points (Long & Nelson, 2012). Downs et al. (2011) have recently expandedthe time-geographic approach to formulate a utilization distribution (UD) modelfrom geo-ellipses connecting recorded animal locations. Models that produce aUD (i.e., a spatial model that gives a probability of occupancy, or time spent, forevery point in the landscape (Van Winkle, 1975; Jennrich & Turner, 1969; Wor-ton, 1989; Seaman & Powell, 1996; Marzluff et al., 2001; Fieberg & Kochanny,2005; Keating & Cherry, 2009)) contain more spatial structure and informationcompared with models that outline potential areas of use (e.g., Minimum ConvexPolygons (MCP) and PPA) and, therefore, are generally preferred in analysis ofanimal space-use (Fieberg & Kochanny, 2005; Fieberg & Börger, 2012).In this chapter, I first advance time geographic approaches for space-use esti-mation by developing a novel approach that quantifies the probable time-densityof occupancy within geo-ellipses bounding the potential space use of an individ-ual. Deriving a UD based on the probability of time spent at a given point in thelandscape provides a logical advancement of the TGDE model in line with typicalspace-use constructs in the wildlife ecology field. Secondly, I present a Bayesianframework for modeling the maximum speed parameter, critical as input to time-geographic approaches, that provides a construct for interpreting this user selectedparametrization of the model. Thirdly, I apply the model using data collected froman African elephant (Loxodonta africana) specifically exploring the effects of dif-ferential temporal sampling regimes and model parameter inputs on model output.From this example, I demonstrate how model parametrization can be biologicallyinterpreted. Finally, I compare the omission and commission error rates between anabsolute movement path (generated) and UD estimates of the ETD model, BBMM,56Chapter 4: Elliptical Time-Density Model To Estimate Wildlife Utilization DistributionsTGDE and the traditional kernel density estimator (KDE), providing a platform bywhich to contrast my model with commonly used approaches.4.2 Elliptical Time-Density Model DevelopmentSimilar to other time-geographic approaches, I begin development of the ETDmovement model by considering a pair of sequentially acquired positions froma tracked animal (see Figure 4.1). I assume the animal was at position ~pi at timeti and then at position ~p j at time t j, where Tj = t j − ti and j = i+ 1. Together iand j index a chronologically sorted list of recorded locations. I assume no knowl-edge of where the animal traveled in between the recorded locations and that itcould have taken any complicated route with a path length equal to r j, but do as-sume an average speed of s j =r jTj. The speed s j puts bounds on the area reachableby the animal during time Tj, also known as the ’Potential Path Area’ by Miller(2005); Downs et al. (2011); Long & Nelson (2012). It can be shown (see deriva-tion in Appendix A – Section A.4) that this region is defined by an ellipse with areaA j = pir j4√r2j −D2j where D j is the straight line distance between ~pi and ~p j. Thegoal in deriving an animal’s utilization distribution (UD) is to know where in thelandscape the animal is likely to have spent its time over the period it was beingmonitored. Mathematically, a UD is a surface that maps, for every point ~z in R(defining the extent of all points that could possibly be occupied by the animal),the probability density of finding the animal at a given~z. From delineation of theelliptical area possibly reached during a time Tj I can calculate a ’time-density’value as ρ j =TjA jin units of hr/km2.Although the true mean speed of the animal s j along the true path length r j isunknown, it is bounded by a lower value of smin =~|p j−~pi|Tj(i.e., the animal had tomove at least as fast as smin to move along the shortest distance path – a straight linepath from ~pi to ~p j). It is also bounded by some biologically realizable upper limitsmax based on the physiology of the animal being studied. These constraints onspeeds translate into constraints in ellipse areas, and each possible average speedvalue from smin to smax in moving from ~pi to ~p j corresponds to a unique boundingelliptical area. Remembering that the goal is to determine the amount of timean animal is likely to have spent at a given point in the landscape, I can choose57Chapter 4: Elliptical Time-Density Model To Estimate Wildlife Utilization Distributionsa particular point ~z, and note that it can only be reached if the animal moves atan average speed greater than or equal to sz, j =|r j|Tj=(|~z−~pi|+|~p j−~z|)Tjwhere sz, j ≤smax. If sz, j > smax then point ~z is unreachable by the animal in time Tj and thecorresponding UD value will be zero. If point~z is reachable, then I can estimate theamount of time spent at~z by integrating the time-density value over a differentialarea at~z. Time-density values at~z can vary according to the area of the ellipticalbounding region being considered. I proceed by computing the expected time-density value function at a point~z: Θ j(z) = E{ρz, j}by calculating the expectationof time density values from each possible ellipse equal to, or greater-than, theellipse required to move between ~pi via a point~z to reach ~p j in time Tj:Θ j(~z) =ˆ smaxsz, jf (s)ρ j(s)ds (4.1)where f (s) is the probability density function of average speed over time Tj andwhere the volume integral of the elliptical time-density function Θ j(z) over allpoints~z across the overall region R being considered is equal to the time Tj:˛RΘ j(~z)dA = Tj (4.2)In practice, the integral in equation 4.2 is approximated by discretizing thelandscape into a grid where each cell has an area ∆A, and the discrete set of eval-uation points {~zm} are taken as the grid-cell center points. The integral is thenapproximated by the sum:m∑k=1Θ j(~zm)∆A = Tj (4.3)where k = 1 . . .m indexes the set of discrete evaluation points {~zm} reachable intime Tj. The discrete UD is a probability mass function whereby the UD value ofa given grid-cell is the probability of use by an animal within the grid-cell and theprobabilities across all grid-cells are normalized to sum to one.It follows that the animal’s UD can be constructed by adding the fractionalamounts of time spent per landscape area as determined using the elliptical time-58Chapter 4: Elliptical Time-Density Model To Estimate Wildlife Utilization DistributionszDjPiPjTime Period = TjZ-PiPj-Z|rj|= |Z-Pi|+|Pj-Z|Figure 4.1: Path and ellipse geometry.density function Θ j from each successive point pair within the movement dataset:UD(z) =∑ jΘ j(~z)TTotal(4.4)where TTotal = ∑n−1j=1 Tj is the total time-span of the movement dataset.59Chapter 4: Elliptical Time-Density Model To Estimate Wildlife Utilization Distributions4.3 Weibull Probability Density FunctionSelection of the probability density function f (s) in equation 4.1 should be basedon choosing the mathematical form that best-fits the speed distribution of the data,and f (s) can either be a parametric or non-parametric function. The most basicassumption is that f (s) is uniform, in which case each time-density value ρ j(s) inequation 4.1 is equally likely. However, from empirical observation we know thatthe probability distribution of speeds is unlikely to be uniform and we generally ex-pect that faster speeds are less likely than slower ones. The two-parameter Weibulldistribution has a wide range of flexibility in representing variations in shapes andhas previously been used to model animal movement (Morales et al., 2004). HereI incorporate a two-parameter Weibull distribution in equation 4.1 to condition thetime-density expectation functionΘ j, although a Gamma distribution or other sim-ilarly versatile function would be equally useful for this approach. Equation 4.1then becomes:Θ j(~z) =ˆ smaxsz, j4kpiλ s( sλ)k−1 e−( sλ )k√s2t2j −D2jds (4.5)where k is the Weibull shape parameter and λ is the Weibull scale parameter. Thereis no known analytical solution to equation 4.5 but the integration can be performedusing numerical methods.The shape and scale parameters that define the functional form of the Weibulldistribution in equation 4.5 are generally not known but can be empirically esti-mated by fitting a Weibull curve to the distribution of straight line speeds fromconsecutive pairs of positions{~pi,~p j}in the movement dataset. The likelihoodfunction to be maximized is then:L =n−1∏j=1kλ(s jλ)k−1e−( s jλ)k(4.6)and the best-fit parameters solved for using standard maximum likelihood estima-tion methods (e.g., the optim library for R) (Clark, 2007; Gelman & Hill, 2007;Bolker, 2008).60Chapter 4: Elliptical Time-Density Model To Estimate Wildlife Utilization Distributions4.3.1 Multi-Temporal DataIn empirically collected movement datasets, the time interval between sampled lo-cations, Tj, may vary considerably owing to missed fixes or studies that purposelychoose to vary the temporal sampling regimes (Katajisto & Moilanen, 2006). Inthe case of datasets with irregular time intervals between locations, we would ex-pect the Weibull distribution to vary its shape and scale parameters as a functionof the temporal sampling regime Tj, making it necessary to explicitly model thisvariation. I can therefore add an additional parametrization to the Weibull modelby writing the scale parameter as a function of Tj:λ (Tj) = aT bj cTj (4.7)where a, b, c are three parameters to be estimated in addition to the shape parameterk. The likelihood function can then be written as:L =n∏j=1kaT bj cTj(s jaT bj cTj)k−1e−(s jaT bj cTj)k(4.8)4.3.2 Maximum Speed ParameterThe maximum speed value smax, effectively limits the size of the area reachable byan animal in moving between successive recorded locations (Downs et al., 2011;Long & Nelson, 2012) and is therefore an important input parameter to the ETDmovement model. The maximum speed value can be chosen in several ways: 1)based on a known biological speed limit for a given species given its physiology, 2)using the maximum empirically measured speed in the tracking dataset, or; 3) usinga value that corresponds to a percentile of the empirically best-fit two-parameterWeibull cumulative distribution function (CDF) whereCDFWeibull = 1− e−(sλ )k(4.9)A desired maximum speed value for a given percentile is then determined us-61Chapter 4: Elliptical Time-Density Model To Estimate Wildlife Utilization Distributionsing:smax = λ (ln(|1−α|))1/k (4.10)where α is the percentile value (e.g., 50th percentile).Using a percentile value of the Weibull distribution has the benefit that themaximum speed value can vary according to the temporal resolution at which theanimal is being sampled, as in the case when using the multi-temporal parametriza-tion. Alternatively, using the top speed attainable by an animal over short time pe-riods will lead to an over-estimation of the area reachable when considering longertime intervals, and either the biological or empirically-derived maximum speed val-ues would have to be specified in consideration of the temporal sampling regime. Ifthe smin value for a given positional pair{~pi,~p j}is greater than or equal to the smaxvalue (i.e. smin ≥ smax) then the corresponding ellipse eccentricity becomes infiniteand the model collapses to a straight line connecting the positional pair (also calledthe degenerate ellipse (Long & Nelson, 2012)).Depending on the choice of the maximum speed value, and as a result of dis-cretization of the integral in equation 4.3 into discrete grid cells, there may beinstances when no evaluation points are reachable between a position pair even ifsmin is less than smax. For example, in the case of a degenerate ellipse where thepoint pair separation represents the maximum speed in the dataset, then no evalua-tion points will be reachable, unless they fall exactly on the straight line connectingthe positional pair. In this situation, we employ the technique of Wall et al. (2013)of first joining the point pair with a straight line and calculating a constant time-density value along the line in units of hours/meter, then clipping the line based onthe geometry of the underlying grid, such that any grid intersecting the line willhave a time-density value equal to Θ j(~z) = dzTj where dz is the fractional length ofthe straight line crossing the grid cell associated with~z.4.4 Elliptical Time-Density Model ApplicationI applied the ETD model to a movement dataset collected from an African elephant(Loxodonta africana) in the Gourma region of Mali (Wall et al., 2013) to high-light use of the ETD model with real data. Additionally, in order to demonstrate62Chapter 4: Elliptical Time-Density Model To Estimate Wildlife Utilization Distributionsmodel behaviour as a function of varying temporal sampling regimes typically en-countered in applied scenarios, I calculated the ETD model under three differenttemporal sampling scenarios: 1) the full, high resolution hourly sampled GPS data(dataset ’D1’), 2) by randomly down-sampling D1 to produce a randomly varyingtemporal resolution dataset with 50% of the original points (dataset ’D2’), and; 3)by regularly down-sampling D1 to produce a low temporal resolution data withsampled locations once every 24 hours (dataset ’D3’). For each dataset, the ETDmodel was calculated using an output grid size of 500 meters.4.4.1 ETD Model SoftwareTo calculate the ETD model I developed software implemented as part of the Ar-cMET extension for Esri ArcMap GIS software (Esri, 2013; Wall, 2014) and writ-ten using the C# programming language. The algorithm begins by first creating alandscape-wide grid of user-specified cell size that covers the entire extent of thedataset (although, in order to prevent edge effects, an additional expansion optionallows the grid to cover an area greater than the locations dataset by a user-specifiedexpansion ratio (default =1.1)).Once the grid is created, the grid cell center-point coordinates are determinedand these become the evaluation points (i.e. the set of points {~zm}) for the time-density function evaluation. Each pair of points in the location’s dataset is thenconsidered independently and in parallel, thus speeding the calculation time con-siderably on machines with multiple logical cores. For each point pair, the straight-line speed (smin) value between points is established. The speed required to reacheach landscape evaluation point (sz) is then calculated and used as the lower boundfor the integral in equation 4.5. If an evaluation point is unreachable without mov-ing faster than smax then it is not considered further. The time-density function isevaluated for each of the points~zm reachable within time Tj . The integral in equa-tion 4.5 is approximated using a trapezoidal Riemann sum with a user specifieddifferential speed unit (default = 0.001 km/hr). A user defined cut-off parameterallows a minimum output UD probability value to be set (default value = 1E-15),below which the particular grid cell will be assigned a value of zero, and the restof the grid cells will have their values adjusted accordingly so that the total sum of63Chapter 4: Elliptical Time-Density Model To Estimate Wildlife Utilization Distributionsvalues equals one (equation 4.4).4.4.2 Speed Parameter SelectionI modeled the speed distributions of datasets D1, D2, D3 using a two-parameterWeibull distribution using a Bayesian framework. For datasets D1 and D3, Istarted with non-informative uniform prior distributions for both shape and scaleparameters and used Markov Chain Monte Carlo (MCMC) with Gibbs Samplingusing WinBUGS software called from within R (R Core Team, 2013) using theR2WINBUGS library (Gelman & Hill, 2007), to determine the best-fit parametersfor the Weibull distribution (λ and k from Equation 4.5). I ran three MCMC chainseach with 100,000 iterations (first 50,000 discarded to allow for burn-in) and con-firmed chain convergence using a potential scale reduction factor value of 1.1 as acut-off (Gelman & Hill, 2007). A complete listing of the procedure and parameterestimates can be found in Appendix A – Section A.1 and Section A.3. A similarprocedure was followed for dataset D2 except that parametrization of the scale fac-tor using Equation 4.7 allowed for variation in the scale parameter as a function ofthe temporal separation between recorded points (Appendix A – Section A.2).I explored how the choice of maximum speed value affected the ETD modeloutput by computing the ETD model for dataset D1 and a variety of maximumspeed parameter values. I calculated the ETD model using: 1) the maximum speedvalue in the dataset (Model: D1-MaxSpeed), 2) using the 99% CDF value (Model:D1-99), and; 3) using the 50% CDF value (Model: D1-50). For each of these threemodels, I calculated the core hotspots (defined as the 50% probability contour),the home range (defined as the 95% probability contour (Jennrich & Turner, 1969;Anderson, 1982)), and the total use area based on the 99% probability contour area.4.4.3 ETD Model Accuracy AssessmentI tested the accuracy of the ETD model by comparing UD percentile contours totrue known UD percentile contours for a given dataset as described previously. Toestablish a true UD, I used a 15-minute temporal resolution dataset collected froman African elephant over a two-week period (n = 1522 positions). Using this ’true’path, I established a fine-resolution (10 meter) graticule and calculated the amount64Chapter 4: Elliptical Time-Density Model To Estimate Wildlife Utilization Distributionsof time spent within each grid cell as a percentage of the total time.I down-sampled the true, 15-minute dataset at hourly intervals and calculatedETD models using 0%, 30%, 50%, 70%, 90%, 99% percentile maximum speedvalues (note that the 0% model does not allow any off-path movement and effec-tively connects data points with straight lines; i.e, infinitely eccentric ellipses) usingWeibull shape and scale parameters derived from the distribution of hourly speeds:shape = 0.8638; scale = 0.2906. For additional comparison, I also calculated theBBMM model (animal mobility variance = 893.5 m2; telemetry standard deviation= 28.85 m2), a TGDE model parametrized using the maximum dataset speed (2.55km/hr) and a linear decay function, and a fixed bivariate Gaussian kernel (KDE)model (smoothing factor hre f = 875) using ArcMET software (Wall, 2014). Foreach of the nine modeled UDs (ETD0, ETD30, ETD50, ETD70, ETD90, ETD99,TGDE, BBMM, KDE) and the true UD (TrueUD), I calculated UD areas at 10%,20%, 30%, 40%, 50%, 60%, 70%, 80%, 90%, 99% percentile levels.I calculated errors of omission and commission to assess the accuracy in cap-turing space-use along the true movement path of each model. An error of commis-sion was defined to be the number of pixels that fell within a model UD percentilecontour that were not within the corresponding TrueUD percentile contour (pix-els marked as being used that should not have been — Figure 4.7-A) expressedas a percentage of the total number of unused pixels in the TrueUD for a givenpercentile level. An error of omission was defined as the number of pixels not con-tained within a model UD percentile contour but that fell within the correspondingTrueUD percentile contour (pixels not marked as being used by a model contourbut that should have been — Figure 4.7-B) expressed as a percentage of the totalnumber of used pixels in the TrueUD for a given percentile level. I defined a to-tal error metric to be Total Error =√omission2 + commission2 to summarize bothcommission and omission errors (Figure 4.7-C).4.5 ResultsConceptually, the morphology of the time-density function kernel can be visual-ized in Figure 4.2 where two hypothetical ETD kernels have been generated fordiffering positional separations for a pair of points separated by one hour of time65Chapter 4: Elliptical Time-Density Model To Estimate Wildlife Utilization Distributionsusing the same Weibull parametrization and a maximum speed parameter value of6 km/hr. On the left is a positional pair that are close together with an smin valueof 0.3 km/hr compared with the right side where the positional pair are located farapart and have an smin value of 5 km/hr. The morphology shifts from a peakedcircular function, to an elongated elliptical form, as the separation of the positionalpair increases, and eventually collapses to a straight line as smin approaches smax.Understanding the performance of a movement model under differing temporalsampling strategies is an important component in model testing and in the appli-cability of the movement model within generalized animal tracking scenarios. Icontrasted the ETD model calculation under the three selected temporal samplingregimes D1, D2 and D3 (Figure 4.3 d-f). The maximum speed parameters derivedfrom the Weibull fit were D1: 6.44 km/hr, D2: 5.82 km/hr, D3: 1.70 km/hr. Arealvalues for core areas, home ranges and total use areas across the three datasetsdemonstrate similar trends depending on temporal sampling regime (Figure 4.4).As temporal sampling frequency decreases, the ETD model morphology erodesand becomes more spatially diffuse and less peaked (Figure 4.4). For example, thearea of the UD 50% percentile core area inflates by a factor of 4.7 when movingfrom hourly to 24-hour sampling, the UD 95% percentile area inflates by a factorof 3.6, and the 99% percentile UD total use area inflates by a factor of 3.2 timeswhen moving from an hourly sampling regime to 24-hour sampling for this dataset.The maximum speed parameter value influences the calculation of the ETDmodel (Figure 4.5). Using a maximum speed value equivalent to the empirically-derived maximum speed value of a given dataset led to the UD with the largest99% percentile total use area, and 95% percentile home range area (Figure 4.6).In contrast, 50% percentile core areas were generally equivalent across all threeETD models. Using successively lower maximum speed values, that is, the 99%and 50% percentile Weibull speed distribution values, had the effect of concen-trating the three space-use levels into smaller, probabilistically dense regions. Iwould expect this to be the case given that, for a lower maximum speed parameter,a greater number of point pairs are necessarily connected by straight lines, thuslimiting reachable areas.66Chapter 4: Elliptical Time-Density Model To Estimate Wildlife Utilization Distributions       0.3 Km/Hr5.0 Km/HrFigure 4.2: An example of two different elliptical time-density function morpholo-gies for a pair of points acquired spatially close together (left) and far apart (right)and their relative locations along the Weibull speed distribution curve (bottom).Vertical lines indicate the locations of the pairs of sequentially acquired animallocations and shading illustrate the relative probability of where the animal mighthave been found in between the recorded locations.67Chapter 4: Elliptical Time-Density Model To Estimate Wildlife Utilization DistributionsThere was a general exponential increase in commission errors with increasingpercentile levels. The KDE model committed the greatest number of commissionerrors, followed by the TGDE, ETD99, BBMM, ETD90, ETD70, ETD50, ETD30models and the ETD0 model committing the least (Figure 4.7-A). This trend showsthat as models progressed towards greater restriction (e.g., ETD0 & ETD30) wherefewer off-linear movements are allowed, they committed fewer commission errorsat all percentile levels. All models showed a peak in commission errors at highpercentile levels.Omission errors showed very different trends. Above the 20% percentile UDcontour, the ETD0 model committed the greatest number of omission errors aswould be expected because of the restrictiveness to straight-line paths betweenpoints. KDE and TGDE caused the highest number of omission errors at the 10%and 20% percentile levels but these converged to zero by the 99% percentile level(Figure 4.7-B). The ETD99 model, BBMM, and ETD90 demonstrated the best per-formance in terms of low omission error rates across all percentile levels. Overall,the ETD99 model had the lowest root mean square error (Total Error) when consid-ering both errors of omission and commission across all percentile levels, althoughthe ETD90 model had the least total error at the 90% and 99% percentiles (Figure4.7-C). The ETD99 and BBMM showed similarly low total error values betweenthe 30% and 80% percentiles.68Chapter 4: Elliptical Time-Density Model To Estimate Wildlife Utilization DistributionsProbability0 - 0.000040.00005 - 0.000210.00022 - 0.000530.00054 - 0.000940.00095 - 0.001520.00153 - 0.002170.00218 - 0.002990.003 - 0.004020.00403 - 0.00750.00751 - 0.01046a. b. c.d.!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!! ! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!! !!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 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!! !!!!!!!!!!!! !!!!!!!!!! !!!!! !!!!!!!!!!!!!!!!!!!!!!!!!e. f.0 75 15037.5 KilometersFigure 4.3: The ETD movement model. UD probability values have been colorcoded to range from low chance of occurrence (green) through to a high chanceof occurrence (red), while blank (white) areas had less than 1E-15 probabilityof occurrence and were subsequently set to zero probability. A) Dataset D1 (1hour resolution) B) Dataset D2 (50% randomly deleted points resulting in variableresolution up to 20 hours data-gap) C) Dataset D3 (24 hour re-sampled dataset).D) ETD model of D1 using max speed value and parameters from Table A.1 E)ETD model of D2 using max speed and the multi-temporal parametrization of theWeibull distribution with parameters found in Table A.2 F) ETD model of datasetD3 using Weibull parameters found in Table A.3.69Chapter 4: Elliptical Time-Density Model To Estimate Wildlife Utilization Distributions50% Area 95% Area 99% AreaD1D2D3Area [Km2 ]02000400060008000100001200014000Figure 4.4: Comparison of the 50%, 95% and 99% percentile areas calculatedfrom ETD models based on the datasets D1, D2 and D3. The maximum speedvalue found within each dataset has been used as the maximum speed value in theETD model.70Chapter 4: Elliptical Time-Density Model To Estimate Wildlife Utilization Distributionsa. b.c. Probability0 - 0.000050.00006 - 0.000230.00024 - 0.00050.00051 - 0.000850.00086 - 0.00130.00131 - 0.001930.00194 - 0.002740.00275 - 0.003870.00388 - 0.006470.00648 - 0.011460 30 6015 KilometersFigure 4.5: ETD UDs calculated from dataset D1: A) ETD calculated using themaximum speed (6.43 km/hr) b) ETD calculated using the 99% empirical Weibullspeed value (3.01 km/hr) c) ETD calculated using 50% empirical Weibull speedvalue (0.29 km/hr)71Chapter 4: Elliptical Time-Density Model To Estimate Wildlife Utilization Distributions50% Area 95% Area 99% Area50%99%MaxSpeedArea [Km2 ]010002000300040005000Figure 4.6: Comparison of the 50%, 90% and 99% ETD model percentile con-tour areas calculated for the elephant ’Salif’. The ETD has been parametrizedin three ways: using a maximum speed value of 50% and 99% of the empiricalWeibull speed distribution and by using a constant speed equivalent to the maxi-mum empirically-derived speed (6.44 km/hr) found in the tracking dataset.72Chapter 4: Elliptical Time-Density Model To Estimate Wildlife Utilization Distributions      A.     B.     C.Figure 4.7: Accuracy assessment of the ETD, BBMM and KDE models. Modelswere compared with the true UD calculated from the 15-min data. A) Errors ofcommission. B) Errors of omission C) Total error taking into account both omis-sion and commission errors (Total Error =√omission2 + commission2 ).73Chapter 4: Elliptical Time-Density Model To Estimate Wildlife Utilization Distributions4.6 DiscussionThe ETD movement model provides a useful framework for estimating animalspace-use based on discrete time tracking data. Elliptical based modeling of move-ment, rooted in the theory of time-geography, is a unique approach to estimat-ing animal space-use, yet development in this direction has been relatively recent(Downs, 2010; Downs et al., 2011; Long & Nelson, 2012). The ETD model buildson this foundation and, by doing so, offers several distinct properties relative toother methods of animal UD estimation, including biologically-based parametriza-tion that avoids assumptions regarding the underlying movement process. The lackof biological realism or interpretability in model parametrization has been raisedas a weakness in previous space-use and movement modeling approaches.4.6.1 Trajectory-Based ModelAn important characteristic of the ETD model is that it is developed based on con-sideration of the trajectory of an animal and explicitly incorporates the temporalityof recorded positions by considering pairs of observed locations in their tempo-ral sequence in the parametrization of the geo-ellipses used to estimate space use.Use of the multi-temporal parametrization of the Weibull scale function in equa-tion 4.7 lets the ETD model adapt to changing temporal lengths between posi-tional pairs and makes the model flexible in order to handle any temporal samplingregime with biological realism. Explicit treatment of the serial structure withintrajectory-based models obviates consideration of independence issues that typi-cally arise with other non-trajectory based spatial-use estimators (Swihart & Slade,1985, 1997; Horne et al., 2007). The recent development of trajectory-based space-use models, including the BBMM (Horne et al., 2007), the dBBMM (Kranstauberet al., 2012), the TGDE model (Downs et al., 2011) and the PPA model (Long &Nelson, 2012), has been a departure from methods such as KDE (Worton, 1989)that focus on the point pattern of recorded locations but don’t explicitly model tem-porality or movement between points. Trajectory-based models are critical when74Chapter 4: Elliptical Time-Density Model To Estimate Wildlife Utilization Distributionsinterested in the connectivity or directionality of movements within a landscape(Horne et al., 2007).The ETD model introduced here has several strengths relative to other recentlydeveloped trajectory-based methods. The method requires no assumptions aboutthe form of movement used by the animal in contrast to both the BBMM anddBBMM models that assume Brownian motion despite its known short-comingsfor modeling the movements of most species (Horne et al., 2007). Rather, the ETDmodel simply establishes constraints on movement based on the empirically ob-served data or, alternatively, a user’s knowledge of the biology of the species. Mycomparison of omission-commission error demonstrates the strength of the ETDapproach in that the ETD99 model provided the best estimate of space used (low-est error rate) relative to BBMM, TGDE or KDE (Figure 4.7). This analysis alsoprovides a useful framework for determining the strengths and weaknesses of dif-ferent UD model structures.In contrast to the approach (PPA) of Long & Nelson (2012), ETD is a proba-bilistic model leading to a UD, whereas the PPA model establishes overall boundsof where an animal might have traveled between locations. This outer boundingoutput makes the PPA more similar to a minimum convex polygon (MCP) approachthat delineates the outer bounds of movement when considering independent fixes(White & Garrott, 1990). As a result of this fundamental difference, I do not di-rectly compare the ETD method to this approach.Finally, Downs et al. (2011) used two probability density functions - uniformand linearly decreasing - to calculate probability density values at landscape pointswithin the maximum ellipse area. The ETD approach is fundamentally differentin that by calculating the expected time-density value (of all elliptical areas cor-responding to speeds equal-to, or greater-than, the minimum speed necessary toreach a landscape point) using the probability distribution of speed (equation 4.1),I address the question of how long an animal is likely to have spent at a given pointin the landscape.75Chapter 4: Elliptical Time-Density Model To Estimate Wildlife Utilization Distributions4.6.2 ParametrizationSpace-use models have generally been classified as being either parametric or non-parametric (White & Garrott, 1990; Kernohan et al., 2001). I consider the ETDto be non-parametric given that the model is developed solely on empirical data.Although I selected the probability density function f (s) in equation 4.1 to bethe two-parameter Weibull distribution because of its close fit to the empiricallyobserved speed distribution, the ETD is not limited to this distribution, and param-eters can be drawn from other distributional forms (e.g., Gamma) or by using theempirical distribution itself. The maximum speed parameter is the primary user-defined parameter affecting model output. But unlike many models, this parametercan be selected based on biologically relevant emergent properties of the under-lying data. Within the BBMM model, for example, Long & Nelson (2012) havenoted that the animal mobility variance parameter, which controls the spatial extentof each Brownian bridge density function connecting positional pairs, and is a crit-ical model parameter for BBMM, is difficult to interpret. Similarly, the smoothingparameter used in the popular KDE model (Worton, 1989) is also difficult to link tothe underlying biology of the species and its initial selection can even be subjective(Katajisto & Moilanen, 2006; Horne et al., 2007; Kie et al., 2010). Even should auser choose to parametrize ETD subjectively, the parametrization and model outputcan be interpreted biologically, a strength lacking from other approaches.The ability to vary the maximum speed parameter, either as a percentage of thefitted Weibull distribution, or biologically, based on prior knowledge of an indi-vidual animal’s movement characteristics (e.g., elephant biomechanics (Langmanet al., 1995; Hutchinson et al., 2003)), is important in constraining the extent ofthe ETD model output. Use of higher maximum speed parameter values are leastprone to errors of omission but lead to the largest area of use in any given scenario(Figure 4.7). However, it is biologically unrealistic for most terrestrial animals tofrequently move at their top speeds (although this may in fact be true for certainaquatic or avian species). As such, using a high maximum speed value (e.g., the99% value) may inherently over-estimate the areas used by the animal leading toerrors of commission (Figure 4.7). Selection of maximum speed parameter mayalso be driven by the goals of the intended output of the space-use model and be76Chapter 4: Elliptical Time-Density Model To Estimate Wildlife Utilization Distributionsguided by the particular questions the analyst is asking. The model user must alsodecide what the consequences are for a given modeling scenario in committingomission errors by selecting a low maximum speed value versus commission er-rors when selecting a high value. Interestingly, for the elephants sampled here, the99% percentile maximum speed value model (ETD99) provides the least overallerror when considering all UD percentile contour areas and was nearly matched bythe BBMM model between the 30% and 80% percent contour areas.Choice of a maximum speed value of anything less than the empirically-derivedmaximum speed will result in the generation of straight line segments between po-sitional pairs, rather than elliptical regions (i.e., infinitely eccentric ellipses withzero area). The ETD model handles this situation by calculating the time-densityvalue along the straight line segment and therefore every positional pair contributestowards the overall UD. Skipping the positional pair if the maximum speed pa-rameter is below the speed necessary to move between positions — as conductedby Downs et al. (2011) — biases the UD. The connectivity property of the ETDmodel ensures that connectivity of the sequentially recorded dataset is preserved inthe output UD, a particularly important quality when assessing animal movementcorridors (Horne et al., 2007).The effects of the maximum speed parameter are also linked to the user-selectedoutput UD grid cell size. If the selected grid cell size is too coarse, then manylandscape evaluation points (grid cell center points) will become unreachable, es-pecially as the minimum straight line speed value smin approaches the maximumspeed parameter value. A finer grid cell size will therefore result in a more preciseoutput UD. A consequence of choosing a finer output grid is increased computationtime and system resource requirements, thus this decision will likely be a balanceamongst these trade-offs.Determining the best-fit parameters for the two-parameter Weibull distributionfrom empirical data is based on using straight line segments to connect positionalpairs in the tracking dataset. An argument against this approach might follow thelines that since the animal rarely moves in straight lines between points, espe-cially as the temporal separation between observed locations increases, the Weibullparametrization is not representative of the true movement speed distribution of theanimal and is likely to be an under-estimate of the speeds capable by the animal.77Chapter 4: Elliptical Time-Density Model To Estimate Wildlife Utilization DistributionsHowever, we are modeling probable space-use between points and, therefore, de-riving the top speed from the animal’s movements at the sampling interval is abiologically sensible solution. Further refinement of the method could attempt toincorporate biologically relevant structure in the parametrization of the Weibullmodel. For instance, circadian, movement state specific, landscape-related or sea-sonal patterns in movement could be modeled directly and used to parametrizeETD for relevant time periods. Such refinement would likely offer more accurateparametrization of movement properties without increasing computational require-ments, should such structure be incorporated post hoc. In addition, the error struc-ture of the location estimates (GPS points or otherwise) can be modeled to incor-porate additional uncertainty to the output UD, though the utility of incorporationof location error relates to the data (high versus low accuracy), underlying gridparametrization (coarse versus fine), and movement characteristics of the animal.4.7 ConclusionThe ETD model estimates the UD of an animal from discrete-time positional dataand can be used with both regularly and irregularly sampled datasets of varyingtemporal frequency. The ETD movement model builds on the concept of ellip-tical constraining regions and time-geography by introducing a new time-densityfunction that determines the most likely time-density value (time spent per unitlandscape) at a particular landscape point and is an important conceptual departurefrom other methods. The model is non-parametric and makes no assumption aboutthe mechanistic movement behavior of the observed animal, providing an unbi-ased estimate of the animal’s temporal space-use. Time information is implicitlyencoded in the model formulation, freeing the output UD estimate from statisticalissues of auto-correlation. The ETD model development presented in this chap-ter, along with freely available software for calculating the ETD model, provides aframework for incorporation of the ETD model within generalized animal trackingstudies.78Chapter 5Characterizing Properties AndDrivers Of Long DistanceMovements By Elephants(Loxodonta africana) In TheGourma, Mali5.1 IntroductionFree and wide-ranging movements by terrestrial herbivores at landscape scales arean important characteristic in many ecological systems, both for survival of in-dividuals and successful functioning of ecosystems (Berger, 2004; Bolger et al.,2008). Long distance movements of animals can affect ecological characteristicssuch as community structure, population size or carrying capacity (Fryxell & Sin-clair, 1988b), community interactions between nutrient transport and vegetationgrowth (McNaughton et al., 1988), and predator-prey dynamics (Fryxell & Sin-clair, 1988b).Movement strategies are generally related to system-specific spatio-temporalresource heterogeneity (Jonzén et al., 2011; Holt & Fryxell, 2011) and itinerantmovements of animals tend to coincide with seasonal resource pulses as a way toimprove energy and nutrient intake in variable environments (Fryxell & Sinclair,1988b,a; Wilmshurst et al., 1999; Holdo et al., 2009). These movements are typ-ically categorized as seasonal nomadism, migration or dispersal, and thought tobe more common in landscapes with limitations on resource availability although79Chapter 5: Characterizing Properties And Drivers Of Long Distance Movements By Elephants(Loxodonta africana) In The Gourma, Malimore precise definitions are still needed (Börger et al., 2011).Many systems involving long-distance movements by animals are under criti-cal threat or have been lost due to human impacts and environmental change (Harriset al., 2009; Dobson et al., 2010). A species’ inability to maintain long-distanceranging habits can have a domino effect on the entire ecosystem (Dobson et al.,2010). Maintaining the integrity of systems with large scale animal movementsis often contingent on just a few, relatively innocuous, spatial bottlenecks that aremovement crux points, easily disturbed and vulnerable to human influence (Bergeret al., 2006, 2008; Sawyer et al., 2009). Additional research that provides a de-tailed ecological understanding of these movement systems and associated cruxesis a conservation priority (Wilcove & Wikelski, 2008). As highlighted in recentframeworks for the study of movement ecology (Nathan et al., 2008), it is criticalfor conservation to define the where, when, how and why of large scale animalmovement systems. Here, I provide an analysis focused on addressing these ques-tions of one of the planet’s widest-ranging terrestrial movement systems: that ofdesert-adapted African elephants (Loxodonta africana) living in the Gourma regionof Mali.Expansion of the Sahara 5500 years BP (Kröpelin et al., 2008) and over -exploitation led to the widespread eradication of elephants in North Africa (Bouchéet al., 2011). As a result, the Gourma elephants are now the northernmost popu-lation in Africa (Blake et al., 2003) and a critical population with respect to theconservation status of the endangered elephants of north-west Africa (Blanc et al.,2007; Bouché et al., 2011). They inhabit an ecological extreme for the specieswhere the environment is harsh and highly variable, spanning a wide ecologicalgradient. Initial investigation has found that the Gourma elephants move season-ally in what appears to be a large-scale migration (Blake et al., 2003), but themovement tactics and drivers of their unique space-use patterns have not yet beencritically assessed.In this study, I use Global Positioning System (GPS) tracking data on the ele-phants coupled with remotely sensed landscape covariate data in order to char-acterize the Gourma elephant movements and their drivers. I first focus on spa-tially quantifying the movements by using both traditional home range metricsand a novel non-parametric time-density approach for mapping animal movements80Chapter 5: Characterizing Properties And Drivers Of Long Distance Movements By Elephants(Loxodonta africana) In The Gourma, Maliand identifying high density use areas. I also develop and apply a new velocity-grid method for both summarizing movements at the landscape-scale and identi-fying spatially-clustered regions of similar movement behavior. In principle, thevelocity-grid approach is similar in function to state-space techniques for analyz-ing and categorizing movement trajectories (Patterson et al., 2008). These methodsallow me to characterize the where, when and how of their space use patterns.Water availability and forage abundance and quality are factors known to af-fect the movements and distribution of elephants in arid and savannah ecosystems(Western, 1975; Western & Lindsay, 1984; Chamaillé-Jammes et al., 2007; Loarieet al., 2009). As a result of their long gut-length and massive energy intake require-ments, elephants are thought to be heavily reliant on forage abundance (Owen-Smith, 1988) and respond spatially to vegetation availability (Harris et al., 2008;de Beer & van Aarde, 2008). Also, as obligate drinkers their movements are con-strained by access to water. I address why the observed spatial patterns and move-ments might emerge as a result of these biological properties by analyzing theirmovements and range in relation to vegetation and rainfall. In combination, thisinformation provides a detailed overview of the movement ecology of the Gourmaelephants that can help in the understanding and protection of this unique popula-tion of African elephants.5.2 Materials And Methods5.2.1 Study AreaThe Gourma elephants, numbering around 350 individuals (Bouché et al., 2009),are presently found in the region south of the Niger river lying between the townsof Douentza and Gossi and extending south into northern Burkina-Faso (bound-ing coordinates: 3.1°W, 0.8°E, 16.6°N, 14.3°S). The region (Figure 5.1) lies inthe Sahelian eco-region (Grove, 1978). The physiography is a mixture of undulat-ing dune structures of sandy substrate covered in grasses (Cenchrus biflorus) andAcacia scrub (Sinclair & Fryxell, 1985; Blake et al., 2003), with patches of denservegetation and forest found in water drainage areas that together make up 54% ofthe region. Large flat clay pans, laterite plateaus and sandstone inselbergs cover a81Chapter 5: Characterizing Properties And Drivers Of Long Distance Movements By Elephants(Loxodonta africana) In The Gourma, Malifurther 46% of the ground area. Vegetation communities include Balanites aegypti-aca, Acacia raddiana, Acacia seyal, Pterocarpus lucens, Grewia bicolour, Bosciasenegalensis, Acacia nilotica and Salvadora persica among others. The only tarredroad is the RN16 highway. Traditional nomadism and transhumance (Breman &de Wit, 1983) is practiced by the majority Fulani and Touareg ethnic groups, whofollow their livestock to water and pasture. Recent sedenterization is leading tochanges in land use and expansion of an agricultural lifestyle.Rainfall follows a north-south gradient with cumulative annual totals rangingbetween 110 mm in the north and 600 mm in the south. Based on average an-nual rainfall totals from 1998 to 2008, measured at three rain gauge sites at Boni,Gossi and I-n-adianatafane (Fig. B.1), the months early-June to late-Septemberwere defined as the wet season, with rainfall peaking in July-August (Fig. B.1).Temperatures follow a seasonal cycle with the months of November-January beingrelatively cool with night-time temperatures below 10 degrees Celsius, and peak-ing during the hot season in May, when daytime highs can reach above 50 degreesCelsius.During the dry season, surface water is limited to a series of shallow lakes thatare recharged by precipitation. These lakes often occur along drainage paths or theinterface between dunes and plateaus. Adiora, Agofou, Banzena and Gossi are theonly lakes within the current elephant range that usually retain water throughoutthe year, although even they can also dry up completely. Droughts have affectedthe region over the years (Agnew & Chappell, 1999), with the most recent oneoccurring in 2009 (Douglas-Hamilton & Wall, 2009).5.2.2 Elephant Position DataIn March 2008, nine Global Positioning System (GPS) tracking collars were de-ployed on four female and five male elephants (Table B.1). Individuals were ran-domly selected from across the study area, but each female was selected so as torepresent a separate herd. Each collar (manufactured by Televilt Positioning AB,Lindesberg, Sweden) was set to acquire a GPS position every hour.GPS data collected from collars were filtered using an upper, biologically basedthreshold speed of 7 km/hr to weed out erroneous fixes caused by GPS error. I cal-82Chapter 5: Characterizing Properties And Drivers Of Long Distance Movements By Elephants(Loxodonta africana) In The Gourma, Maliculated the consistency of collars at reporting accurate GPS fixes every scheduledhour during the working lifetime of the collar (Table B.1). All spatial data wereprojected to the Universal Transverse Mercator (UTM) WGS-84 reference sys-tem (Zone 31N). All further calculations were made on this filtered and projecteddataset.5.2.3 Home Range Metrics: MCP, Kernel, aLoCoH & Time-Density100% Minimum Convex Polygon (MCP) home ranges (Mohr, 1947; White & Gar-rott, 1990) and Localized Convex Hull (LoCoH) home ranges parametrized usingmaximum displacement (aLoCoH) (Getz et al., 2007) were calculated for both totalavailable data (n=8; data from the bull ‘El Mozaar’ were dropped from all analysesbecause of its poor quality — see Table 5.1 and Table B.1) and, for those indi-viduals with at least one year of data; 1st year data only (n = 6). 50% and 90%Gaussian kernel home ranges using least-squares cross validation (LSCV) werealso calculated using Hawth’s Tools (Beyer, 2004).Grid areas were calculated using total and 1st year data as follows: a 500 meterresolution grid (selected to be approximately double the median hourly movementdistance and aligned with the closest whole number 500 meter UTM division inboth easting and northing) was draped over the terrain and any grid that containeda fractional track segment was counted towards the grid area. Ratios of MCP rangesto grid ranges were calculated using 1st year movement data. The ratio providesa metric of how concentrated the movement of each animal is within the spacedelineated by the MCP area.A time-density grid was generated for each elephant to look at the distributionof time spent per unit of landscape across the study region; in effect, an estimationof an elephant’s utilization distribution (UD) (Marzluff et al., 2001). The numberof hours an elephant spent within each 500 meter grid cell was determined bysumming the fractional linear path lengths between successive GPS points that fellwithin a particular 500 meter grid cell. Consider a pixel G at row i and column j.The time spent within G is then calculated as:83Chapter 5: Characterizing Properties And Drivers Of Long Distance Movements By Elephants(Loxodonta africana) In The Gourma, MaliFigure 5.1: Map of the study area showing combined GPS positions from nineAfrican elephants between March 23, 2008 and September 30, 2010 (females – red;males – blue). Areas of overlap are highlighted in green. The Global MinimumConvex Polygon (GMCP) calculated from all data merged is outlined. The back-ground image, based on the MODIS Vegetation Continuous Fields (VCF) product,is overlaid on a digital elevation model showing areas of vegetation (green) anddunes (light-brown),bare-ground and rock (brown) and permanent water (blue).Select geographic names: Adiora (1), Agofou (2), Banzena (3), Boni (4), Gossi(5), Inani (6), I-n-adiatafane (7), La porte des éléphants (8), Teze (9).84Chapter 5: Characterizing Properties And Drivers Of Long Distance Movements By Elephants(Loxodonta africana) In The Gourma, MaliTG =N∑k=1dksk(5.1)where dk is the fractional length of track segment k that intersects pixel G, N isthe total number of track segments in the animal’s trajectory and sk is the animal’slinear speed over track segment k.Time-density grids for each elephant were normalized by dividing each gridcell value by the total tracked time for the particular elephant. A merged grid wasgenerated for both males and females where each pixel represents a percentage ofthe total tracked hours spent within the grid cell. The male and female percentagegrids were then multiplied to generate a percentage overlap grid.A search was made for time-density hot-spots by identifying particular groupsof pixels where elephants were spending the majority of their time. I used the upper5% percentile value, calculated from the respective male and female time-densitygrid values, to define a cut-off point for each grid. Only those pixels in the upper5% were considered further. I then ranked clusters of adjacent pixels (hot-spots) indescending order based on the total number of pixels in the grouping (adjacency ofa pixel to another was defined as requiring two pixels to touch on any of the fourpossible sides or four corners).5.2.4 Linear Movements & Velocity-GridsFirst-year total movement path distance was calculated for those elephants with atleast 95% temporal coverage for the first full year of data collection. The maximumlinear path distance moved by each elephant within a 24 hour period was calculatedusing a running window in which any 24 hour section that contained less than 95%temporal coverage was excluded. Maximum hourly displacements were calculatedas the maximum straight-line distances between any two successive data-positionscollected within 1.1 hours of each other.Summarizing landscape-level movement characteristics and data geovisualiza-tion are key components for identifying patterns (Kwan & Lee, 2003). I developeda novel velocity-grid method to illustrate the relative movement patterns and speedsof elephants throughout the range. Initially, a grid of a specified pixel size is estab-85Chapter 5: Characterizing Properties And Drivers Of Long Distance Movements By Elephants(Loxodonta africana) In The Gourma, Malilished spanning all data in the landscape. Statistics are calculated using all tracksegments that originated from within the given grid and include mean speed, meanheading and the mean positive dot-product of unit track segments calculated asfollows:∑i 6= j |cosθi j|∑k=N−1k=1 N− k(5.2)where θi j is the angle between track segment j and segment i and the summationof the absolute cosine value is made only for unique combinations of i and j sincei  j = j  i. The average dot-product value results in a range between 0 (undirectedmovement) and 1 (directed movement). To summarize the Gourma elephant move-ments, I created a relatively coarse 5 x 5 km grid chosen to generalize the move-ment tracks. Separate male and female velocity-grids were created from mergeddata from each sex.Several graphical representations of the output of this technique are possible.Firstly, raster representations of each of the three output grids (mean speed, dotproduct index, or mean heading) can be made by visualizing each individual grid.Alternatively, a combined approach can be used such that for each pixel, a singleoutput vector, with its origin at the center of the given pixel, is created, pointing inthe mean track direction and colored according to the mean dot-product value (0– green, 0.5 – yellow, 1 – red). The length of the vector is scaled to represent themean of the speeds within each grid such thatV L = GR((S¯SP)(SPL−MV L)+MV L)(5.3)where GR is the raster grid resolution, S¯ is the mean speed of tracks within thegrid cell, SP (set point), SPL (set point length ratio) and MV L (minimum vectorlength ratio) are parameters. SPL and MV L are given as proportions of GR whileS¯ and SP are in the units of speed and GR is in the units of the input movementdataset (either projected or unprojected map units).A k-means cluster analysis (Tou & Gonzalez, 1974) was used to classify themale and female mean speed and mean dot-product grids into two classes. The86Chapter 5: Characterizing Properties And Drivers Of Long Distance Movements By Elephants(Loxodonta africana) In The Gourma, Maliclassification was made to segment the velocity-grid into areas of slower, non-directional movement and those of faster, directed movement. To quantify thedegree of spatial-connectedness of directed and undirected grid cells, I calculateda mean ‘contiguity’ index (LaGro, 1991) for clustered patches of both directed andundirected grid cells using the ‘CONTIG’ algorithm in Fragstats 3.3 (McGarigalet al., 2002).5.2.5 Movement PatternI assessed localized changes in range use over the study period by calculating andplotting the centroid coordinate of positions that fell within successive week-longperiods (weekly arithmetic mean of X and Y hourly UTM coordinates) for everymale and female elephant. North-South movements and east-west movements wereconsidered independently.5.2.6 NDVIVegetation biomass and verdancy are both measurable using spectral indices (Peñue-las & Filella, 1998). NDVI is an indicator of vegetation productivity phenology(Rouse et al., 1973). To understand drivers of the elephant migration, I exam-ined NDVI selection patterns throughout the range. NDVI was measured usingthe SPOT-Image 10-day aggregate S10 data product (available at http://www.vito-eodata.be/PDF/portal/Application.html), which has a 1000 meter pixel resolution.A global MCP (GMCP) range calculated from all available data from both maleand female elephants was used to delineate an overall study region (Figure 5.1)from which the mean NDVI values (NDVIGMCP) were calculated over each 10-dayperiod between Apr 1, 2008 and Sept 30, 2010. A localized mean NDVI value(NDVIaLoCoH) was calculated from concomitant 10-day aLoCoH home ranges andcompared to the ecosystem-wide value. The difference between the localized aLo-CoH mean NDVI value and the global mean MCP value (NDVIGMCP) was termed‘DiffNDVI’.Di f f NDV I = NDV IaLoCoH −NDV IGMCP (5.4)87Chapter 5: Characterizing Properties And Drivers Of Long Distance Movements By Elephants(Loxodonta africana) In The Gourma, Mali5.2.7 Statistical AnalysesI used paired and unpaired t-tests to look at inter-sex, season and photo-perioddifferences of mean hourly path distances as well as for comparison of mean first-year cumulative distances between sexes. I also used t-tests to compare 1st yearhome range metrics between male and female elephants. Wilcoxon Rank Sum testswere used when assumptions of normality were violated as dictated by Shapiro-Wilk normality tests (Crawley, 2007).Differences in selection for NDVI between males and females and during wetand dry seasons were assessed using a linear mixed-effects model (Pinheiro &Bates, 2000) with a continuous time autoregressive lag-1 correlation (corCAR1)structure to account for temporal and spatially correlated observations of NDVIbetween successive 10-day periods. Statistical modeling was performed using thenlme package in R (Pinheiro & Bates, 2013). The model specification was:Di f f NDV Iit = β0 +β1SEXi +β2SEASONit +β3SEXiSEASONit +αi + εit (5.5)where DiffNDVI is the difference between NDVIaLoCoH and NDVIGMCP forelephant i at time measurement t, αi are the random effects associated with elephanti and having variance Var(αi)∼ N(0,σ2αI) where I is the identity matrix, N is thenormal distribution and σ2α a constant. εit are the model residuals with varianceVar(εit)∼ N(0,R) and covariance matrix:R =C(k) i = i′0 i 6= i′(5.6)where C(k) is defined as:C(k) = σ2e−|ti j−ti j′ |φ (5.7)where k = ti j− ti j′ , j indexes successive measurement times, σv2 is a constantand φ is a constant related to the practical range of the correlated time-series (Sch-abenberger & Pierce, 2001).88Chapter 5: Characterizing Properties And Drivers Of Long Distance Movements By Elephants(Loxodonta africana) In The Gourma, MaliFigure 5.2: Weekly mean position centroid Northing (a.) and Easting (b.) coordi-nates for female (solid line) and male (dashed line) elephants plotted against themonth in which they occurred. Wet season months are shaded gray.5.3 Results5.3.1 Movement PatternA strong north-south annual movement component was observed among all indi-viduals (Figure 5.2). A strong east-west movement was also observed in all femaleelephants and one male, that when combined with the north-south movements,took the form of a circular pattern traversed in a counter-clockwise direction (Fig-ure 5.1). The remaining four males adopted different patterns including ‘figure 8’and ‘L’ shape landscape movements, and thus the east-west movements were notas clearly defined. Movements south coincided with the onset of rains while move-ments north were less coordinated and varied by sex, with males taking longer toreturn to the northern range.5.3.2 NDVI SelectionElephants tended to use areas of greater NDVI in the study ecosystem throughoutthe study duration, with the strongest differentiation between areas used (aLoCoH)versus ecosystem total (GMCP) during the start of the wet seasons (Figure5.3).Model selection, based on log-likelihood ratio deletion tests, indicated covariates89Chapter 5: Characterizing Properties And Drivers Of Long Distance Movements By Elephants(Loxodonta africana) In The Gourma, MaliFigure 5.3: Time series NDVI values showing the 10-day global MCP mean value- NDV IGMCP - (solid line), the 10-day aLoCoH values - NDV IaLoCoH averaged overall nine elephants (dashed line) and the predicted values from our NDVI selectionmodel (dash-dot line). n is the number of samples used in calculating the means.of sex, and the interaction of sex by season, did not provide additional explanatorypower of NDVI selection. The reduced model explained a significant amount of thevariation in the data (p< 0.001). Both wet (y¯ = 5.86; p< 0.001) and dry (y¯ = 2.57;p < 0.001) season mean NDVI selection values were significantly greater thanzero while wet season selection was significantly greater than dry season selection(p < 0.001). The estimated within-individual practical range parameter (Equation5.7) between repeat time measures was φ = 0.52. The estimated standard deviationof the random inter-elephant variation was σvα = 0.0005 and the standard deviationparameter (Equation 5.7) of intra-elephant variation was σv= 6.925372.5.3.3 Home RangeNo significant difference was found between female 1st Year MCP home ranges(µ¯ = 24,196 km²) and those of males (µ¯ = 15,860 km²) (t = 1.986, p = 0.1303,Table 5.1). The largest recorded total MCP range was 32,062 km² by female ’Ra-mata’. Grid ranges were smaller than MCP ranges and no significant differencebetween 1st year female (µ¯ = 1,415 km2) and male (µ¯ = 1,200 km2) grid rangeswas found (t = 0.987, p = 0.380, Table 5.1). Ratios of 1st year MCP to 1st yeargrid range areas ranged between 22.0 and 11.7 (Table 5.2) with a mean ratio forfemales of 17.1 and 13.2 for males, indicating male range was more concentratedin space than that of females. Total and 1st year aLoCoH home range, and total50% and 90% kernel home ranges are provided (Table 5.2).90Chapter 5: Characterizing Properties And Drivers Of Long Distance Movements By Elephants(Loxodonta africana) In The Gourma, MaliTable 5.1: Summary of statistical analyses of linear metrics and home ranges.Calculation Statistic Female Male Significance(Female > Male)Hourly Displacement(km/hr)Mean 0.47 0.45 No Diff (p = 0.397)1st Year Path Distance(km)Mean 3,968 3,984 No Diff (p = 0.977)Total MCP Range(km²)Max 32,062 20,906 –1st Year MCP Range(km²)Mean 24,196 15,860 No Diff (p = 0.130)1st Year Grid Range(km²)Mean 1,415 1,200 No Diff (p = 0.380)MCP/Grid Ratio Mean 17.1 13.2 –Time Spent North ofN16Sum 65.2% 47.7% –Of the total time-density home range grid cells occupied within the landscape,male and female overlap was 23.9% (Figure 5.1, green pixels). Max grid cell valueswere 1.32% of total tracked hours for females and 1.07% for males (Figure 5.4).The top six male and female time-density hot-spots were found to correspond withthe top six 50% kernel home range areas as ranked in order of size (Figure 5.4) andencompassed 28.2% (female) and 31.6% (male) of the total tracked hours.91Chapter5:CharacterizingPropertiesAndDriversOfLongDistanceMovementsByElephants(Loxodontaafricana)InTheGourma,MaliTable 5.2: Summary of home range metrics. Where insufficient data was available to calculate a given metric, the table entrywas left blank.Elephant1st YearMCPArea(km²)TotalMCPArea(km²)1st YearLoCoHArea(km²)TotalLoCoHArea(km²)1st Year500mGrid Area(km ²)Total500mGrid Area(km ²)1st YearMCP/GridRatioTotal 50%KernelArea(km ²)Total 90%KernelArea(km ²)Bahati (F) – 15515 – 2051 – 584 – 64 503Mariam (F) 19573 20347 4081 4235 1182 1291 16.6 120 898Ramata (F) 31139 32062 5061 5379 1380 1727 22.6 199 1337Tombouctou (F) 21877 23658 4835 5399 1682 2221 13.0 276 1816Achar (M) 11745 12023 2504 3660 1005 1516 11.7 126 689Ali FarkaTouré (M) 16275 17612 4210 5407 1072 2057 15.2 93 902Amadou (M) – 18262 – 4001 – 1175 – 84 794El Mozaar (M) – – – – – – – – –Salif Keita (M) 19561 20906 5484 7479 1522 2979 12.8 220 1755Mean: 20028 20048 4362 4701 1307 1694 15 148 1087SD: 6481 6003 1051 1603 266 733 4 75 49292Chapter 5: Characterizing Properties And Drivers Of Long Distance Movements By Elephants(Loxodonta africana) In The Gourma, Mali5.3.4 Linear MovementsHourly speeds and displacements had a maximum value of 6.10 km/hr for fe-males and 6.43 km/hr for males (Table 5.3). There was no significant difference inmean hourly speed between males (s¯male = 0.45 km/hr) and females (s¯ f emale = 0.47km/hr) (t = 0.904, p= 0.397, Table 5.1) but night-time speeds (s¯night = 0.52 km/hr)were significantly greater than daytime speeds (s¯day = 0.36 km/hr) for all elephants(Paired t-test; t = 7.783, p < 0.001). A significant difference in seasonal hourlyspeeds was found (Paired t-test; t = 2.933, p = 0.019) with a higher wet seasonvalue (s¯wet = 0.48 km/hr) compared to a lower dry season value (s¯dry = 0.41 km/hr).Six collars yielded datasets longer than a year in duration. From these six, themean male 1st year distance of 3,984 km was not significantly different from themean female distance of 3,968 km. (t = 0.031, p = 0.977; Table 5.1). The greatestdistance covered by any of the elephants in a single 24 hour period was performedby the female ‘Bahati’ who moved 64.7 km. This occurred immediately after hercollar was attached, suggesting this high value does not represent normal behavior.The longest 24-hour male movement was 49.0 km.Velocity-grids (Figures 5.5a and 5.5b) segmented into directed versus undi-rected grid cells using k-means clustering show that females (Figure 5.5c) had pro-portionally fewer directed grids than males (Figure 5.5d) (19.3% of total grid cellscompared to 26% for males). Females had an area-weighted mean contiguity indexvalue of 0.20 (directed movement) and 0.61 (undirected movement) while maleshad an area-weighted mean contiguity index value of 0.28 (directed movement)and 0.63 (undirected movement).93Chapter 5: Characterizing Properties And Drivers Of Long Distance Movements By Elephants(Loxodonta africana) In The Gourma, MaliFigure 5.4: (a.) Female Time-Density home range as percent of total hours tracked.Values range from 0% (green) to 1.32% (red). (b.) Male Time-Density home rangeas percent of total hours tracked. Values range from 0% (green) to 1.07% (red) anduse the color scheme as females. The top six hot-spot areas are named while the50% kernel density areas have been encircled in black.94Chapter 5: Characterizing Properties And Drivers Of Long Distance Movements By Elephants(Loxodonta africana) In The Gourma, MaliTable 5.3: Summary of linear path metrics from each elephant. In some cases,insufficient tracking data was acquired to calculate a given metric and values havebeen left correspondingly blank.Elephant 1st YearPathDistance(km)Max HourlyDisplacement(km)Max 24Hour PathDistance(km)Bahati (F) – 5.39 64.68Mariam (F) 3541 6.10 34.08Ramata (F) 3629 6.08 32.63Tombouctou (F) 4734 6.06 49.33Achar (M) 3725 5.74 35.05Ali Farka Touré (M) 3602 5.22 46.62Amadou (M) – 5.24 49.00El Mozaar (M) – – –Salif Keita (M) 4624 6.43 31.61Mean: 3976 5.78 42.87SD: 549 0.45 11.58Table 5.4: Results of statistical comparison between Mali elephants and Kenyaelephants.Calculation Statistic Mali Kenya Significance(Mali>Kenya)1st Year Path Distance (km) Mean 3,976 3,523 No Diff(p < 0.056)1st Year MCP Range (km²) Mean 20,028 1,388 Greater(p < 0.001)1st Year Grid Range (km²) Mean 1,307 468 Greater(p < 0.001)95Chapter 5: Characterizing Properties And Drivers Of Long Distance Movements By Elephants(Loxodonta africana) In The Gourma, MaliFigure 5.5: (a.) Female and (b.) male velocity-grids. Arrows originate from thecenter of 5 km grid cells from which calculations were made. Arrow direction indi-cates mean track direction, arrow length indicates the mean speed and the coloringindicates similarity in track direction as calculated using the mean of the abso-lute value of track dot-products (red=high; green = low). Results of the k-meansclassification for (c.) females and (d.) males. The ‘Directed’ class (high mean dot-product and high mean speed) is shown in white and the ‘Undirected’ class (lowmean dot-product and low mean speed) is shown in gray.96Chapter 5: Characterizing Properties And Drivers Of Long Distance Movements By Elephants(Loxodonta africana) In The Gourma, Mali5.4 Discussion5.4.1 Circular Movement PatternsThe north-south annual movements performed by all individuals, and east-westmovements performed by some, suggest that resource gradients are important tothe Gourma elephants’ ecology and survival. Numerous factors exist that con-tribute to the timing of the latitudinal movement pattern. Principal among theseis thought to be the annual rainfall cycle and elephant movements are generallyknown to be strongly controlled by water availability during the dry season (West-ern, 1975; Smit et al., 2007; Chamaillé-Jammes et al., 2007; de Beer & van Aarde,2008). At the peak of the dry season, water within the elephant home range islimited to a series of shallow, surface fed lakes that exist only in the northern rangeand are prone to drying completely during drought years (Douglas-Hamilton &Wall, 2009). Furthermore, available water is used heavily by livestock and people,leading to competition with elephants (Ganamé et al., 2009). The movement south(Figure 5.2) coincides with the onset of sufficient rain for surface water poolingand alleviates the reliance on larger lakes. Closely associated with rainfall quan-tity is plant productivity, and a north-south NDVI gradient emerges that peaks inSeptember (Figure B.2). Both male and female elephants reached the southernbounds of their range prior to peak rainfall in July/August, with the movementsouth being faster than the more gradual return north between August and January(females) and from August to April (males). The elephants tended to leave thesouthern point of the range before peak NDVI had occurred in September, but ata time when NDVI was also relatively high in the north. NDVI declines to a min-imum by the months of February-April, when cow/calf groups are again locatedin proximity to permanent water (Figure B.2). Selection for higher than averageNDVI occurred during both the wet and dry season, but particularly during the wetseason when elephants were not dependent on surface water points (Figure 5.3).The timing and rate of desiccation of water sources in the south have not yet beenmeasured, but may also influence movement behavior.Previous work in the Malian Sahel by Breman & de Wit (1983) demonstratesthat plant nutritional quality increases along a south to north gradient. Their study97Chapter 5: Characterizing Properties And Drivers Of Long Distance Movements By Elephants(Loxodonta africana) In The Gourma, Malishowed that north of the 300 mm/yr isohyet is where water availability, as com-pared to nitrogen and phosphorous, begins to limit plant growth, and protein lev-els were found to increase, peaking in July and August. As such, this southernmovement may indicate temporary selection for higher biomass and plant verdancyrather than a search for limiting nutrients as described in other migration systems(Holdo et al., 2009). Prior to peak NDVI, the elephants began moving north intolower biomass areas. It is possible the movements are driven by the faster greeningof the southern portion of their range once the rains begin, followed by a slowerdiffusion northward to access higher quality resources prior to their desiccation asthe rains cease.The east-west movement patterns are not well understood but possibly emergefrom elephants trying to reach specific, localized resources, such as mineral de-posits (Weir, 1972) or east-west gradients in vegetation species, while still main-taining an overall optimal latitudinal movement strategy, and results in the observedcircular pattern. Further study of elephant diet and vegetation nutritional quality inthe different parts of the range is needed in order to gain a more comprehensive un-derstanding of the relationship between the temporal movements of elephants andthe dynamics of vegetation protein, nutrient levels, and biomass and their resultingselection for vegetation type at varying times of the year.5.4.2 Spatio-Temporal Partitioning Of Movement BehaviorThe velocity-grid method is a conceptually straightforward, spatially-explicit methodof empirically characterizing modes of movement behavior and complements othersophisticated model-based, state-space approaches (Morales et al., 2004; Preisleret al., 2004). The velocity-grid methodology was able to differentiate explicitmovement patterns by classification of combined directional similarity and speedof movement metrics using the k-means classification algorithm (Figure 5.5), whichresulted in mapped ranges of quick, directed movement compared to ranges ofslow, undirected movement and is highly useful for geolocating and identifyingcharacteristics of a migration path. Beyond the two base classes, it is theoreticallypossible to extend the method to include other biologically interesting modes ofmovement behavior.98Chapter 5: Characterizing Properties And Drivers Of Long Distance Movements By Elephants(Loxodonta africana) In The Gourma, MaliAs seen in Figures 5.5c and 5.5d, and as indicated with the contiguity index,grids of directed and undirected movement tended to form connected spatial blocksindicating aggregated regions of similar movement behavior. Notably, the twolargest contiguous female directed-clusters occurred where their movement trackcrossed the RN16 highway. Similar road response behaviour has been recordedin Loxodonta cyclotis (Blake et al., 2008). Although there was no significant dif-ference between overall male/female movement speeds, males had 6.7% more di-rected grid cells than females, and this could be the result of male ‘musth’ behaviordriving periods of increased speed and directed movement (Rasmussen, 2005).Like seasonal differences recorded elsewhere in Africa (Western & Lindsay,1984; Wittemyer et al., 2007b; Young et al., 2009), the greater distances moved inthe wet compared to dry season are likely a function of water availability and ele-phants not being tied to specific dry season water points. The significantly greaternight-time movement speeds likely arise from the cooler temperatures and the po-tential for fewer interactions with people (Graham et al., 2009).5.4.3 Spatial Utilization HeterogeneityThe time-density methodology quantifies the amount of time spent by an elephantper unit area, providing a time-weighted UD which gives fine-grained detail of rel-ative and absolute elephant spatial-temporal use across the study site. It is morestraight forward to interpret than other methods which require smoothing (thoughtime-density requires choosing a bin size) or assume certain distributional forms,and is similar to the idealized nonparametric estimator proposed by White & Gar-rott (1990). Time-density grids showed heterogeneous utilization of the landscapeby both males and females (Figure 5.4), indicating a spatial partitioning betweendifferent spatial resources. Interestingly, none of the aggregated high-use areas(hot-spots) overlapped amongst the sexes and suggests different resource prioritiesand life strategies between males and females.Higher female MCP/Grid area ratio values indicate more concentrated localmovements and ‘negative’ space (areas not visited) compared to males. Clusteringof water and vegetative resources, which correlate with underlying physiography,most likely explains the emergent spatial distribution. Only 23.9% of occupied99Chapter 5: Characterizing Properties And Drivers Of Long Distance Movements By Elephants(Loxodonta africana) In The Gourma, Malilandscape units were shared. The maximum range size reported here was thelargest in areal extent (MCP) ever recorded for elephants (150.4% larger than inNamibia (Leggett, 2006) and 29.1% larger than in Botswana (Chase, 2007)). Thedaily and annual travel distances of the Gourma elephants were notably similarto those of other arid lands elephant populations (W = 41, p < 0.56; Table 5.4),whereas home ranges were significantly larger (W = 54, p < 0.001, Table 5.4),indicating the Mali elephants spend less time per unit landscape than other semi-arid elephants but expend similar energy budgets on movement. This is likely areflection of the widely distributed nature of resources in the Sahel relative to otherelephant habitats in Africa. Of interest are the seemingly viable resources outsidethe currently recorded range, such as the water abundant Niger River to the north,that are seldom used. Further study is needed to look at vegetation gradients in re-lation to elephant nutritional requirements and at human presence and settlementsoutside of the recorded range, to understand this lack of use. For example, vege-tation abundance along the Niger river may simply be too low and human densitytoo high, to sustain elephant populations north of their current range.5.4.4 Conservation PrioritiesEstablishment of anthropogenic barriers and habitat-loss have historically beenprime factors in the collapse of migratory systems (Bolger et al., 2008). Identifica-tion of vulnerable crux-points, both spatial bottle-necks and core spatial resources,along frequently used movement paths is a critical step towards conservation ofwide-ranging systems. Here, we identified high use regions by assessing the rela-tive proportion of time spent per grid square across the landscape. High-use regionsidentified using the time-density methodology corresponded well with those fromthe traditional kernel estimator. These hot-spots (e.g. Lake Banzena – Figure 5.4)are critical to the spatial integrity of this recorded movement system and may becrux points on which the survival of the population is dependent.The velocity-grid cartographic output and directed grid cell classification high-lighted possible bottle-necks to the movements of the Mali elephants. The mostprominent example based on the directed class patch size and constraining localtopography was identified at position 7 (Figure 5.1). Known locally in French as100Chapter 5: Characterizing Properties And Drivers Of Long Distance Movements By Elephants(Loxodonta africana) In The Gourma, MaliLa Porte des Éléphants (Translation from French: Elephant Doorway) it corre-sponds to a one mile (1.6 km) wide valley through sandstone inselbergs (FigureB.3). Spatial cruxes, such as La Porte des Éléphants, appear to be critical elementsto the continued functioning of this exceptional system.101Chapter 6A Pan-African Analysis OfFine-Scale Elephant RangingBehaviour6.1 IntroductionThe search for the physical, environmental, social and biological drivers of move-ment is of primary interest in the field of movement ecology. Understanding move-ment of a species leads to ecological, conservation and species management in-sight that may be critical for long-term species survival (Geremia et al., 2014).Elephants are known to have large ranging patterns that can sometimes be con-nected by long-distance, easily severed, filamental corridors complicating the con-servation and management of their needs for space and the geometry of that space(Douglas-Hamilton et al., 2005; Wall et al., 2013). Elephants live in highly vari-able environments where access to resources and their spatial decision makingabilities are a critical part of their survival (Foley et al., 2008; Croze, Harvey &Lindsay, 2011). Many elephant populations also currently reside in regions un-dergoing rapid transformation through anthropogenic expansion, and developmentthat has brought them into close proximity with humans, leading to a rise in human-elephant conflict (HEC) (Thouless, 1994; Hoare & Du Toit, 1999; Jackson et al.,2008; Graham et al., 2009). Recent resurgence in illegal killing of elephants fortheir ivory tusks has further compounded these issues (Wittemyer et al., 2014).One method of characterizing spatial behaviour is calculation of an animal’shome range – the areal extent within which an animal resides and uses over a giventemporal period (Burt, 1943; White & Garrott, 1990; Kie et al., 2010). Concep-102Chapter 6: A Pan-African Analysis Of Fine-Scale Elephant Ranging Behaviourtually, the size and geometry of the range circumscribed by an animal should re-flect relationships between the animal and its surrounding environment and internalstate. Compared with other metrics such as linear distance, range area is a uniqueperspective on the movement process because it encapsulates several movementproperties such as the geometric pattern of movement (e.g., correlated, directedmovement versus uncorrelated, random movement) and habitat selection (e.g., siteaffinity and time-spent) that are reflected by the areal morphology and size. Ex-pansion of range logically provides greater access to important resources and couldbe be expressly driven by an animal in search of increasing resource intake but atincreased energetic costs. Movement can also be thought of as a process being in-fluenced by the external environment, such as an elephant moving into hilly terrainwhere its rate of movement must slow as it climbs hills, despite a constant poweroutput, thus leading to a smaller range size as compared to an equivalent period oftime on flat terrain.Technological advances (e.g., Google Earth Engine (GEE) (Hansen et al., 2013b))are facilitating access and processing of environmental covariate information withunprecedented computational efficiency and power. Enterprise movement databasessuch as Loxobase (Chapter 2) or Movebank (Fiedler & Davidson, 2012) provide averitable mine of information on animal movement with data on hundreds of in-dividuals across multiple geographic regions. Emerging spatio-temporal analysistools (e.g., the Regional Raster Stats tool (Wall, 2014) or Env-DATA tool (Dodgeet al., 2013)) can link temporally-dynamic movement patterns to localized envi-ronmental conditions, enabling us to establish a realistic view of the environmentencountered by an animal at a given point in time and space. Statistical modelingof exogenous and endogenous variables concomitant with observed patterns arethen used to reveal the functional nature of these relationships, providing insightinto the dynamics and drivers of ranging behaviour.Of the many possible drivers of movement, I focus on four broad functionalgroupings of variables known, or believed to influence, elephant ranging patterns:i) Vegetation, ii) Terrain, iii) Anthropogenic influence, and; iv) Dataset. Dataseteffects encompass both the Sex of the animal and the Region where the movementdata were collected. To explore the influence of these drivers and attempt to answerthe question ’What are the factors influencing elephant range size across Africa?’,103Chapter 6: A Pan-African Analysis Of Fine-Scale Elephant Ranging BehaviourI will use data from the Loxobase dataset described in Chapter 2 (approximately3.2 million fixes) to model the relationship of short temporal period (16-day) rangesizes with a selection of covariates estimable in each of the four distinct ecoregions:Desert, Savannah, Bushveld and Forest. Given the wide range of habitats utilizedby elephants across these regions I expect there will be a high degree of variation inelephant range size. I first establish a priori predictions of range behaviour basedon current theory and previously published results.Vegetation Satellite remote sensing has made it possible to spatially quantifyvegetation health, productivity and, in some cases, abundance over reasonablyshort frequencies and over large areas (Pettorelli et al., 2014). An accepted methodof measuring vegetation health and productivity is the Normalized-Difference Veg-etation Index (NDVI) (Rouse et al., 1973; Pettorelli et al., 2011), which is calcu-lated as the ratio of the difference in reflectance of near-infrared and red wave-lengths. Young et al. (2009) used SPOT NDVI datasets to examine elephant distri-bution in Kruger Park, South Africa and discovered that elephant density increasedin areas with higher NDVI. Loarie et al. (2009) found that elephants exhibited se-lection for localized areas of higher than average Enhanced Vegetation Index (EVI)(a measure similar to NDVI but that is less correlated with biomass). Bohrer et al.(2014) used NDVI to analyze movements of elephants up and down the elevationgradient on Mt. Marsabit in Kenya and concluded Marsabit elephants follow a’surf’ model (Bischof et al., 2012; Fryxell & Avgar, 2012) by tracking a particularlevel of vegetation greenness. Frequency analysis of net 3-hour displacements ofelephants in Samburu, Kenya show that movement patterns were the least auto-correlated (i.e., the most random) at peak NDVI values (Wittemyer et al., 2008),further suggesting that vegetation productivity has a direct influence on elephantforaging strategy and movement patterns.NDVI also provides a means to assess the state of cyclical wet and dry seasonsin Africa, after accounting for values lagged by several weeks after the commence-ment of rains (Wittemyer et al., 2007a; Bohrer et al., 2014). De Villiers & Kok(1997) found home range increased for both male and females during the wet sea-son in Kruger National Park, South Africa. Similar results have been reported byLindeque & Lindeque (1991) and Wittemyer et al. (2007b). Western & Lindsay104Chapter 6: A Pan-African Analysis Of Fine-Scale Elephant Ranging Behaviour(1984) reported a wet season range expansion by the Amboseli elephants but nosignificant seasonal migration away from the park. With results apparently at oddswith those of De Villiers & Kok (1997), Grainger et al. (2005) reported no effectof season on the home range of elephants living in Kruger Park. Similarly, Ntumiet al. (2005) found that season had no effect on the home range of elephants in theMaputo reserve, Mozambique.Evolutionary sexual dimorphism in elephants has resulted in males growingto 5/3 the mass of females (Owen-Smith, 1988) and, as a result, males posses acorrespondingly longer gut length that allows them to extract greater nutritionalvalue from food and can thus utilize more marginal vegetation areas compared tofemales (Owen-Smith, 1988). However, they also require correspondingly greaterquantities of vegetation compared to smaller females and juveniles. These physi-ological principles suggest that we will see differences in vegetation selection andpossibly range size, especially during periods of low vegetation quality. de Beer& van Aarde (2008) suggest that, based on nutritional requirements, dry seasonranges should be larger than wet season ranges in arid environments and that wateravailability curbs the nutritional requirements of elephants. In Chapter 2 I foundthere was significant sexually-based variation in range area size measured over oneyear periods, but it is not clear whether the same pattern exists at shorter 16-daytime scales.Hypothesis 1: Elephant range size will decrease as vegetation quality increaseswithin the range areaHypothesis 2: Elephant range size will decrease as vegetation abundance increaseswithin the range areaAnthropogenic Influence Anthropogenic presence in its various forms (e.g.,roads, settlements, poaching and insecurity) is a known factor influencing elephantranging behaviour (Blom et al., 2005; Laurance et al., 2006; Blake et al., 2007;Buij et al., 2007; Chase & Griffin, 2009). The dynamic between elephant move-ment and distribution and human presence is critically important and the humanfootprint (Sanderson et al., 2002) is growing at extreme rates. Hoare & Du Toit(1999) have shown that elephant density can remain relatively stable up to a criti-105Chapter 6: A Pan-African Analysis Of Fine-Scale Elephant Ranging Behaviourcal threshold of human density, at which point elephant presence disappears almostcompletely. Blake et al. (2008) have shown that a measure of human presence —roads — has a direct consequence on elephant range. Based on tracking data fromforest elephants (Loxodonta cyclotis) in the Congo Basin, they discovered that thepresence of roads limited range size. Additionally, only one road-crossing wasever observed outside of protected areas, and the elephant’s speed increased four-teen times the mean during the crossing.Blom et al. (2005) also found a negative relationship between forest elephantpresence and the human footprint (‘human-trace’) within the Dzanga-Sangha Pro-tected Complex in the Central African Republic. They used an index for human-trace based on distance from roads, distance from villages, hunting trace, collectiontrace, passage trace, and total human trace. Using Principle Component Analysis(PCA) they found that 39% of elephant distribution could be explained by the hu-man footprint.Douglas-Hamilton et al. (2005) were the first to show that elephants tend tomove through unprotected areas at high speeds ,and often at night, in order to avoidconflict with humans – a behaviour they called streaking. Graham et al. (2009)looked at elephant spatial behaviour in relation to a risk landscape in Laikipia,Kenya. The risk landscape was dependent not on human presence and density buton the level of tolerance to elephant presence. They found that elephants tended tooccupy high-risk areas more at night than during the day, and traveled at higher-speeds in high risk areas than in low-risk regions.Although many protected areas for elephants do exist, range analysis has inmany cases shown that gazetted boundaries for wildlife reserves are far smallerthan the home ranges of most elephants. For example, in Amboseli, Kenya, ele-phants range over an area 20 times the size of Amboseli National Park (Croze &Moss, 2011) which has important implications for their conservation. In ZakoumaPark, Chad, seasonal movements take elephants beyond the boundaries of the re-serve where they are likely to be the target of intense poaching (Dolmia et al., 2007)and at least 2,000 elephants have been killed in this manner (WCS, 2008).Hypothesis 3: Elephant range will decrease in areas of high anthropogenic influ-ence (human footprint)106Chapter 6: A Pan-African Analysis Of Fine-Scale Elephant Ranging BehaviourHypothesis 4: Elephant range will decrease inside of protected areasTerrain Wall et al. (2006) looked at the effect of slope on elephant distribution asrecorded from 54 elephants tracked within Samburu National Reserve. They foundthat the probability of finding an elephant decreased exponentially with increasinghill slope. They looked at the energetics of moving up hills as a possible explana-tion for this relationship and found that it takes a 5,000 kg elephant 2500% moreenergy to move a vertical meter than to move a horizontal meter.Hypothesis 5: Elephant range size will decrease with increasing hilliness (slope)6.2 Methods6.2.1 GPS TrackingGlobal Positioning System (GPS) tracking collars were deployed onto 247 ele-phants between 1998 and 2013 in an intensive, pan-African tracking program ledby Save the Elephants, Kenya. The animals, datasets, database, study regions andtracking system are fully described in Chapter 2. Of the 247 animals, 5 animalswere dropped from the analysis because their datasets occurred before the availabil-ity of the remotely-sensed imagery products used to calculate covariate information(i.e. Christo-Jacob, Douglas; FortySix; Lewa1; Sage).6.2.2 Range AreaI selected the non-parametric ’adaptive’ Localized Convex Hull (aLoCoH) rangeestimator (Getz & Wilmers, 2004; Getz et al., 2007) because of its ability to cap-ture hard-edges in ranging patterns (Getz et al., 2007) and its ability to excludeareas not visited by an animal. In order to limit HR estimates to those areas es-timated to have been actually used by animals and not include areas that mighthave only been traversed during bouts of longer distance movement (e.g., streak-ing behaviour (Douglas-Hamilton et al., 2005)), I adopted the definition of HR asspecifying the 95% isopleth area of the aLoCoH regions (Jennrich & Turner, 1969;White & Garrott, 1990; Kernohan et al., 2001; Fieberg & Kochanny, 2005; Getzet al., 2007).107Chapter 6: A Pan-African Analysis Of Fine-Scale Elephant Ranging BehaviourHR area polygons were calculated for each animal using available movementdata concomitant with remotely sensed imagery (16-day NDVI image composites- see description of NDVI product below) using the ArcMET aLoCoH algorithm(Wall, 2014). The ’a’ parameter was estimated based on the maximum separationof any two points following guidelines in Getz et al. (2007). 16-day periods ex-tended beginning on Feb 18, 2000 until Dec 31, 2013 (319 total) defining 12,446aLoCoH range polygons based on the available movement data. aLoCoH polygonswere then used for extracting image statistics for a variety of concomitant variables(covariates).6.2.3 CovariatesCovariate measurements were separable into 4 functional groupings: i) Vegeta-tion ii) Anthropogenic iii) Terrain, and; iv) Animal/Dataset effects. Raster-basedcovariates were processed using GEE (Program C.1) allowing highly parallelizedand fast computation of raster statistics. For each of the 12,446 aLoCoH rangepolygons, the polygon shape was used to perform a spatial selection of pixels inthe underlying raster (i.e. pixels spatially and temporally intersecting the polygon)and from that area I was able to compute a single mean value. Esri ArcMap soft-ware was used for processing the remaining covariates and joining the data tablesoutput from GEE.VegetationNDVI NDVI was calculated using the Moderate-resolution Imaging Spectrora-diometer (MODIS) Nadir Bidirectional Reflectance Distribution Function (BRDF)Adjusted Reflectance (NBAR) (Schaaf et al., 2002) MCD43A4 16-Day productmade available in the GEE computational environment. The 16-day product selectscloud-free pixels from the given temporal period to produce a composite NDVI im-age (i.e., the pixel values could have been measured at any date within the giventemporal period) with 500 m pixel size and values ranging from -1– 1 (https://lpdaac.usgs.gov/ products/ modis_products_table/ mcd43a4).108Chapter 6: A Pan-African Analysis Of Fine-Scale Elephant Ranging BehaviourPercent Tree Cover Percent tree cover was calculated using the MODIS Vegeta-tion Continuous Fields (VCF) Collection 5 Version 1 MOD44B Percent Tree Coverdataset (available at: https:// lpdaac.usgs.gov/products/modis_products_table/mod44b).The VCF Percent Tree Cover product estimates the proportion of woody vegetativecover > 5 m tall in a 250 m pixel (Townshend et al., 2011; Carroll et al., 2011).Anthropogenic VariablesProtected Area Intersection Protected area polygons were acquired from theWorld Database on Protected Areas (WDPA) (IUCN & UNEP-WCMC, 2013). Acustom ArcGIS script was run to determine the percent of overlap of each aLo-CoH range polygon with protected areas available in the WDPA database (valuesranging from 0% overlap to 100% overlap in area).Human Footprint The human footprint (HF) (Sanderson et al., 2002) was mea-sured using the Last of the Wild Project, Version 2, Global Human FootprintDataset (WCS et al., 2005). The HF dataset is calculated from 9 input variables(population density, built-up areas, night-time lights, land use, land cover, coast-lines, roads, railroads, navigable rivers) that are used to assess the relative footprintof human activity normalized by region and biome within 1-km grid cells. The HFraster product was manually uploaded for processing using GEE.Terrain VariablesElevation Elevation values within aLoCoH polygon areas were calculated fromthe NASA’s Shuttle Radar Topography Mission 90 m v4 elevation dataset (Jarviset al., 2008) available in GEE. Elevation was not included as a covariate but wasused to derive slope and TRI estimates below.Slope Slope values were derived from NASA’s Shuttle Radar Topography Mis-sion 90 m v4 elevation dataset (Jarvis et al., 2008) available in GEE. Values rangefrom 0- 90 degrees.109Chapter 6: A Pan-African Analysis Of Fine-Scale Elephant Ranging BehaviourTerrain Ruggedness Index (TRI) TRI was proposed by (Riley et al., 1999) as amethod of using elevation raster data to compute an estimate of the ruggedness ofthe terrain. Consider the following grid of 8 pixels surrounding pixel X:1 2 34 X 56 7 8TRI is defined as T RI = ∑8i=1 (Ei−X)2 where Ei are the elevation values inthe 8 grid cells surrounding the elevation value X . Calculation of TRI was im-plemented using a custom algorithm in GEE based on the SRTM 90m elevationproduct.Dataset VariablesSex Sex was a categorical variable coded as either male or female and used toexamine the effect of sex on ranging behaviour.Region Region was coded as either ’West’, ’Central’, ’East’ or ’South’ corre-sponding to the major geographical region of an aLoCoH polygon within the con-tinent.Species Species (i.e., Loxodonta africana or Loxodonta cyclotis) were separableby Region whereby all elephants within the Central region are L. cyclotis comparedwith L. africana in the West, East and South regions.Name Individuals animals were identified using a unique Name variable.Temporal Granularity IndexThe sampling regime of a movement dataset is known to affect the value of move-ment metrics (Börger et al., 2006) and is therefore an important dataset property toquantify, especially when attempting to compare datasets across a range of differ-ing sampling regimes. Sampling regime (also called ’temporal granularity’ (Laubeet al., 2007; Long & Nelson, 2013)) can be defined by three properties: i) the110Chapter 6: A Pan-African Analysis Of Fine-Scale Elephant Ranging Behaviournumber of points sampled between the beginning and end of a study period, ii)the temporal span between points and; iii) the overall duration of the study period.Sampling regimes vary widely amongst tracking studies: systematic shifts in fre-quency may be introduced in the study to better capture certain species-specificbehaviours, such as switching to a less-frequent daytime sample frequency and amore frequent nocturnal sample frequency when tracking nocturnal predators, ormay also vary randomly, such as tracking marine cetaceans where positional fixfrequency is dictated by the diving behaviour and breathing pattern of the animal,or simply when a tracking unit sampling systematically fails to record a positionat the specified time leading to intermittent gaps. Reporting just one of the threeproperties defining the sampling regime is insufficient to encompass the others. Forexample, a dataset where positions were sampled 499 times on the first day of amonth-long study period and again once at the end has a very different regime to adataset where 500 positions were sampled evenly throughout the month. Lackingfrom current definitions of sampling is a method to encapsulate all three samplingregime properties. I therefore propose the temporal granularity index (TGI):T GI =∑mi=1 T 2iT 2total(6.1)where Ti are the time-spans between the n recorded fixes in the total time periodTtotal for the movement dataset of an individual animal and m = n− 1 (SectionC.1). TGI values range between 1 and asymptotically approach 0 as the numberof sampled fixes within a period Ttotal increases (Figure C.2). TGI values are com-parable for equivalent time-periods only and TGI is minimized for regular intervalsampling (Section C.1). TGI values were calculated for each 16-day period usingthe Temporal Metrics tool within the ArcMET software (Wall, 2014).111Chapter 6: A Pan-African Analysis Of Fine-Scale Elephant Ranging BehaviourTable 6.1: Summary of analysis covariatesCovariate Description Values SourceName Name of individualanimalChapter 2Table S1TrackingDatasetSex Animal’s sex Male/Female TrackingDatasetRegion Region West,Central,East,SouthTrackingDatasetTGI TemporalGranularity Index0-1 TrackingDatasetNDVI Mean NormalizedDifferenceVegetation Index(NDVI) valueswithin 16 dayaLoCoH HR-1 - 1 MODISMCD43A4NDVIPercent TreeCoverMean Percent TreeCover0 - 100% MODISVCFMOD44BProtectedAreaIntersectionPercent Overlap ofaLoCoH area withProtected Areas0 - 100% WPDAHumanFootprintMean value ofhuman footprintwithin aLoCoHarea.0 - 100 WCS HFSlope Mean slope withinaLoCoH area0–90degreesSRTMTRI Mean TerrainRuggedness Indexwithin aLoCoHarea=0 m SRTM112Chapter 6: A Pan-African Analysis Of Fine-Scale Elephant Ranging Behaviour6.2.4 Statistical ModelingTwo modeling approaches were adopted for exploring the relationship betweenrange area and explanatory variables. The first was to use linear mixed-effects(LME) models (Pinheiro & Bates, 2000; Schabenberger & Pierce, 2001; West et al.,2007; Zuur et al., 2009) fit using the nlme package (Pinheiro & Bates, 2013) for Rstatistical software (R Core Team, 2013). The second approach was to use gener-alized additive mixed models (GAMM) fit using the mgcv package for R (Wood,2006; Zuur et al., 2009). Mixed effects models account for intra-animal depen-dence among range area observations and allow the effect of each animal to bemodeled as a random variable, improving model generality. Covariates were first’centered’ by subtracting their mean value to reduce collinearity (West et al., 2007;Zuur et al., 2009) (Table C.1).LMEInitially all covariate variables were included in the LME model specification, in-cluding interactions between Sex and Region using the categorical variable SexRe-gion. A log-normalizing transform was applied to aLoCoH areas log10Area =log10(aLoCoHArea) (Gelman & Hill, 2007; Zuur et al., 2009) after initial modeldiagnostics indicated problems of non-normality. The covariates TRI and slopewere found to be nearly collinear (Figure C.3), and therefore, Aikake’s Informa-tion Criterion (AIC) was used to select between models fit independently witheither Slope or TRI. The full model specification, in terms of a single observationof aLoCoH area for animal i at time t , was:113Chapter 6: A Pan-African Analysis Of Fine-Scale Elephant Ranging Behaviourlog10Areait ∼ SexRegioni+NDV Iit +NDV I2it+Treeit +Tree2it+Slopeit +Slope2it (6.2)+HFit +HF2it+PAit +PA2it+T GIit +T GI2it+SexRegioni×NDV Iit +SexRegioni×NDV I2it+SexRegioni×Treeit +SexRegioni×Tree2it+SexRegioni×Slopeit +SexRegioni×Slope2it+SexRegioni×HFit +SexRegioni×HF2it+SexRegioni×PAit +SexRegioni×PA2it+αi + εitwhere a random intercept αi is specified for each animal and the within-animalresiduals are given by εit . αi and εit are assumed to follow normal distributionsdefined by:αi ∼ N(0,D)εit ∼ N(0,Ri)whereD =Var(αi) =σ2α 0 · · · 00 σ2α.... . .0 σ2α= σ2αIand114Chapter 6: A Pan-African Analysis Of Fine-Scale Elephant Ranging BehaviourRi =Var(εit) = σ2rs1 e−|t1−t2 |ϑ · · · e−|t1−t j |ϑe−|t2−t1 |ϑ 1.... . .e−|t j−t1 |ϑ 1and, where the variance for each Sex in each Region is allowed to vary, σ2rs. Anexponential decay in covariance was modeled between within-animal observationswith an absolute difference in time k = |t j − t j′ | (i.e. continuous auto-regressivestructure with practical range parameter ϑ (Schabenberger & Pierce, 2001)). Theresidual covariance matrix was modeled as block diagonal with zeroes on non-diagonal entries implicating independence of inter-animal errors:σ2 = R =R1 0 · · · 00 R2.... . .0 RnLikelihood ratio tests (LRT) were used to test covariate parameters fit withrestricted maximum likelihood (REML) (West et al., 2007). Optimal model selec-tion was made with LRT of simplified, nested models based on parameters fit usingmaximum likelihood estimation (ML) (West et al., 2007). Once all non-significantterms were removed, the reduced model was re-fit using restricted maximum like-lihood (REML) to provide reliable estimates for regression parameters. Model fitwas assessed using graphical methods (Zuur et al., 2009).GAMMThe GAMM model followed a similar specification as the LME model except in thefixed effects terms where spline smoothers were used in place of 1st and 2nd orderlinear parameters. Interaction terms (i.e., fitting separate splines to combinationsof sex and region) caused numerical estimation problems and were not used withinthe GAMM model. A log-normalizing transformation of the dependent variablewas used after initial model diagnostics indicated non-normality of residuals and115Chapter 6: A Pan-African Analysis Of Fine-Scale Elephant Ranging Behaviourfurther numerical estimation issues prevented the use of either Poisson or Binomialdistributions. The full model specification for a single aLoCoH area for animal i attime t , was:log10Areait ∼ β0 +β1×SexRegioni+s(NDV Iit)+s(Treeit)+s(Slopeit) (6.3)+s(HFit)+s(PAit)+s(T GIit)+αi + εitwhere s() are smooth regression splines and the covariance and random effectsparameters are the same as the LME model described previously. Optimal modelselection was made by successively dropping covariates from the model and testingusing LRT and AIC of reduced, nested models.6.3 ResultsA total of 12,446 aLoCoH ranges areas were initially calculated based on the avail-able data. aLoCoH range areas were filtered to limit 16-day datasets with the equiv-alent of 24-hour sampling or less (i.e. a Temporal Granularity Index of ≤ 0.0625)resulting in 11,295 samples from 226 individual elephants.Elephant 16-day aLoCoH 95% home range areas varied between 0.43 Sq.km(Male, East Africa) to 1042 Sq.km (Male, West Africa) (Figure 6.1) and followedthe same pattern in range area as yearly range areas (Chapter 2): West > South >East > Central.116Chapter6:APan-AfricanAnalysisOfFine-ScaleElephantRangingBehaviourllllllllllllllllllll lllllllllllllllllllllllllllFemale.Central Female.East Female.South Female.West0.00.51.01.52.02.53.0aLoCoH Area Sq.Km (Log10)Figure 6.1: 16-day aLoCoH range areas by Sex and Region (Data are Log10 transformed.)117Chapter 6: A Pan-African Analysis Of Fine-Scale Elephant Ranging BehaviourEmployment of a multi-level linear model (me1) was found to improve mod-eling of the relationship between aLoCoH area and covariates compared with anon mixed-effects linear model (m1) (LRT=1522.1; p<0.001; REML). Allowingfor heterogeneity of residual variance based on both Sex and Region (me2) furtherimproved model fit (LRT=660.4; p<0.001; REML). The practical range parameterwas estimated as ϑ = 0.2 and indicates relative independence between succes-sive range area observations. LME model parameters were estimated based on’treatment’ contrasts (Table C.2). Estimated residual variance was greater in males(Std.Dev=2.4 Sq.km) than females (Std.Dev=2.0 Sq.km) while estimated standarddeviation of the random intercept was 1.5 Sq.km. LME model residuals were nor-mally distributed (Figure C.4).LRT indicated that all LME model covariates were significant including Sex,Region and both 1st and 2nd order terms for NDVI, Tree Cover, Human Footprint,Protected Area Intersect, Slope and TGI variables. Interaction terms between Sex& Region and all covariates were also found to be significant. Direct interpreta-tion of the numerical values of model coefficients (Table C.2) is complicated bythe number of covariates and the interactions between covariates and, therefore,graphical methods were used to interpret model results (Figures C.6, C.7, C.8, C.9,C.10, C.11).Modelling the relationship between range area and covariates using general-ized additive mixed modeling (GAMM) led to similar results as the LME modeland both provide unique perspective on the relationship. Inclusion of animal as arandom intercept improved model fit (LRT=1780.9; p<0.0001; REML). Introduc-tion of a heterogeneity structure by both Sex and Region further improved model fit(LRT=872.1611; p<0.0001; REML). Model selection based on LRT & AIC foundthat all model covariates were significant (Table C.3 & C.4) and retained in the fi-nal model. As expected, modeling the correlation structure of within animal rangearea observations led to the same practical range parameter as the LME model(ϑ = 0.2 ), indicating the relative independence of consecutive observations. Di-agnostic analysis of the final GAMM model residuals (QQ-plots & residuals vs.fitted) indicate close approximation to a normal distribution (Figure C.5).The estimated degrees of freedom (edf) of the spline smoothers indicate the re-lationship between covariates and range area to be generally non-linear (Table C.4),118Chapter 6: A Pan-African Analysis Of Fine-Scale Elephant Ranging BehaviourTable 6.2: Summary statistics of covariate values by regionCovariate Region Min Mean MaxNDVIWest 0.085 0.178 0.389Central 0.266 0.627 0.872East 0.150 0.404 0.838South 0.178 0.401 0.730Tree CoverWest 0.19 0.76 1.90Central 7.08 42.84 78.76East 0.86 7.10 64.98South 3.04 6.15 25.77HFWest 4.56 17.03 34.67Central 1.00 5.92 21.00East 0.00 25.10 54.00South 0.00 11.44 76.33SlopeWest 0.47 0.775 2.285Central 1.63 4.527 12.591East 0.67 2.948 19.327South 0.33 1.865 7.216PAWest 0.00 0.921 1.000Central 0.00 0.759 1.000East 0.00 0.676 1.000South 0.00 0.964 1.000TGIWest 0.001 0.004 0.058Central 0.003 0.029 0.062East 0.001 0.006 0.062South 0.001 0.017 0.061119Chapter 6: A Pan-African Analysis Of Fine-Scale Elephant Ranging Behaviourwhich supports use of the GAMM to model the relationship between range area andcovariates compared with linear models. AIC showed the GAMM (AIC=7089.8)to be a slight improvement over the LME model (AIC=7094.6).There was a 50% correlation between NDVI and percent tree cover, indicat-ing some entanglement by NDVI in measuring both biomass and phenologicalresponse. The Enhanced Vegetation Index (EVI) has also been used to in an at-tempt to separate these two components (Loarie et al., 2009). The relationshipbetween range size and NDVI was found to vary by both Sex and Region (Fig-ure C.6). There was a general increasing trend in range area with NDVI althoughpredictions in East Africa (Male and Female) and Central Africa (Male) show aparabolic curvature with decreasing range at the higher NDVI values. Range sizewas similar between Central and East African elephants for NDVI values above ~0.8. Southern African elephants showed a positive quadratic curvature compared tothe negative curvature in West, Central and East Africa. Presence of the significantinteraction between Sex, Region and NDVI indicate differing behavioural trendsacross the regions and sexes.Tree cover values were very low in West Africa (< 1.9%) and therefore makeit difficult to evaluate trends. Tree cover values were highest in Central Africaas expected (7% - 78%) and followed a general linear increasing trend in rangesize (Male and Female) in contradiction to Hypothesis 2. Patterns in eastern andsouthern Africa were very different, with a general decrease in range size withincreasing tree cover percentage in support of Hypothesis 2. Males in southernAfrica showed extreme variation in range size at tree percent cover between 10-20%.Human Footprint values had the greatest range in southern Africa, between 0and an index of 76, while the forests of central Africa were calculated to be the’wildest’ with a mean index of 5.9 (Table 6.2). A marked drop in range area is seenfor increasing HF index values for all regions (Figure C.8) in support of Hypothesis3. A notable HF threshold index of ~35 corresponded with a dramatic decrease inrange area with increasing HF.The relationship between protected area (PA) intersection and range area demon-strated a maximum for middle values of intersection, whereas range area was aminimum for both low and high values of intersection. This trend is seen across120Chapter 6: A Pan-African Analysis Of Fine-Scale Elephant Ranging Behaviourboth sexes and West, East and Southern Africa, but far less pronounced in Cen-tral Africa (Figure C.10) and in contradiction to Hypothesis 3. PA intersectionranged between 0 (completely outside PAs) and 1 (completely within PAs). South-ern African elephants had the highest intersection of range area with protectedareas and East African elephants the lowest (Table 6.2), although this result maybe swayed by the non-random distribution of collar deployments in relation to pro-tected areas (Figure 2.3 in Chapter 2).Mean slope values within range areas were less than 20 degrees. Range areafollowed a pattern of decreasing size with increasing mean slope across all regionsin support of Hypothesis 5 (Figures C.9 & 6.2). Slope values in West Africa werelimited to very low values (< 2.3º; Table 6.2) representative of the flat Sahelianterrain. Elephants in East Africa used the hilliest terrain (up to 20º mean slope).There was a decreasing trend in area with increasing temporal granularity index(TGI) (i.e., range values were smaller when sampling frequency was lower) (FigureC.11). An interaction between TGI & Sex/Region was not included in the modelbecause the sampling regime of a dataset is not expected to vary by either factor.Based on the GAMM, range size was relatively stable up to a TGI ~ 0.026 (theequivalent of 10-hour sampling), beyond which range area began to decrease withfurther increase in TGI.121Chapter 6: A Pan-African Analysis Of Fine-Scale Elephant Ranging Behaviour−0.2 0.0 0.2 0.4−2.0−1.00.0NDVICenters(NDVICenter,5.9)0 20 40 60−2.0−1.00.0TreeCenters(TreeCenter,7.44)−20 0 20 40 60−2.0−1.00.0HFCenters(HFCenter,7.61)0 5 10 15−2.0−1.00.0SlopeCenters(SlopeCenter,8.2)−0.8 −0.6 −0.4 −0.2 0.0 0.2−2.0−1.00.0PACenters(PACenter,8.61)−0.01 0.01 0.03 0.05−2.0−1.00.0TCICenters(TCICenter,2.9)Figure 6.2: GAMM model smoothers of Log10(area (Sq.km)) vs. explanatoryvariables display with a rug graph. Addition of covariate mean values (Table C.1)can be used to recover original, non-centered covariate values122Chapter 6: A Pan-African Analysis Of Fine-Scale Elephant Ranging Behaviour6.4 DiscussionUse of a landscape area (i.e. a home range) by an animal can be viewed as selec-tion for that area in preference over other areas – a conceptual approach embodiedby the resource selection analysis (RSA) framework (Manly et al., 2002; Boyce,2006). Interpretation of an animal’s home range could theoretically scale from thearea occupied by individual footprints on the ground to the entire landscape ex-tent in which a population currently, or might have formerly existed, and its spatialrepresentation remains a contentious issue in movement ecology (Osborn, 2004;Fieberg & Börger, 2012). Many adopted methods focus on the region that the ani-mal had the potential of using over a given time frame (e.g., Wall et al. (2014b)). Ichose to analyze areas of concentrated use (defined by the 95% area isopleth) as ameasure of both movement activity and resource selection.6.4.1 Model InterpretationInterpretation of maximization of range area with mid-range NDVI follows thatelephant range is generally constrained until vegetation conditions reach a nec-essary level of quality, after which range is unimpeded but decreases again withvery high quality vegetation because greater resource availability can be found ina smaller area. The results indicate rejection of Hypothesis 1 – that elephants in-crease range area with decreasing vegetation quality. The general increase in rangearea with low tree cover may or may not support Hypothesis 2. For example,although tree cover may be low, there may be ample supply of grass or shrubsnot quantified by the biomass estimate of the percent tree cover product. Rangearea expansion at low tree cover values (especially in East Africa) is not imme-diately interpretable. Although evaluating presence and not range area, Muelleret al. (2008) found that Mongolian gazelle selection followed a quadratic curvethat was maximized at mid-range NDVI values and concluded that gazelle weretiming movements to eat green grass before hard-to-digest fiber reached a certainlevel. Elephant selection of vegetation is undoubtedly more complicated than wasencapsulated by either NDVI or tree cover and also depends on variables such ascanopy height and structure (Barnes et al., 1991), nutritional quality, tannin levelsand taste, and possibly a host of other variables.123Chapter 6: A Pan-African Analysis Of Fine-Scale Elephant Ranging BehaviourVegetation structure is another important component and linked to measures ofhabitat permeability and movement behaviour (Avgar et al., 2013). Elephants inCentral Africa are known to prefer secondary forest where vegetation understoryprovides better browsing opportunities (Barnes et al., 1991). The range modelfor Central African elephants in relation to tree cover percentage predicts rangeincrease at high values of tree cover. Although it is not possible to differentiateforest type (i.e. old growth vs. secondary) based on this single covariate, it can beassumed that very high values of tree cover percentage indicate old-growth, closed-canopy forest where vegetative understory, and therefore available resources, arediminished. I hypothesize that the observed range size increase in Central Africaat high values of tree cover are therefore a result of increased permeability byelephants through forest without understory and diminished access to vegetationrequiring range expansion.The results of decreased range area with increasing human footprint follow re-sults from previous studies reporting influence of human-based activity on elephantmovement (Barnes et al., 1991; Blom et al., 2005; Laurance et al., 2006; Blakeet al., 2007; Buij et al., 2007; Chase & Griffin, 2009). The ~35 human footprintindex threshold value suggests an important dynamic between range behaviour andat least one of the 9 variables encapsulated by the HF index (i.e. population density,built-up areas, night-time lights, land use, land cover, coastlines, roads, railroads,navigable rivers). Road avoidance behaviour has been reported by Blake et al.(2008), who also showed that road-less wilderness area was strongly related tohome range size (based on the same set of GPS data as used in this study).Range size is also linked to the percentage of intersection of range with pro-tected areas, but the results show disagreement with my prediction of decreasingrange within protected areas (Hypothesis 4). Particularly in East, West and South-ern Africa, a negative parabolic curve shows that range area increases for mid-rangeprotected area intersection values (i.e., ranges that were part inside and outside ofa given protected area). One possible interpretation of this result is that mid-rangeintersection values would be generated if an animal moved from one PA to anotherby crossing non-PA regions. However, the choice of a 95% HR estimator was madeto limit inclusion of longer distance, displacement-type movements (e.g., streaks)in the range definition, which should curb the effect of generating mid-range in-124Chapter 6: A Pan-African Analysis Of Fine-Scale Elephant Ranging Behaviourtersection values when crossing from one PA to another. A second interpretationis that PA’s create an edge effect where an animal crosses from inside to outsidethe PA and back again because of access to some resource outside the PA. Theround trip generates an overall larger range area than if the animal stayed withinthe bounds of the PA completely or stayed outside.Hilly terrain affected range size by reducing range size with increasing meanslope as predicted in Hypothesis 5. This result is interpretable along similar ener-getic arguments as made by Wall et al. (2006) whereby range size, which is alsolinked to movement speed, must decrease when encountering elevation gains (orlosses) because of the added energetic requirements for negotiating hills.Analytical complexity arises when considering continental level datasets be-cause the behaviour of accepted metrics used to quantify movement (e.g., homeranges, utilization distributions, linear path distances) are still poorly understoodwith regards to data quality, and when making comparisons across highly variablesampling regimes (e.g., how do we compare movement data sampled every 24-hours with data sampled at hourly intervals?). Various studies have reported on thedependence in movement metrics according to sampling frequency, but have onlyconsidered the number of positions acquired within a given time-frame, generallyassuming regular sample intervals (Börger et al., 2006; Rowcliffe et al., 2012). Toaddress this issue and lack of mathematical terminology, I developed a new index(Temporal Granularity Index) to encapsulate a description of the number of posi-tions, temporal spread and overall period spanned by a movement dataset. Tempo-ral Granularity Index (TGI) was included as a covariate to account for movementdatasets with differing temporal sampling regimes. The GAMM showed that rangearea stayed relatively stable with increasing TGI up to an 10-hour equivalent sam-pling regime. This result is useful for future work involving calculation of rangearea, although results are limited to the assessment of aLoCoH areas at the 95%isopleth level. Further work is needed to extend the use of TGI for other space-useestimators and over differing temporal scales.125Chapter 6: A Pan-African Analysis Of Fine-Scale Elephant Ranging Behaviour6.4.2 Future DirectionsA large number of covariates covering four functional groupings (Vegetation, An-thropogenic, Terrain, Animal/Dataset) were included in the current modeling ap-proach. Unaccounted covariates may possibly explain residual variance thus im-proving model fit; here I briefly outline possible future directions for refining thecurrent modeling approach.Wittemyer et al. (2007b) have shown that social dominance amongst elephantherds has implications for elephant distribution in areas of key resources, and dom-inant families occupy relatively smaller ranges than subordinate families. The stateof ’musth’ in male elephants is also known to impact ranging behaviour and musthbulls can increase their travel speeds and ranging area in search of females (Gan-swindt et al., 2005; Rasmussen et al., 2008).Heterogeneity of resources in the landscape and their spatial configuration canlogically alter range geometry and size. Grainger et al. (2005) used a series ofhabitat metrics to encapsulate habitat heterogeneity and found a decrease in rangesize with increased habitat patch richness density. Similarly, de Beer & van Aarde(2008) used a suite of heterogeneity indices to examine elephant range use inEtosha, Namibia (patch density, largest patch index, landscape shape index, conta-gion and Shannon diversity index) and found range size decreased with increasedheterogeneity and water point density. Therefore future modeling of range shouldincorporate measures of resource heterogeneity.Although satellite based remote sensing has greatly enhanced our ability tomeasure landscape variables over wide geographical regions, difficulty remains instandardization of certain key environmental variables. For example, ambient tem-perature is a factor known to affect elephant movement behaviour. Kinahan et al.(2007) have shown that elephants will select for areas in the landscape that havelower rates of temperature change as well as higher canopy cover in order to as-sist with thermoregulation. Ambient temperature may be a key factor in predictingrange area size, but standardization of the measurement of ambient temperaturewas not possible in the current study from a lack of consistent meteorological sta-tion data across all regions. Similarly, precipitation records (Osborn, 2004) werenot available to analyze in conjunction with all movement datasets and therefore126Chapter 6: A Pan-African Analysis Of Fine-Scale Elephant Ranging Behaviourtheir use was precluded.Consideration of movement response in the context of spatio-temporal scaleis a key part of movement ecology analyses (Wiens, 1989; Morales & Ellner,2002; Johnson et al., 2002a,b; Frair et al., 2005; Boyce, 2006; Fryxell et al., 2008;de Knegt et al., 2011). Implicit in the definition of range is the time period overwhich range is measured, inextricably linked to the spatial scale of the underlyingmovement process through the animal’s velocity pattern (i.e., speed and direction).Disentangling the effects of different movement factors can be challenging, andthe relative importance of some variables may increase at different spatio-temporalscales (Boyce, 2006; de Knegt et al., 2011). A localized temporal disturbance suchas an encounter with capsicum pepper (Sitati & Walpole, 2006), biting ants (Go-heen & Palmer, 2010) or angry honey bees (Vollrath & Douglas-Hamilton, 2002;King et al., 2007) may illicit a temporary response in an elephant’s range patternover very short temporal scales whereas abiotic factors such as soil nutrient avail-ability (Weir, 1972) or terrain (Wall et al., 2006) are essentially temporally static.However, these same effects may vary hugely across very short spatial scales (e.g.,the concentration of sodium at single point (salt lick) or presence of a vertical cliffthat spans a 0 m horizontal spatial distance). In this study I characterized rangingpatterns at relatively short, 16-day periods; however, the observed relationships areonly valid for the selected 16-day temporal periods. Further research is thereforeneeded to characterize ranging pattern at a variety of temporal scales, in order togeneralize these results further.6.5 ConclusionIn conclusion, the modeling approach presented here adds valuable information tothe body of knowledge about elephant ranging behaviour and movement ecology.Elephant ranging behaviour is a complex process driven by many variables. Ex-ploration of patterns of 16-day range area size, as a function of seven covariatesbased on movement data collected from 226 animals in four distinct regions acrossAfrica, revealed ranges to be highly variable with 3 orders of magnitude differencebetween minimum and maximum recorded range area sizes. Associated covariatesspanned a wide range of values extending from conditions encountered in the desert127Chapter 6: A Pan-African Analysis Of Fine-Scale Elephant Ranging Behaviourenvironment of Mali to the tropical forests of the Congo. Diagnostics of both LMEand GAMM models indicate reasonable model fit and justify their utility in model-ing range size. The scope of this study therefore provides a firm basis on which tomake population-level inference of short temporal range patterns. Five hypotheseswere tested in relation to range area variation with vegetation quality and quantity,anthropogenic influence (human footprint), protected areas and terrain. Future re-search should aim to characterize range area at multiple temporal scales in orderto generalize the relationships developed here, as well as include other relevantcovariates to improve model fit. The characterization of range patterns related tohuman footprint and the discovery of edge effects of range in relation to protectedareas have direct conservation and management implications.128Chapter 7ConclusionThe key focus linking my research chapters together is the geospatial analysisof elephant tracking data. Enveloped within this main research topic are a num-ber of important themes that pervade the dissertation: the development of novelgeospatial software and analytical methods, the development of new ways of link-ing movement data with environmental information, the use of multiple spatialand temporal scales for analysis (including fine-scale region-specific analysis andalso large-scale, trans-continental analyses), the explicit treatment of serial corre-lation in tracking data, furtherment of our ecological understanding of elephantmovement, and application of tracking to elephant conservation. The specific ob-jectives of my doctoral research can be defined by the questions: i) “What is anappropriate method to collect, store, disseminate, visualize and analyze elephanttracking data?” (Chapter 2), ii) “Can we leverage real-time tracking data for man-agement and conservation?” (Chapter 3), iii) “Can we estimate wildlife space-usefrom tracking data?” (Chapter 4), iv) “What does tracking data tell us about themovement patterns of the Sahelian elephants in Mali?” (Chapter 5), and; v) “Whatdoes tracking data tell us about the factors influencing elephant range size acrossAfrica?” (Chapter 6). These questions and research themes were addressed acrossfive research chapters, enabled by unique access to elephant tracking data collectedby the organization Save the Elephants. Below, I summarize my work in relationto each of these questions, highlight the major contributions, and outline futureresearch directions.Is there an appropriate method to collect, store, disseminate, visualize and an-alyze elephant tracking data? As noted by Urbano et al. (2010) “good manage-ment of GPS-based locations is an essential step towards better science”. In 2008when I started my thesis research, there were no publicly available tools specifi-129Chapter 7: Conclusioncally designed for managing tracking data that were easily applicable to the prob-lem of integrating movement data from elephants across Africa. Accordingly, thefirst challenge overcome in my research was to build Loxobase: a novel trackingsystem using a centralized, enterprise design promoting a common data storage for-mat for improving the analytical work-flow and data collaboration amongst users.I designed two custom APIs and Downloader software to allow users easy accessto data ’on-the-fly’, either in Google Earth to geovisualize data in the context ofterrain and satellite imagery, or to download to a local synchronized database foringestion within either ArcGIS Desktop or R statistical software. In addition to ele-phants, Loxobase now also houses data from Grevy’s zebra (Equus grevyi), blackrhino (Diceros bicornis), white rhino (Ceratotherium simum), sable antelope (Hip-potragus niger), lion (Panthera leo), pastoralist cattle and vehicles, totaling over5 million recorded positions. The Loxobase system has been adopted for appliedconservation and management applications in both Kenya and South Africa, (e.g.,by Northern Rangelands Trust in Kenya and SAN Parks in South Africa), with over140 users and represents a major advance in tracking data management technology.Beyond the issues of managing and visualizing tracking data is the questionof data analysis software and how best to process large datasets. To date, a num-ber of specialized software programs have been developed for the analysis of GPStracking data with varying degrees of functionality, utility and code longevity (e.g.,(Hooge & Eichenlaub, 2000; Beyer, 2004; Calenge, 2006; Rodgers et al., 2007;Calenge et al., 2009)). In order to implement new methods of tracking data anal-ysis (e.g., ETD and velocity-grid), and cast other existing methods (e.g., BBMM& aLoCoH) within a common analytical and computational framework, I imple-mented a new extension for Esri ArcMap software (ArcMET: Movement EcologyTools for ArcGIS) specifically designed for the analysis of wildlife tracking data.ArcMET is coded in C# and built using the Esri ArcObjects class library. TheArcMET code base and class libraries provide the necessary functionality neededin many analyses such as trajectory filtering, trajectory metrics (e.g., distances,speeds, tortuosity), animal home ranges and utilization distributions, among otherspecialized tools, and was used throughout the analyses performed in this doctoralresearch. ArcMET was developed specifically with five core principles that im-prove movement data analyses: i) common data storage format, ii) temporal and130Chapter 7: Conclusionspatial window selection, iii) batch processing of multiple movement datasets, iv)calculation logs, and; v) parallel processing to improve computation time. Ar-cMET made possible the large-scale computing operations necessary for the com-parative analyses of elephant movements across Africa performed in Chapters 1 &6. I have made the ArcMET extension, along with an extensive user manual, freelyavailable online (www.movementecology.net).Can we leverage real-time tracking data for management and conservation?African elephants are under siege both from escalating problems as a result of theexpansion of the human-footprint in Africa and associated human-elephant con-flict, and from the acute threat of ivory poaching. Although the root of these prob-lems are largely political and cultural, technology does have a role to play in mit-igating the issues. In particular, real-time monitoring (RTM) is a nascent area ofwildlife conservation and management research largely facilitated by recent andrapid improvements in tracking technology and expansion of communications net-works. Analyzing an animal’s trajectory over a recent window of time (e.g., themost recent 24 hours) can provide insight into the animal’s positional and move-ment behaviour as it is happening. Building on the ArcMET code base, I developeda series of four algorithms designed to run continuously within the Loxobase archi-tecture to analyze incoming tracking data streams from collars in order to provideinformation about current movement and spatial states. The Proximity and Ge-ofencing algorithms work in conjunction with a spatial database to determine thespatial state of an animal in relation to geographic objects, while the Immobility andMovement Rate algorithms monitor specific aspects of movement to discern modesof distress from normal behaviour. A dissemination service sends both SMS andE-mail messages to subscribed users in the event of an alert being triggered, andhas a separate API for geovisualization of alerts using Google Earth. The RTM sys-tem has been implemented to monitor the behaviour of ~100 elephants in Kenyaand South Africa and is the first reported algorithmic monitoring used for appliedconservation and management of elephants.Can we estimate wildlife space-use from tracking data? Animal home rangehas been the subject of much discourse in the wildlife tracking literature (Laver131Chapter 7: Conclusion& Kelly, 2008; Fieberg & Börger, 2012) and can be summarized as “the extentof area with a defined probability of occurrence of an animal during a specifiedtime period” (Kernohan et al., 2001). Early research into methods for calculat-ing home range stressed the need for temporally uncorrelated positional data; thatis, every position contributes completely new information to the overall rangingarea used by the animal (Swihart & Slade, 1985, 1997; Rooney et al., 1998; Otis& White, 1999). More recent approaches have been to embrace autocorrelationin frequently sampled data, and a new group of temporal estimators are emergingthat explicitly incorporate temporality of recorded locations into the model for-mulation (Horne et al., 2007; Downs, 2010; Downs et al., 2011; Long & Nelson,2012). Building on the concepts of time-geography (Hägerstrand, 1970; Long &Nelson, 2012), I developed a new probabilistic space-use estimator called the ellip-tical time-density (ETD) model. ETD is a non-parametric method that assumes nounderlying form for movement behaviour, unlike some models that consider move-ment to follow some specific mechanistic process, such as the correlated randomwalk model (CRW) (Turchin, 1998) or Brownian motion (Horne et al., 2007). ETDuses the inherent constraints on speed that arise from the biology of a species toestimate a set of elliptical regions within which the animal must have been locatedfor a known amount of time based on a finite travel speed. The ellipse regionsare generated by considering speeds between the minimum speed needed to movefrom the first recorded position to the second recorded position up to the maxi-mum possible speed of travel. A uniform time-density value is calculated for eachellipse region, and the expected value of time-density for any point in the land-scape can be calculated as the expectation of all elliptical regions intersecting aparticular point (the time-density function). A utilization distribution is generatedby evaluating the time-density function for every landscape pixel and normaliz-ing the resulting spatial function. Modeling the speed distribution of an animal isan important component of the ETD approach and I used a Weibull distribution(Morales et al., 2004) to model the speeds of elephants. To test the ETD approachI developed a methodology for comparing errors of omission and commission us-ing a base, true utilization distribution calculated from 15-minute elephant datacompared with output from ETD and several other accepted space-use estimatorscalculated from hourly down-sampled data. The ETD model, parametrized using132Chapter 7: Conclusionthe 99% value of the Weibull speed distribution as the maximum speed (i.e., modelETD99 in Chapter 4) was found to have the lowest overall error when consideringall UD isopleth levels. The ETD method, along with a Bayesian approach for de-termining Weibull distribution parameters, have been implemented as a softwaretool available within the ArcMET extension.What does tracking data tell us about the movement patterns of the Sahelianelephants in Mali? Within the Gourma region of Mali live a unique populationof Sahelian elephants. The northernmost elephants in Africa, they are subject toenvironmental extremes for the species, with daytime temperatures reaching overfifty degrees Celsius during the dry season and only a single rainy season thatleaves the area prone to drought (Douglas-Hamilton & Wall, 2009). The mostrecent population estimate from 2009 suggests there are a minimum of 350 ele-phants remaining. Given the lack of conservation infrastructure, regional politicalinstability and war, the large region covered by their movements and their uniquestatus as the last remnant Sahelian elephants in Africa, they are a critical popu-lation for study and conservation. My research has shown that monitoring usingsatellite-based tracking and imagery are effective methods for studying the Gourmaelephants.Using tracking data collected at hourly intervals from nine individuals between2008 - 2010, I was able to quantify the ranging patterns of the Gourma elephantsin fine spatio-temporal detail. Range areas were much larger than in other Africanpopulations and the female ’Ramata’ covered a minimum convex polygon rangearea of 32,000 Sq.km – a current record for the species. The Gourma elephantswere found to track a strong north-south seasonal precipitation gradient beginningwith a quick movement south at the onset of rain in May/June, followed by a grad-ual return north, with the final months of the dry season (March-April) spent at thenorthern part of the range and confined to shrinking surface water sources. Femalesled the movement back north – a result that may have to do with the higher lev-els of protein in grasses found in the north of the range (Breman & de Wit, 1983)and the need to supplement their diet for the purposes of lactation. Comparing lo-cal 10-day range areas (aLoCoH) with a landscape-wide MCP range calculated bypooling all recorded locations, I found that the Gourma elephants selected higher133Chapter 7: Conclusionthan average NDVI throughout the year but particularly at the beginning of thewet season. Travel speeds were found to increase during the wet season and alsoat night, suggesting thermal and environmental influences on movement. Femaleand male ranges only overlapped by 24% and males were found to have distinctforaging areas not used by females.Spatially analyzing velocity can provide insight as to how an animal’s move-ment behaviour changes in space. In order to characterize the velocity patterns ofthe Mali elephants, I developed a velocity-grid technique for statistically summa-rizing velocities at landscape scales. A dot product index summarizes the meandot product for path segments intersecting a given landscape grid cell while meanspeed and mean direction complete the triad of movement information. The velocity-grid output provides a means to easily visualize animal velocities and can also beclassified using information classification methods (e.g., k-means) in order to iden-tify spatial regions of common velocity behaviour. Applying this technique to theMali elephant system led to identification of high-speed movement regions andslower speed foraging regions. The velocity-grid method has been made availablewithin ArcMET and is a unique contribution to movement visualization.What does tracking data tell us about the factors influencing elephant rangesize across Africa? Movement is assumed to be the result of an animal’s spatio-temporal interaction with both exogenous environmental variables (e.g., water avail-ability) and endogenous, physiological variables (e.g., thermal stress). Concomi-tant observation of both movement and covariates provides the basis upon whichhypotheses can be tested and inference made about the drivers of movement. Infer-ence is strengthened when considering large sample sizes of individuals recordedacross a wide range of conditions (White & Garrott, 1990; Millspaugh & Marzluff,2001; Avgar et al., 2013). Building on this theoretical basis, I undertook the firstever continent-wide analysis of movement data on African elephants, by collat-ing datasets from 247 animals across 4 distinct ecoregions: Desert (West), forest(Central), bushveld (South) and savannah (East) and coupling environmental mea-surements to estimates of range area. I then modeled range area using covariatesof Sex, Region, NDVI, tree cover, protected areas, human footprint and slope us-ing both linear and generalized additive mixed effects models. Broad geographical134Chapter 7: Conclusionscale analyses such as these are important for understanding elephant species at thepopulation level and also provide broader context for other, smaller spatial scale(e.g., site specific) assessments of movement behaviour.Comparing movement metrics (e.g., range area estimation, trajectory prop-erties) is complicated when data are acquired under variable sampling regimes.Tracking data is, for technological, ecological and economical reasons, collectedunder a wide range of temporal sampling regimes. In this research I faced theproblem of how to analyze tracking datasets sampled under regimes ranging fromhourly intervals up to 24 hour intervals. Few studies reported in current literaturedirectly address the effects of variable positional sampling on movement metrics(Börger et al., 2006). I developed the Temporal Granularity Index (TGI) as an at-tempt to quantify both the number of sampled locations and their spread in timewhen considering a set period of time (e.g., 16-days). By focusing on the time-spans between recorded positions instead of the number of positions within a setperiod I arrived at a more realistic understanding of how data was being sampled.For example, a dataset containing 500 samples from the first day of a month longperiod and nothing thereafter represents a very different sampling regime than 500points spread evenly throughout the month, yet is indistinguishable when consider-ing only the sample number. TGI was used within the PanAfEl statistical modelingapproaches as a continuous covariate to account for variations in sampling regimes.It was found that TGI was an important explanatory variable when modeling 16-day range behaviour.Linking movement to environmental conditions is an important theme in move-ment ecology (Nathan et al., 2008; Hebblewhite & Haydon, 2010). Recording ex-ternal, environmental conditions concomitant with an animal’s location can providekey insight into observed spatial behaviour (Dodge et al., 2013). These insights arefacilitated by the growing number of remote sensing image products and environ-mental datasets available to ecologists (Turner et al., 2003). Linking tracking datawith satellite-derived remote sensing imagery is complicated by the temporalityof certain image products that are updated regularly (e.g., MODIS NDVI) and therequirement that the executing program have access to both tracking and remotesensing information. Image values may be extracted at individual GPS locations— typical in resource selection analyses (Mueller et al., 2008) — or may be statisti-135Chapter 7: Conclusioncally summarized across areas. My approach was to use new Google Earth Engine(GEE) technology. Google is acquiring and storing vast quantities of publicly avail-able satellite imagery onto Google servers (https://earthengine.google.org/#index).An API provisioned for the Python programming language allows manipulation ofimagery and execution of custom algorithms. The advantage of the GEE approachis its highly parallelized infrastructure (Hansen et al., 2013b) and the decouplingof the user from raster image management. The current analysis would barely havebeen possible without the advent of GEE technology and, therefore, the PanAfElanalysis approach is currently right at the forefront of analyses coupling movementdata with remote sensing information.Results of the PanAfEl analysis found that ranging patterns were regionallydependent, ordered according to West > South > East > Central. The statisticalmodeling approach has revealed interesting interplay between covariates and rang-ing behaviour. Specifically, five hypotheses were tested related to elephant rangearea across the continent: H1: Elephant range size will decrease as vegetationquality increases within the range area, H2: Elephant range size will decrease asvegetation abundance increases within the range area, H3: Elephant range size willdecrease in areas of high anthropogenic influence, H4: Elephant range size willdecrease inside of protected areas, and; H5: Elephant range size will decrease withincreased hilliness (slope).H1 was rejected because it was found that range area followed a paraboliccurve with increasing vegetation quality i.e., range area was a minimum at lowvalues of vegetation quality and expanded to a maximum at mid-values of NDVIbefore again decreasing at high values of NDVI. H2 was also rejected on accountof the more complicated behaviour of range with vegetation abundance. Rangesize did generally decrease with increasing vegetation abundance for low valuesof abundance, but tended to increase again at higher levels of abundance (percenttree cover), a result interpreted as increased mobility in closed canopy forest withless understory. The metric of abundance used here was based on tree cover andtherefore did not capture the abundance of grass and woody vegetation under fivemeters, and so this result must be interpreted with caution. H3 was supported and athreshold value of 35% was discovered whereby there was a steep decline in rangesize with increasing human footprint. H4 was rejected because, although range136Chapter 7: Conclusionarea did decrease inside protected areas, range area decreased again when ele-phants were fully outside of protected areas. A maximum range area was seen forelephants spending 60% - 70% of time within protected areas and the rest outside,a result interpreted as an edge effect between protected areas and range behaviour.H5 was supported and range area was found to decrease with increasing slope.Future DirectionsIn the future, I hope to extend and continue this research in a variety of ways. Ifirst plan to expand Loxobase to include accelerometer data that is fast showing itsvalue for behavioural monitoring in elephants (Soltis et al., 2012) and is increas-ingly incorporated into collar designs. A single reading from an accelerometer hassimilar data content as a GPS coordinate (e.g., x, y, z, time). Accelerations aretypically sampled at much higher frequencies (e.g., 320 Hz) however, creating or-ders of magnitude more data than GPS. Efficient means of storing, compressingand disseminating these data will need to be developed in order to provide similaraccess to GPS data within Loxobase. Expanding Loxobase to include accelerom-eter data will also require developing routines in ArcMET for efficient processingof tri-axial acceleration data.Continuous-time monitoring of elephant behaviour using accelerometers hasalready begun, but is currently limited to brief duration periods (Wilson et al.,2006, 2007; Soltis et al., 2012). Compared with GPS positioning, accelerometryhas the potential to identify elephant behaviour, such as movement immobility, farquicker than can be estimated by geospatial analysis alone (Soltis et al., 2012).Other sensors (e.g, heart-rate monitors) also have the potential to provide criticalinformation about an animal’s state and behaviour. I hope to expand and improvethe RTM system by analyzing both accelerometry and physiological informationthat could significantly improve current species monitoring. Reducing the timetaken to identify an event such as the mortality of an individual could significantlyhelp in wildlife conservation and management. I also hope to expand the suite of al-gorithms now being used to monitor elephants. Recent models such as behaviouralchange point detection (Gurarie et al., 2009) may be helpful in determining whentransitions in movement states occur, such as a bull elephant entering into ’musth’.137Chapter 7: ConclusionFurthermore, coupling real-time remote sensing information with movement datacould help in the interpretation of observed behaviour (e.g, elephants responding tothunderstorms) and paint a holistic picture of what the animal may be experiencing.The Elliptical Time-Density method as presented could be expanded as fol-lows; firstly, explicit incorporation of the error in a positional reading should beincluded in the model specification. At the moment, location error translates intouncertainty of the speed distribution but without explicit consideration for the ac-curacy of individual positions. Secondly, a means to capture hard landscape edgesis needed to limit estimation of use where an animal could not physically travel,such as if a fence-line or other boundary prevented access to a particular part of thelandscape. Finally, further refinement of the speed distribution would help improveestimation of space-use. For example, animals may move with different speed pat-terns at different times (e.g., a bull elephant in musth), or because of terrain orother landscape variables. Recasting the speed distribution estimation with spatialand temporally varying parameters could provide improved model fit.Determination of whether the Mali elephants are migratory is an importantquestion that still needs answering. Migration is defined as an adaption by a groupto access ephemeral resources available to migrant animals that confer an evolu-tionary advantage over non-migratory individuals. Whether or not the Mali ele-phants are truly migratory, or simply nomadic, remains unclear. Current insecurityhas made the Gourma region unsafe for field work. However, north-south tran-sects measuring the abundance of grass, vegetation types, protein and surface wateravailability would provide tremendous insight into the dynamics of the movementsof the elephants. Furthermore, recent surf models have been proposed for her-bivores moving in tandem with vegetation verdancy along geographical gradients(Bischof et al., 2012; Avgar et al., 2013; Bohrer et al., 2014). Although I haveshown that the Mali elephants show selection preference for vegetation greenness,it would be useful to test the observed latitudinal pattern of movement in the con-text of an NDVI surf model (Bischof et al., 2012).The PanAfEl analysis has revealed both strengths and weaknesses in a continental-wide analysis approach. The analysis was strengthened by the inclusion of a largenumber of individual animals providing strong support to model results. How-ever, tracking data was collected over large areas and differing time periods and,138Chapter 7: Conclusiontherefore, space-borne remote sensing was the most viable method to measure en-vironmental covariates across all regions. Nonetheless, certain measurements (e.g.,surface water, temperature, rainfall) are not as easily quantified using remote sens-ing imagery, but are important factors to explain observed ranging patterns. Are-analysis of this dataset might therefore focus on improvement and expansion ofpossibly missing, but important, covariate information to improve model fit. Fur-thermore, re-analysis at alternate temporal scales (e.g., 6-month or yearly scales)may provide further insight into the factors influencing observed ranging patterns.Finally, the recent rise in demand for elephant ivory has driven the illegalkilling of more than 100,000 elephants across Africa since I commenced this doc-toral research. Approaches that place this illegal killing within a geospatial contextand tie together population monitoring with fine scale GPS tracking are needed.Even if the demand for ivory can be curbed, and the current proliferation of illegalkilling across Africa stopped, the issue of conserving space for elephants in theface of the expanding human footprint remains a problem that needs addressing.Results of this research have underlined that elephants are wide-ranging animalsand have regionally distinct movement patterns suggesting the need for context-specific conservation approaches. Geospatial analyses and ongoing tracking ofelephant movement are, therefore, important components of the interdisciplinaryapproach needed to protect elephants into the future.139BibliographyAfESG, 2013. African Elephant Specialist Group 2012 Continental Totals("2013 AFRICA" analysis). 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Springer New York.164Appendix AETD Chapter SupplementaryInformationA.1 Dataset D1Here is a listing of the steps used for finding the best-fit parameters for the Weibulldistribution based on the speeds of the elephant ’Salif’ (Dataset D1):• Straight line speeds between successive points were computed within Ar-cGIS ArcMap (Esri, 2013) software using the ’Trajectory Path Tool’ in Ar-cMET (Wall, 2014).• Data were then exported from ArcMap to a csv file (e.g., “SalifTrajecto-ryD1.csv”).• I set up the BUGS model (note that the parametrization of the Weibull distri-bution is different in BUGS and uses a rate parameter (Bolker, 2008) wherethe scale is recovered from λ = 1r1/k ) as follows:Algorithm A.1: SalifBUGSD1.bugmodel{f o r ( i i n 1 : n ){s p e e d s [ i ] ~ dweib ( shape , r a t e )}# P r i o r sshape ~ d u n i f ( 0 , 1 0 )r a t e ~ d u n i f ( 0 , 1 0 )}165• I ran the BUGS model using R (R Core Team, 2013) with 3 chains and100,000 iterations per chain. Results are shown in table A.1. Here is the Rcode:Algorithm A.2: Dataset D1 Analysis R Codel i b r a r y (R2WinBUGS) # r e q u i r e s t h e R2WinBUGS l i b r a r y#Read i n Datas a l i f <−r e a d . csv ( " E : / PhD / T h e s i s / E l l i p t i c a l Time D e n s i t y Range Pape r /A n a l y s i s / ETD−D1 / S a l i f T r a j e c t o r y D 1 . csv " , h e a d e r =T )# F i l t e r s p e e d s t o any t e m p o r a l s e p a r a t i o n l e s s t h a n 48 h o u r sspeeds <−salif$SPEEDKMHR [ salif$TOTALTIMEHRS <48]max ( s p e e d s ) #Max Speed Value# Se tup t h e BUGS model i n p u t sn= l e n g t h ( s p e e d s )s a l i f . da t a <− l i s t ( " s p e e d s " , " n " )s a l i f . i n i t s <− f u n c t i o n ( ){l i s t ( shape = r u n i f ( 1 , 0 , 1 0 ) , r a t e = r u n i f ( 1 , 0 , 1 0 ) )}s a l i f . params <−c ( " shape " , " r a t e " )s a l i fBUGSFi l e <−"/ A n a l y s i s / ETD−D1 / SalifBUGSD1 . bug "# Execu te t h e BUGS models a l i f .1<−bugs ( d a t a = s a l i f . da t a , i n i t s = s a l i f . i n i t s , p a r a m e t e r s . t o . s ave = s a l i f .params , model . f i l e = sa l i fBUGSFi l e , n . c h a i n s =3 , n . i t e r =100000 , bugs .d i r e c t o r y ="C : / Program F i l e s / WinBugs / WinBUGS14 " , debug=TRUE)# De f i ne f u n c t i o n t o r e c o v e r s c a l e from BUGS r a t e p a r a m e t e rs c a l e <− f u n c t i o n ( r , k ){1 / ( r ^ ( 1 / k ) )}# R e s u l t s o f t h e BUGS model# shapek= s a l i f . 1 $mean$shapek# r a t er = s a l i f . 1 $mean$ra t er# s c a l elambda= s c a l e ( r , k )lambda# d e v i a n c ed e v i a n c e = s a l i f . 1 $mean$devianced e v i a n c e# E r r o r t e r m sshapeSD= s a l i f . 1 $sd$shapeshapeSD166r a t eSD = s a l i f . 1 $ s d $ r a t era t eSDdevianceSD= s a l i f . 1 $ s d $ d e v i a n c edevianceSD# Dete rmine t h e speed c o r r e s p o n d i n g t o t h e 0 . 9 9 c u m u l a t i v e d i s t r i b u t i o nv a l u espeed99 = q w e i b u l l ( 0 . 9 9 , k , lambda )# P l o t t h e d i s t r i b u t i o n o f s p e e d s a g a i n s t t h e f i t t e d Weibu l l d i s t r i b u t i o nc a i r o _ p d f ( f i l e n a m e = " / F i g u r e s /SM − S a l i f W e i b u l l F i t −D1 / S a l i f W e i b u l l F i t −D1 .pdf " , wid th =5 , h e i g h t =5 , p o i n t s i z e =10)h i s t ( speeds , f r e q =FALSE , b r e a k s =100 , main = " " , x l a b =" Speed (Km/ Hr ) " , y l a b ="P r o b a b i l i t y D e n s i t y " )a b l i n e ( v=speed99 , c o l =" g r e e n " , l t y =2)y<−d w e i b u l l ( speeds , k , lambda )l i n e s ( s p e e d s [ o r d e r ( s p e e d s ) ] , y [ o r d e r ( s p e e d s ) ] , c o l =" b l u e " )dev . o f f ( )Table A.1: BUGS Weibull Parameter Best-Fit Values for Dataset D1Parameter Estimate SDShape (k) 0.8034567 0.004345202Rate 1.899745 0.01284436Deviance 12389.82 1.834203167Speed (Km/Hr)Probability Density0 1 2 3 4 5 60.00.51.01.52.02.53.0Figure A.1: Weibull speed distribution for elephant ’Salif’ (Dataset D1). Thedashed vertical green line corresponds to the 99% cumulative distribution speedvalue.A.2 Dataset D2Here is a listing of the steps used for finding the best-fit parameters for the Weibulldistribution after randomly resampling speeds of the elephant ’Salif’ (Dataset D2):• Straight line speeds between successive points were computed within Ar-cGIS ArcMap (Esri, 2013) software using the ’Trajectory Path Tool’ in Ar-cMET (Wall, 2014).• Data were then exported from ArcMap to a csv file (e.g., “SalifTrajecto-ryD2.csv”).• I setup the BUGS model (note that the parametrization of the Weibull distri-bution is different in BUGS and uses a rate parameter (Bolker, 2008) wherethe scale is recovered from λ = 1r1/k ) as follows:168Algorithm A.3: SalifBUGSD2.bugmodel{f o r ( i i n 1 : n ){s p e e d s [ i ] ~ dweib ( shape , r a t e [ i ] )r a t e [ i ]<− ( a *pow ( t [ i ] , b ) ) *pow ( c , t [ i ] )}# P r i o r sshape ~ d u n i f ( 0 , 1 0 )a ~ d u n i f ( 0 , 1 0 )b ~ dnorm ( 0 , 0 . 0 0 1 )c ~ d u n i f ( 0 , 1 0 )}• I ran the BUGS model using R (R Core Team, 2013) with 3 chains and100,000 iterations per chain. Results are shown in table A.2. Here is the Rcode:Algorithm A.4: Dataset D2 Analysis R Codel i b r a r y (R2WinBUGS) # r e q u i r e s t h e R2WinBUGS l i b r a r ys a l i f <−r e a d . csv ( " / A n a l y s i s / ETD−D2 / S a l i f T r a j e c t o r y D 2 . csv " , h e a d e r =T )# F i l t e r s p e e d s t o any t e m p o r a l s e p a r a t i o n l e s s t h a n 48 h o u r sspeeds <−salif$SPEEDKMHR [ salif$TOTALTIMEHRS <48]max ( s p e e d s ) #Max Speed Valuet <−salif$TOTALTIMEHRS [ salif$TOTALTIMEHRS <48]# Se tup t h e BUGS model i n p u t sn= l e n g t h ( s p e e d s )s a l i f . da t a <− l i s t ( " s p e e d s " , " t " , " n " )s a l i f . i n i t s <− f u n c t i o n ( ){l i s t ( shape = r u n i f ( 1 , 0 , 1 0 ) , a= r u n i f ( 1 , 0 , 1 0 ) , b=rnorm ( 1 , 0 , 1 0 ) , c= r u n i f( 1 , 0 , 1 0 ) )}s a l i f . params <−c ( " shape " , " a " , " b " , " c " )s a l i fBUGSFi l e <−"/ A n a l y s i s / ETD−D2 / SalifBUGSD2 . bug "# Execu te t h e BUGS models a l i f .1<−bugs ( d a t a = s a l i f . da t a , i n i t s = s a l i f . i n i t s , p a r a m e t e r s . t o . s ave = s a l i f .params , model . f i l e = sa l i fBUGSFi l e , n . c h a i n s =3 , n . i t e r =100000 , bugs .d i r e c t o r y ="C : / Program F i l e s / WinBugs / WinBUGS14 " , debug=TRUE)# De f i ne f u n c t i o n t o r e c o v e r s c a l e from BUGS p a r a m e t e r i z a t i o ns c a l e <− f u n c t i o n ( a , b , c , t , k ){169( a * ( t ^b ) * ( c ^ t ) ) ^(−1/ k )}# R e s u l t s o f t h e BUGS modelk= s a l i f . 1 $mean$shape # shape paramka= s a l i f . 1 $mean$a # a paramab= s a l i f . 1 $mean$b #b parambc= s a l i f . 1 $mean$c # c paramcdev= s a l i f . 1 $mean$deviance # model d e v i a n c edev# E r r o r t e r m skSD= s a l i f . 1 $sd$shapekSDaSD= s a l i f . 1 $sd$aaSDbSD= s a l i f . 1 $sd$bbSDcSD= s a l i f . 1 $sd$ccSDdevSD= s a l i f . 1 $ s d $ d e v i a n c edevSDHere the rate (r) is modeled as r = atbct . We can recover the normal ’scale’parameter λ using λ = 1r1/k = (atbct)−1/k. Results of the BUGS run leads to thevalues for the parameters in Table A.2.Table A.2: BUGS Weibull Parameter Best-Fit Values for Dataset D2Parameter Mean SDShape (k) 0.8562829 0.006315276a 1.869576 0.03920066b 0.1359912 0.05094528c 1.000677 0.02089086Deviance 5436.109 2.746925A.3 Dataset D3Here is a listing of the steps used for finding the best-fit parameters for the Weibulldistribution based on the speeds of the elephant ’Salif’ after down-sampling to a170regular 24 hour resolution (Dataset D3):• Straight line speeds between successive points were computed within Ar-cGIS ArcMap (Esri, 2013) software using the ’Trajectory Path Tool’ in Ar-cMET (Wall, 2014).• Data were then exported from ArcMap to a csv file (“SalifTrajectoryD3.csv”).• I setup the BUGS model (note that the parametrization of the Weibull distri-bution is different in BUGS and uses a rate parameter (Bolker, 2008) wherethe scale is recovered from λ = 1r1/k ) as follows:Algorithm A.5: SalifBUGSD3.bugmodel{f o r ( i i n 1 : n ){s p e e d s [ i ] ~ dweib ( shape , r a t e )}# P r i o r sshape ~ d u n i f ( 0 , 1 0 )r a t e ~ d u n i f ( 0 , 1 0 )}• I ran the BUGS model using R (R Core Team, 2013) with 3 chains and100,000 iterations per chain. Results are shown in table A.3. Here is the Rcode:Algorithm A.6: Dataset D3 Analysis R Codel i b r a r y (R2WinBUGS) # r e q u i r e s t h e R2WinBUGS l i b r a r y#Read i n Datas a l i f <−r e a d . csv ( " / A n a l y s i s / ETD−D3 / S a l i f T r a j e c t o r y D 3 . csv " , h e a d e r =T )# F i l t e r s p e e d s t o any t e m p o r a l s e p a r a t i o n l e s s t h a n 48 h o u r sspeeds <−salif$SPEEDKMHR [ salif$TOTALTIMEHRS <48]max ( s p e e d s ) #Max Speed Value# Se tup t h e BUGS model i n p u t sn= l e n g t h ( s p e e d s )s a l i f . da t a <− l i s t ( " s p e e d s " , " n " )s a l i f . i n i t s <− f u n c t i o n ( )171{l i s t ( shape = r u n i f ( 1 , 0 , 1 0 ) , r a t e = r u n i f ( 1 , 0 , 1 0 ) )}s a l i f . params <−c ( " shape " , " r a t e " )s a l i fBUGSFi l e <−"/ A n a l y s i s / ETD−D3 / SalifBUGSD3 . bug "# Execu te t h e BUGS models a l i f .1<−bugs ( d a t a = s a l i f . da t a , i n i t s = s a l i f . i n i t s , p a r a m e t e r s . t o . s ave = s a l i f .params , model . f i l e = sa l i fBUGSFi l e , n . c h a i n s =3 , n . i t e r =100000 , bugs .d i r e c t o r y ="C : / Program F i l e s / WinBugs / WinBUGS14 " , debug=TRUE)# De f i ne f u n c t i o n t o r e c o v e r s c a l e from BUGS r a t e p a r a m e t e rs c a l e <− f u n c t i o n ( r , k ){1 / ( r ^ ( 1 / k ) )}# R e s u l t s o f t h e BUGS model# shapek= s a l i f . 1 $mean$shapek# r a t er = s a l i f . 1 $mean$ra t er# s c a l elambda= s c a l e ( r , k )lambda# d e v i a n c ed e v i a n c e = s a l i f . 1 $mean$devianced e v i a n c e# E r r o r t e r m sshapeSD= s a l i f . 1 $sd$shapeshapeSDra teSD = s a l i f . 1 $ s d $ r a t era t eSDdevianceSD= s a l i f . 1 $ s d $ d e v i a n c edevianceSD# Dete rmine t h e speed c o r r e s p o n d i n g t o t h e 0 . 9 9 c u m u l a t i v e d i s t r i b u t i o nv a l u espeed99 = q w e i b u l l ( 0 . 9 9 , k , lambda )# P l o t t h e d i s t r i b u t i o n o f s p e e d s a g a i n s t t h e f i t t e d Weibu l l d i s t r i b u t i o nc a i r o _ p d f ( f i l e n a m e = " / F i g u r e s /SM − S a l i f W e i b u l l F i t −D3 / S a l i f W e i b u l l F i t −D3 .pdf " , wid th =5 , h e i g h t =5 , p o i n t s i z e =10)h i s t ( speeds , f r e q =FALSE , b r e a k s =100 , main = " " , x l a b =" Speed (Km/ Hr ) " , y l a b ="P r o b a b i l i t y D e n s i t y " )a b l i n e ( v=speed99 , c o l =" g r e e n " , l t y =2)y<−d w e i b u l l ( speeds , k , lambda )l i n e s ( s p e e d s [ o r d e r ( s p e e d s ) ] , y [ o r d e r ( s p e e d s ) ] , c o l =" b l u e " )dev . o f f ( )172Table A.3: BUGS Weibull Parameter Best-Fit Values for Dataset D3Parameter Estimate SDShape (k) 0.8185976 0.02097131Rate 3.470841 0.1301553Deviance -804.4516 1.888728Speed (Km/Hr)Probability Density0.0 0.5 1.0 1.501234567Figure A.2: Weibull speed distribution for elephant ’Salif’ (Dataset D3). Thedashed vertical green line corresponds to the 99% cumulative distribution speedvalueA.4 Ellipse GeometryThis section provides details of the derivation of ellipse area used in the time-density function. I start with the definition of an ellipse that an “ellipse is the setof points in a plane the sum of whose distances from two fixed points F1 and F2 is173constant” (Stewart, 1995, p. 560). This definition leads to the equation|PF1|+ |PF2|= 2a (A.1)If we co-locate the point P at point b in figure A.3 then we can re-write equationA.1 and use the Pythagorean theorem to derive an expression for the distance fromthe ellipse center to a focus point in terms of the semi-minor and semi-major axeslengths:√− f 2 +b2 +√f 2 +b2 = 2a2√f 2 +b2 = 2a (A.2)f =√a2−b2Let D equal the distance between the two foci D = 2 f and let d equal thedistance from focus F1 to point P and then to foci F2: d = 2a. Relating back to themovement geometry of an animal, we consider that a pair of successively recordedlocations are the foci in figure A.3. Point P is then a landscape point and we wishto know the area of the ellipse if the animal were to move from F1 to P and then toF2. D is defined to be the straight-line distance between the two recorded locations(foci). I can substitute the value for D into equation A.2 and solve for the variableb:D2=√a2−b2 (A.3)b =√a2− D24I then use the equation for the area of an ellipse Aellipse = piab (Stewart, 1995,p. 431) to write:Aellipse = pia√a2− D24(A.4)Substituting d = 2a into equation A.4 leads to the an equation for the ellipsearea in terms of the straight line distance between foci (recorded locations) and the174distance moved to reach a point P:Aellipse = pid2√d42− D24(A.5)= pid2√d42− D24(A.6)= pid4√d2−D2 (A.7)F1 F2cbaPfFigure A.3: Ellipse Geometry. c marks the center point and F1,F2 are the foci ofthe ellipse, each a distance f from c. By definition the distance from F1 to P and Pto F2 is constant and equal to the length of the major axis (2a).175Appendix BMali Chapter SupplementaryInformationB.1 Meteorological Data And NDVIFigure B.1: Meteorological data showing monthly temperatures (orange solid line)and rainfall (blue dashed line). Temperature was measured from on-board sensorswithin each elephant collar unit and averaged over the study period. Rainfall wasmeasured with rain gauges at three stations – Boni, I-n-adiatafane and Gossi be-tween the years (1997- 2008 [Boni], 2001-2008 [Gossi], 2008 [I-n-adiatafane]).Values are averaged monthly totals from each station.176Figure B.2: The north-south gradient in NDVI as measured from SPOT NDVIimage tiles spanning the entire study region in 2009. A single image from themiddle 10 days of each month (e.g. day 10 – day 20) was used to extract NDVIvalues for that month.177B.2 Tracking Dataset SummaryTable B.1: Summary data on each tracked individual and collar specifics.Elephant Sex Age Data Starts Data Ends Years Tracked # Positions PerformanceBahati (F) F 28 28-Mar-08 25-Aug-08 0.41 3,410 94.7%Mariam (F) F 16 25-Mar-08 29-May-09 1.18 10,119 98.1%Ramata (F) F 32 24-Mar-08 28-Jul-09 1.34 11,769 99.9%Tombouctou (F) F 35 23-Mar-08 9-Sep-09 1.47 12,842 100.0%Achar (M) M 42 28-Mar-08 12-May-10 2.12 18,330 98.5%Ali Farka Touré (M) M 35 24-Mar-08 25-Jun-10 2.26 19,715 99.8%Amadou (M) M 35 22-Mar-08 26-Feb-09 0.93 8,155 99.6%El Mozaar (M) M 50 28-Mar-08 12-Aug-09 1.38 2,179 18.1%Salif Keita (M) M 40 22-Mar-08 30-Sep-10 2.53 21,972 99.3%Mean: 1.51 12,055 89.8%SD: 0.68 6,967 26.9%178B.3 La Porte Des ÉléphantsFigure B.3: 100+ elephants moving through La Porte des Éléphants on their mi-gration south in June, 2008. Photo courtesy National Geographic Society.179Appendix CPanAfEl Chapter SupplementaryInformationC.1 Temporal Granularity IndexHere I provide a derivation of the temporal granularity index (TGI). Firstly, con-sider a set of recorded fixes Pi =P1,P2, . . . ,Pn, sampled at times ti = t1, t2, . . . , tn overa total period Ttotal . The time-spans between fixes can be defined as Ti = ti+1− tiand where Ttotal = ∑mi=1 Ti and m = n− 1. The time-spans, as seen in Figure C.1are not necessarily equal in length T1 6= T2 6= . . . 6= TmTGI is minimized when all the intervals Ti making up the period Ttotal have thesame values ( i.e., regularly sampling) and follows a 1m curve (Figure C.2).ProofDifferentiate TGI with respect to each of the time intervals Ti and to obtain the setof equations:∂(∑T 21T 2total)∂T1=2T1T 2total∂(∑T 22T 2total)∂T2=2T2T 2total...∂(∑T 2mT 2total)∂Tm=2TmT 2totalSetting each equal to zero and solving leads to180T1 = T2 = T3 = . . . = Tm (C.1)Substituting TTotal = m∗Ti in equation 6.1 leads to T GI = 1m .t2T1t1 tntn-1T2 Tn-1Figure C.1: A hypothetical time-line representing the temporal sampling regime ofan animal tracking dataset.0 5000 15000 25000 350000.00000.00100.00200.0030Number of regular timespans in period TTGI for period TFigure C.2: Variation in TGI for a 1-year period with 3 regular sampling regimes:24 hr, 1-hr and 15 min. TGI follows a 1n curve for the number of time-spans n.181C.2 Covariate InformationSex1.0 3.00.19 0.110 400.06 0.14−0.01 0.040.11 0.0430 400.191.01.60.181.03.0llllllllRegion0.21 0.29 0.49 0.21 0.36 0.37 0.36lllllllllllllllllllllllllllllllllllllllllllllll lllllll lllllllll lllllllllll lNDVI0.50 0.031 0.10 0.077 0.26−0.20.40.27040llllllll lll lllllllllllllllllll lllllllllllllllllllllllllllllllllllllllll llllll llllllllll llll lllll llll lllllllllllll lllllllllllllll lllllllllll llll lllll llllllll llll lllllllll lllTreeCover0.026 0.15 0.045 0.42 0.40lllllllllllllllllllll ll lllll lllllllll lllllllllllll llllllllllllllllllllllllllllll ll lllll llllll llllllll lllll lllll lllll ll lllllllllllllll lll lllllllllllllllllllllllllllll llllll ll lllllllll lll llllllllllll lllllllllllllllllllllllll lll llllllllllllllllllll llll lllllllll l ll lllll lllllllllllll llllllllHF0.26 0.23 0.24−20400.24−0.010.04llllllllllllllllllll llllllllllll llllllllllllllllllllllllllll llllllllllll lllllllllllll lllllllllllllllllll ll lll llllllllllllllllllllllllll lllllll llllll llllllll lllllllllllllllllll lll lllllll llllllllllll ll llll llllllllllllllll lllllll lllllllllllllllll ll llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll llllllllllllllll llllllllllllll llllllllllllllllllllllllllllllllllllllllllllllllllll llll llllllllllllllllllllllllllllllllllllllllllllllllll llllllllllllllllllll ll lllllllll llllllllllllllllllllllllllllllllllllllllllllllllllTGI0.092 0.091 0.092llllllllllllllllllllllllllllll llllllllllllllllllllllllllllllllllllllllllllll llllllllllllllllllllllllllll llllllll lllllll lllll lllllllll llll lllllllllllllllllllllllllll llllllllllll lllllllllllllllllllllllllllllllllllllllllllllll lllllllllllllll lllll lll ll llllllll llllllllllllllllllllllllllllll lllllllllllllllllllllllllllllllll lllllllllllllllllllllllllllllllllllllllllll llllll llllllllllllll llllllll llllllllllllllllllllllllllllllllllllllllllllllllllllllllllll ll lllllllllllllllllllllllllll llllllllllllllllllllllllllllllllllllllllll lllllllllllllllll lllllllll l ll llllllllllll lll llll llllllllllll lllllllllll llll lllllllllll lll llllllllllllllllllllllllllllllllllllllllll lllll ll l lll lllllllllllll llllllllllllllllllllllll PA0.034−0.80.00.028040llllllll llllllllllllllllllll llllll lllllllll llllll lllllllll llllllllllllll llllll lllllllllll llll lll llllllllllllllllllllllllll lllllllll lllll ll llllllllllllllllllllllllllllllllllllllll llllllllllllllllllllllllll lllllllllllllllll lllll lll lllllllllllllllllllllll llllll lllllllllllllllllllllllllllllllllllllll llllllllllll llllllll lllll llllllllllllll lllllllllllllll lllllllllllllllllll lllllllllllllllllllllllllllllllllllll llllllllllll l llll llll lllll l ll lll lllllll lllllllllll l lllllll lllllll lllll ll lllllllllllllll llllllllll lll llllllllll ll lll llll lllll l ll llll llll l llll ll ll lll l ll ll lllllllllllllllllllllll llll l l ll l lllllllllllllllllllllllllllllllllllll llllll llll llTRI1.001.0 1.6llllllllll llllllllllllllllllll llllllll lllllllll lllllllllllllll−0.2 0.4llllll llllllll llllll llllllllllllllll llll l lllllll llllllllllllll llllll ll l l lllll llllll llllllllllllllllll llllllllllllllllllll lllll llllllllllllllllllllllllllllllllllllllllllllll lll llll lllll ll llllllllllllllllllll llllllll llllllllllllllllllllllllllllllllll−20 40lll llllllllllll ll llllllllllll lllllllllllllll lllllll lllllllllllllllllllllllllllllllllllllllllllllllllllll lllllllll llllllllllll l llll llll llll lll l llllllllll llllllllllllll llllll l lllllllll llllllll lllllllllllllll llllllllllllll lllll ll ll llll ll−0.8 0.0ll llll ll ll lllll l ll llll llll l llll ll lll llll lll l ll lll llllllllllllllllllllllllll l llllllllllll l llll lllllllll l lll llllllllllll lllllll lllllllllllllllllllllll0 10010SlopeFigure C.3: Pair-Plot of all PanAfEl covariates182Table C.1: Mean values used to center covariatesCovariate MeanNDVI 0.400Tree 7.201HF 19.077PA 0.799Slope 2.480TGI 0.011183C.3 LME & GAMM Model Diagnosticslllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll ll lllllllllllllllllll−4 −2 0 2 4−4−2024Model lme_final , Normality plotTheoretical QuantilesSample Quantilesllllllllllllllll ll lllllllllll llllllll l llllllllll ll llllllllllllllllllllllllllll lllllllllllllllllllllllll lllll lllllllllllllllllllllll llllll lllllllllllllllll llll lllllllll lllll ll lllll lllllll llllllllll llllllllllllllllllllllll l llllllllllllllllllllllllllllllllll lll lll lllllllllllll llll llllllll llllllllllllllllllllllllllllllllllllllllllllll l lllllllllllllllllllllllllllllllllllll lllll llllllllllllllllllllll llllllll ll lllllllllllllllllll llllllllllllllllllllllllll llll llllllllllllllllllllllll lllllll llllllll llllllllllllll lllllll lll lllllllllllllll llllllllllllllll llllllllllllllllllllllll lllllllllllllll lllllllllllllllllllll lllllllllllllllll lllllllllllllllllllllll llll lllllllllllllllllllllllllll llllllllllll lllllllllllllllllllllllllllllllllllll lll lllllllllllllllllllllllllllllllllllllllll lllllllllllllll llllllllllllllllllllllllllllllllllll lllllllllllllllllllll llllllllllllllllllllllllllllll llllll lllllllllllllllll llllll lllllllllll lllllllllllllllll lllllllll ll lllllllll lllll llllllllllllll lllllllllllllllllllllll lllllllllllllllllllllllll lllllllllllllllll lllllllllllllllllllllll lllllll llllllllllllllllllllllllllllllllllllllllllll llllllllll lllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll lll lllllllll llllllll llll lllllllllll llllllllll llllllllllllllllll lllllll lll lllllllllll llllllllllllllllllllllllllll llllllllllllll lllllllllll lllll lllllllll llllllllllllll lllllllll−0.5 0.0 0.5 1.0 1.5 2.0 2.5−4−2024Model lme_final , Residual PlotPredicted Value (log(aLoCoHAreaKm))residualModel lme_final , Error DistributionModel lme_final residuals (level 1)Frequency−4 −2 0 2 4 60100020003000llllllllllllllll l llllllllllllllll llll l ll llllll l lll lllll lllllllllllll lllllllllllllll lllllllllllllll lllllllllllll lllllllllllllllll llll lllllllllllllllllllllllll lllllllllllll llllll llllllll llllllllllllllllllllllllllllllll llllllllllllllllllllllll lllllllllllllllllllllllllllllll lllllllllllll llllll lllll lllllllllllllllllllllllllllllllllllllllllllllllllllll llllllllllllllllll llllllllllllllllllllllllllllllllll llllllllllllllllllllllllll lllllll l lllllllllllllllllllllllllll lllllllllllllllllllll lll lllllllllllllllllll llllllll lllllllllll lllllllllllllllllllllllllllllllll lllllllllllllllllll llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll llllllllllllllllllllll lllll llllllllllllllllllllllllllllllll lllllllllllllllllllllllllllllllll lllllllllllllllllllllll llllll llllllllllllllllllllllllllllllllllllllll llllll llllllllllllllllllllllllllll lllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll llllllllllllllllllllllllllllllllllllllll lllllllllllllllll lllll llllll lllllllll llllllllllllllll llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll lllllllllllllllllll l llllllllllllllllllll lllllllllllllllllllllllllll lllllllllllll lllllll llllllllllllllll llllllll lllllllllllllllll ll lllllllllllllllllll llllllllllllllll−0.5 0.0 0.5 1.0 1.5 2.0 2.50.01.02.03.0Model lme_final , yhat vs log(aLoCoHAreaKm)Predicted ValueObserved Value lme_finalFigure C.4: LME Model Diagnostic Plot184−4 −2 0 2 4−1.5−0.50.51.5Normal Q−Q PlotTheoretical Quantilesresponse residualslllllllllllllllllll llllllllllllllllll lllllllllllllllll lllllllllllllllllllllllllllllllllllll llll lllll l l llllllllllllllllllllllllllll lll llllllllll llllllllllllllllllllllllll ll ll llllllllllllllllllll l llllllllllllllllll ll llllllllllllllllllllllllllllllll llll l llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll ll llllllllll ll l lllllllllllllllllllllll llllllll lllll lllllllllllllll llllllllllllllllll lllllllllllllllllllllllll lllllllllll lllllllll llllllllllllllllllll lllll lllllllllllllllllllllllllllllllllll llllllllllllllllllllllllllllllll llllllllllll llll llllllllllllllllllllllllllllllllllllllllllllll lllllll lllllllllllll llllllllllllllllllllllllllllll lllllllllllllll lllllllllllllll lllllll l llllllllllllllllll llllllllllll lllllllllllllllllllllllllll lllll lllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll l ll llllll llllllllll ll lllllllllllllllllllllllllllllll lllllllllllllllllllllllllllllllllllllllllllllll lll lllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll llllllllllllllll llll llllllllllllll ll llllllllllllll ll llllllllllllllllllllllllllllllllllllll llllllll llllllll lllllllll llll l llllllllllll llll llllll l lllll−0.5 0.0 0.5 1.0 1.5 2.0−1.5−0.50.51.5Resids vs. linear pred.linear predictorresidualsHistogram of residualsResidualsFrequency−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5050015002500llllllllllll lllllllllllllllllllllllllllllll llllllllllllllllllll lllllllllllllllllllllllllllllllllll ll llllllllllllllllllllllllllllll lllllllllllllllllllllll llllllllllllllllll llllllllllllllllllllll llllllllllllll llllllllllllllllllllllllllllllllllllllllllll lllll llllllllllll lllllllllllllllll lllllllllll lllllll lllllllllllllllll lll lllllllllllllllll lllllllllllllllllllllllllllllllllllllllllllllllll llllllllllllllllll llllllllllllllllllllllllllllllllllllllllll llllll llllll lllllllllllllllllllllllllllllll llllllllllllllllll llllll llllllll lll l lll llllllllllllllll llll llll llllllllllllllllllllllllll llllllllll lll llllllllllllllllllllllllllll llllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll llllllllllll lllll lllllllll lllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll ll llllll llllllllllllllllllll lllllllllll llllllllllllllllllllllllllllllllllll llllllllllll lllllllllllllllllllllllllllllllllllllllllll llllllllllllllllllllllllll llllllll llllllll l llll llllllllllllllllllllllllll llllllllllllllllllllllllll l lllllllllllllllllllllllll lllllll lllllllllllllll lll lllll−0.5 0.0 0.5 1.0 1.5 2.00.01.02.03.0Response vs. Fitted ValuesFitted ValuesResponseFigure C.5: GAMM Model Diagnostic Plot185C.4 LME Model ParametersTable C.2: LME model parameters (based on treatment contrasts)Parameter Estimate Std.Error DF t-value p-valueFemale.Central (Intercept) 0.70658 0.227718 10982 3.102856 0.0019Male.Central -1.43629 1.122392 223 -1.279667 0.202Female.East 0.91952 0.229251 223 4.010958 0.0001Male.East 0.84025 0.229347 223 3.663678 0.0003Female.South 0.92952 0.23354 223 3.98013 0.0001Male.South 1.19021 0.233789 223 5.090956 0Female.West -33.52877 10.52823 223 -3.184653 0.0017Male.West -9.69068 8.488943 223 -1.141565 0.2549NDVICenter -0.09237 0.434338 10982 -0.212671 0.8316NDVICenter2 0.41057 1.109667 10982 0.369995 0.7114TreeCenter 0.0031 0.00953 10982 0.325276 0.745TreeCenter2 0.00002 0.000135 10982 0.135377 0.8923SlopeCenter 0.0284 0.052567 10982 0.540303 0.589SlopeCenter2 -0.00164 0.004981 10982 -0.328784 0.7423HFCenter -0.04311 0.034023 10982 -1.267144 0.2051HFCenter2 -0.00167 0.001583 10982 -1.056292 0.2909TCICenter 0.12771 0.58662 10982 0.217697 0.8277TCICenter2 -65.10743 15.60372 10982 -4.172557 0PACenter -0.30827 0.274988 10982 -1.121036 0.2623PACenter2 -0.92858 0.477214 10982 -1.945838 0.0517Male.Central:NDVICenter 0.70397 1.59648 10982 0.440952 0.6593186Parameter Estimate Std.Error DF t-value p-valueFemale.East:NDVICenter 0.65125 0.436434 10982 1.492209 0.1357Male.East:NDVICenter 0.75047 0.43904 10982 1.709332 0.0874Female.South:NDVICenter 0.35774 0.438962 10982 0.814957 0.4151Male.South:NDVICenter 0.88657 0.439484 10982 2.017305 0.0437Female.West:NDVICenter 1.87702 4.18895 10982 0.448088 0.6541Male.West:NDVICenter 0.59812 2.250594 10982 0.265761 0.7904Male.Central:TreeCenter -0.18819 0.064483 10982 -2.918413 0.0035Female.East:TreeCenter -0.02654 0.009825 10982 -2.700905 0.0069Male.East:TreeCenter -0.02871 0.009835 10982 -2.918724 0.0035Female.South:TreeCenter -0.01929 0.011696 10982 -1.649292 0.0991Male.South:TreeCenter 0.05688 0.011528 10982 4.933599 0Female.West:TreeCenter -9.64697 3.16396 10982 -3.049016 0.0023Male.West:TreeCenter -2.6229 2.698238 10982 -0.972077 0.331Male.Central:HFCenter -0.83949 0.18022 10982 -4.658139 0Female.East:HFCenter 0.04124 0.034054 10982 1.210949 0.2259Male.East:HFCenter 0.05378 0.034067 10982 1.578665 0.1144Female.South:HFCenter 0.03416 0.034063 10982 1.002868 0.3159Male.South:HFCenter 0.03386 0.03407 10982 0.993874 0.3203Female.West:HFCenter 0.06958 0.035337 10982 1.968975 0.049Male.West:HFCenter 0.05876 0.034604 10982 1.698196 0.0895Male.Central:SlopeCenter -0.08397 0.174062 10982 -0.482437 0.6295Female.East:SlopeCenter -0.06706 0.052875 10982 -1.268215 0.2047Male.East:SlopeCenter -0.02505 0.053253 10982 -0.470439 0.6381Female.South:SlopeCenter -0.06061 0.053815 10982 -1.126176 0.2601187Parameter Estimate Std.Error DF t-value p-valueMale.South:SlopeCenter 0.0434 0.056413 10982 0.769271 0.4417Female.West:SlopeCenter -4.6444 2.658422 10982 -1.747052 0.0807Male.West:SlopeCenter -0.90304 0.566721 10982 -1.593443 0.1111Male.Central:PACenter 1.01799 0.640942 10982 1.588275 0.1123Female.East:PACenter -0.34196 0.278122 10982 -1.229521 0.2189Male.East:PACenter -0.41861 0.280587 10982 -1.491926 0.1357Female.South:PACenter -0.07267 0.289886 10982 -0.250682 0.8021Male.South:PACenter -0.09322 0.322978 10982 -0.288636 0.7729Female.West:PACenter -1.45147 0.371206 10982 -3.91015 0.0001Male.West:PACenter -0.84096 0.368135 10982 -2.284388 0.0224Male.Central:NDVICenter2 -3.29618 3.082166 10982 -1.069435 0.2849Female.East:NDVICenter2 -2.27661 1.135967 10982 -2.004116 0.0451Male.East:NDVICenter2 -3.01837 1.155612 10982 -2.611919 0.009Female.South:NDVICenter2 0.08133 1.223996 10982 0.066446 0.947Male.South:NDVICenter2 0.99122 1.242473 10982 0.797779 0.425Female.West:NDVICenter2 -1.45972 11.69209 10982 -0.124847 0.9006Male.West:NDVICenter2 -8.4804 6.306222 10982 -1.344767 0.1787Male.Central:TreeCenter2 0.00185 0.00062 10982 2.988486 0.0028Female.East:TreeCenter2 0.00041 0.000156 10982 2.619642 0.0088Male.East:TreeCenter2 0.00048 0.000152 10982 3.130293 0.0018Female.South:TreeCenter2 -0.0029 0.000615 10982 -4.713434 0Male.South:TreeCenter2 -0.01119 0.000947 10982 -11.81562 0Female.West:TreeCenter2 -0.71719 0.246537 10982 -2.909057 0.0036Male.West:TreeCenter2 -0.12659 0.214897 10982 -0.589094 0.5558188Parameter Estimate Std.Error DF t-value p-valueMale.Central:HFCenter2 -0.02862 0.006619 10982 -4.323572 0Female.East:HFCenter2 0.00082 0.001584 10982 0.514566 0.6069Male.East:HFCenter2 0.00108 0.001586 10982 0.682301 0.4951Female.South:HFCenter2 0.00115 0.001585 10982 0.723871 0.4692Male.South:HFCenter2 0.00134 0.001584 10982 0.845292 0.398Female.West:HFCenter2 0.00489 0.001878 10982 2.603833 0.0092Male.West:HFCenter2 -0.00034 0.001727 10982 -0.198666 0.8425Male.Central:SlopeCenter2 0.02356 0.033429 10982 0.704641 0.481Female.East:SlopeCenter2 -0.00079 0.005008 10982 -0.158061 0.8744Male.East:SlopeCenter2 -0.00748 0.005235 10982 -1.428011 0.1533Female.South:SlopeCenter2 -0.01158 0.006978 10982 -1.659567 0.097Male.South:SlopeCenter2 -0.10619 0.014208 10982 -7.474029 0Female.West:SlopeCenter2 -1.62963 0.829535 10982 -1.964512 0.0495Male.West:SlopeCenter2 -0.55177 0.201027 10982 -2.744746 0.0061Male.Central:PACenter2 1.05991 0.892822 10982 1.187144 0.2352Female.East:PACenter2 -0.18345 0.481805 10982 -0.380766 0.7034Male.East:PACenter2 -0.20422 0.484396 10982 -0.421604 0.6733Female.South:PACenter2 0.31498 0.500772 10982 0.628996 0.5294Male.South:PACenter2 -0.0931 0.599581 10982 -0.155268 0.8766Female.West:PACenter2 -3.69331 0.955394 10982 -3.865743 0.0001Male.West:PACenter2 -1.09191 0.732889 10982 -1.489869 0.1363189C.5 GAMM Model ParametersTable C.3: GAMM model intercept parametersParameter Value Std.Error t-value p-valueIntercept 1.14864 0.06839 16.796 < 2e-16Male.Central -0.04717 0.11595 -0.407 0.684173Female.East 0.23427 0.07411 3.161 0.001576Male.East 0.21672 0.07321 2.96 0.003079Female.South 0.32068 0.08742 3.668 0.000245Male.South 0.31334 0.07664 4.088 4.37E-05Female.West 0.81692 0.12139 6.73 1.78E-11Male.West 0.59022 0.12113 4.873 1.12E-06Table C.4: GAMM model smoother parametersSmoother edf F-Value p-values(NDVI) 5.898 74.62 < 2e-16s(TreeCover) 7.436 30.46 < 2e-16s(HF) 7.613 39.91 < 2e-16s(Slope) 8.2 80.5 < 2e-16s(PA) 8.612 80.97 < 2e-16s(TGI) 2.9 22.57 3.71E-14190C.6 LME Model Predictionslllllllllllllllllllllllllllllllllllll llllllllllllllllllllllll0.2 0.4 0.6 0.80100200300West.FemalePredicted Area (Sq.Km)0.2 0.4 0.6 0.80100200300West.Malel l lll ll ll lll ll lll l lll ll ll l lllll l lllll l ll ll ll lll l ll l lllll l l l l0.2 0.4 0.6 0.80100200300Central.FemalePredicted Area (Sq.Km)0.2 0.4 0.6 0.80100200300Central.Malelll l lllll lll l llll l llll ll l llll ll lllll llll l lllllll l llll l llll lll l l lll lllllllllll llllll lll lllll llllllll l ll llllllllllllll lll lllll l llll llllllll llll lllll l ll ll llll l l llllll l ll llll lll lllll llllllll llllll lll lll lll lll llll llll lll ll lllllll llll llllll l ll ll lllllllllllllll llllllll lllll lllllllll llllll ll lllllll ll lllll lllllll lllllllll l l0.2 0.4 0.6 0.80100200300East.FemalePredicted Area (Sq.Km)0.2 0.4 0.6 0.80100200300East.Malell l l llll ll l llllllllll l ll lllll l ll llllll ll llllllllllllllllll llllll ll lllllllllllll ll ll lllll lllll l llllllllll llll lllllll llll lll ll ll ll ll lll ll llllll0.2 0.4 0.6 0.80100200300South.FemalePredicted Area (Sq.Km)0.2 0.4 0.6 0.80100200300South.MaleFigure C.6: LME model predicted values of area (Sq.km) vs. NDVI using modelfitted values191llllllllllllllllllll0 20 40 60 800100200300West.FemalePredicted Area (Sq.Km)0 20 40 60 800100200300West.Malelllllll ll lll llllll ll l ll lll l llllll l llll lll0 20 40 60 800100200300Central.FemalePredicted Area (Sq.Km)0 20 40 60 800100200300Central.Malelll lllllllllllllllllllllll lllllllllllllll lll llllll ll llllll ll ll lll l ll l ll lll l lll llllll ll lllllll llllll l llllllllllll llllllllllllll l lll lllll0 20 40 60 800100200300East.FemalePredicted Area (Sq.Km)0 20 40 60 800100200300East.Malell llllll llllll l lllllll llllllllllllllllll l lll lll l ll l0 20 40 60 800100200300South.FemalePredicted Area (Sq.Km)0 20 40 60 800100200300South.MaleFigure C.7: LME model predicted values of area (Sq.km) vs. Percent Tree Coverusing model fitted values192lll llllllllllllllll ll l lllllllllllllllllllllllll llllllllllllllllllllllllllllllllll0 20 40 600100200300West.FemalePredicted Area (Sq.Km)0 20 40 600100200300West.Malell lllll llll llll l ll0 20 40 600100200300Central.FemalePredicted Area (Sq.Km)0 20 40 600100200300Central.Malell lllllll llllllllllllllll lllllll llll llll lllllllllll lllllll llll lllllll lllllllllllllllllllllllllllll lll lll l lll lllllll llll lll llllllllllllllllllllllllllll lllllll lll lllll lll llllll llllllllll llll l lllllllll ll ll ll0 20 40 600100200300East.FemalePredicted Area (Sq.Km)0 20 40 600100200300East.Malellllll ll llllllll ll lllll lll l ll llll l l llll ll lllllllllllll lll lll ll l ll llllll l llllll lllll lllllllllllllll lll ll llllll ll0 20 40 600100200300South.FemalePredicted Area (Sq.Km)0 20 40 600100200300South.MaleFigure C.8: LME model predicted values of area (Sq.km) vs. Human Footprintusing model fitted values193llllllllllllllllllllllllllllllllll0 5 10 15 200100200300West.FemalePredicted Area (Sq.Km)0 5 10 15 200100200300West.Malelll ll llll lll ll l ll l lll ll lllllll llllll l ll0 5 10 15 200100200300Central.FemalePredicted Area (Sq.Km)0 5 10 15 200100200300Central.Malellllllll lllllllllll lllll l llll lll lll lll llllll llllllll l l llllllllllllll lllll lllllll l lllllllllllll ll ll ll lllll ll l llll ll lllll lll llll ll ll lllll lll l llllllllllllll lllll lll l l0 5 10 15 200100200300East.FemalePredicted Area (Sq.Km)0 5 10 15 200100200300East.Malell llll ll lll ll lllll ll lll lll lllllll llll llllll lllllllll ll ll lll lll ll lllll lll lll lllllll0 5 10 15 200100200300South.FemalePredicted Area (Sq.Km)0 5 10 15 200100200300South.MaleFigure C.9: LME model predicted values of area (Sq.km) vs. Slope using modelfitted values194lllllllllllllllllll lllllllllllll l llllll ll llll0.0 0.2 0.4 0.6 0.8 1.00100200300West.FemalePredicted Area (Sq.Km)0.0 0.2 0.4 0.6 0.8 1.00100200300West.Malel l lll lll ll lllll llll lll l llll ll l l0.0 0.2 0.4 0.6 0.8 1.00100200300Central.FemalePredicted Area (Sq.Km)0.0 0.2 0.4 0.6 0.8 1.00100200300Central.Malel lllllll lllll llll l lllll ll l ll llll llll lll lllll lllll lll lll ll lllllll llll ll ll ll ll ll ll ll l l llllllllll lll lllll lllll lllll l ll ll lll l ll ll ll lll ll lllll l ll l ll llllllll lll lll llllllll lll l ll ll l lll llllll lll lll ll llllllll llllllll l lll ll llllll l ll l ll l lllll lllll llll ll lll lllllllllll ll ll ll lllll l ll llll lllllll l llllllllll ll ll0.0 0.2 0.4 0.6 0.8 1.00100200300East.FemalePredicted Area (Sq.Km)0.0 0.2 0.4 0.6 0.8 1.00100200300East.Malelllllllll ll lll lll ll ll l llll ll llll lll l ll lllllllll ll lllll llllll ll llll l lllll lll lllllllll ll lll llllll llll lll lll l ll l llll lllllll lll lllllll0.0 0.2 0.4 0.6 0.8 1.00100200300South.FemalePredicted Area (Sq.Km)0.0 0.2 0.4 0.6 0.8 1.00100200300South.MaleFigure C.10: LME model predicted values of area (Sq.km) vs. Protected AreaIntersect using model fitted values195lllllllllllllllllllllll l ll l llll llll lll l ll l llllll lll lllll l llllllllllllllllllllll llll l llllllll lll l lllll lll ll lll llll l lllll ll llll l lllllll llll lllllll ll l llllll lll lll llllllllll ll lll ll llllll llll llllllllllllllll lllll l ll ll lll lllll lllll lll l ll lllllll llll llll lllllll l lllllll l llllll l ll ll ll lllllllllllllllll ll l l llll l lll l llllll llll llllllllll l llllllllllll lll l ll ll lll llllllllll llll ll l ll llllllllllllllll lllllll ll ll lllll l lllllllllllll ll llll ll ll l l l ll l llll ll llll l lllllllllllllllllllllllllllllllllll ll ll llllll llllll ll llllllllllll l ll llll llll llll llllllllllllll l ll l l lll lll ll llll lllllll lllll llll ll0.00 0.01 0.02 0.03 0.04 0.05 0.060100200300Temporal Granularity IndexPredicted Area (Sq.Km)Figure C.11: LME model predicted values of area (Sq.km) vs. Temporal Granular-ity Index (TGI) using model fitted values196C.7 GEE Python ScriptAlgorithm C.1: GEE Raster Covariate Statistics Scripti m p o r t j son , ee , o a u t h 2 c l i e n t , d a t e t i m e , numpy , sys , a r c p yMY_SERVICE_ACCOUNT = ’172830405801 @developer . g s e r v i c e a c c o u n t . com ’MY_PRIVATE_KEY_FILE = r ’ E : \ Development \ Python Code \ E a r t h Engine \ p r i v a t e k e y. p12 ’# A u t h e n t i c a t e & I n i t i a l i z eee . I n i t i a l i z e ( ee . S e r v i c e A c c o u n t C r e d e n t i a l s (MY_SERVICE_ACCOUNT,MY_PRIVATE_KEY_FILE ) )# De f i ne t h e p o s s i b l e Image c o l l e c t i o n s & images t h a t can be used wi th t h i ss c r i p tn d v i I m a g e C o l l e c t i o n s =[ ’MODIS / MCD43A4_NDVI ’ ]n d w i I m a g e C o l l e c t i o n s =[ ’MODIS /MCD43A4_NDWI’ ]# Get t h e d e s i r e d image c o l l e c t i o ncol lName = ’MODIS /MCD43A4_NDWI’ # col lName = s y s . a rgv [ 3 ]# De f i ne t h e bandName of t h e image / c o l l e c t i o nband_Name = ’ ’i f col lName i n n d v i I m a g e C o l l e c t i o n s :band_Name = ’NDVI’e l i f col lName i n n d w i I m a g e C o l l e c t i o n s :band_Name = ’NDWI’e l s e :r a i s e S y s t e m E x i t# De te rmine which ImageStackReduce r t o useimgStackReducer = ee . Reducer . mean ( ) #by d e f a u l t I ’ l l use t h e mean v a l u ef o r now# Dete rmine what t h e r e d u c e d image name w i l l bereducedCalcName=band_Name + ’_ ’ + i m g S t a c k R e d u c e r S t r i n g# Dete rmine which RegionReducer t o usep o l y A r e a R e d u c e r S t r i n g = ’ ’ # p o l y A r e a R e d u c e r S t r i n g = s y s . a rgv [ 5 ]po lyAreaReduce r = Nonei f p o l y A r e a R e d u c e r S t r i n g == ’max ’ :po lyAreaReduce r = ee . Reducer . max ( )e l i f p o l y A r e a R e d u c e r S t r i n g == ’min ’ :po lyAreaReduce r = ee . Reducer . min ( )e l i f p o l y A r e a R e d u c e r S t r i n g == ’mean ’ :po lyAreaReduce r = ee . Reducer . mean ( )e l i f p o l y A r e a R e d u c e r S t r i n g == ’ sampleVar i ance ’ :po lyAreaReduce r = ee . Reducer . s a m p l e V a r i a n c e ( )e l i f p o l y A r e a R e d u c e r S t r i n g == ’ count ’ :po lyAreaReduce r = ee . Reducer . c o u n t ( )e l s e :r a i s e S y s t e m E x i t197# De f i ne t h e r e s a m p l i n g r e s o l u t i o n f o r t h e Reduce Regionp o l y A r e a R e d u c e r S c a l e = 500# De f i ne t h e o u t p u t csv f i l eoutputCSV = r ’ E : \ PhD \ T h e s i s \ PanAfEl \ A n a l y s e s \ S i x t e e n−Day \ C o v a r i a t e s \ NDVI \aLoCoHRangeMODIS16dayNDVIValues_mean . csv ’# De f i ne t h e i n p u t f e a t u r e c l a s si n f c = r ’ E : \ PhD \ T h e s i s \ PanAfEl \ A n a l y s e s \ aLoCoH \ aLoCoH_Merge . gdb \aLoCoHMergeGCS ’ #Make s u r e t h e c o o r d i n a t e s a r e i n GCS#A f u n c t i o n t o s e l e c t t h e band from t h e Imaged e f selectBAND ( img ) :r e t u r n img . s e l e c t ( [ band_Name ] )# De f i ne t h e UNIX Epoch s t a r t d a t eepoch = d a t e t i m e . d a t e t i m e ( 1 9 7 0 , 1 , 1 , 0 , 0 , 0 )d e f conver tUnixTimeToDateTime ( unixTime ) :t = d a t e t i m e . d a t e t i m e . u t c f r o m t i m e s t a m p ( i n t ( unixTime / 1 0 0 0 ) )r e t u r n t . s t r f t i m e ( ’%Y−%m−%d %H:%M:%S ’ )d e f conver tDateTimeToUnixTime ( inpu tT ime ) :r e t u r n i n t ( ( inputTime−epoch ) . t o t a l _ s e c o n d s ( ) *1000)d e f Bu i ldGEEFea tu reFromArcGISFea tu reClas s ( ArcGISFea tu re ) :par tnum = 0M u l t i p o l y g o n = [ ] # Th i s w i l l ho ld t h e d i f f e r e n t po lygon p a r t s f o ra s i n g l e f e a t u r e i n t h e ArcGIS f e a t u r e c l a s sf o r p a r t i n ArcGISFea tu re :l i n e a r r i n g s = [ ] # t h i s i s a s i n g l e po lygonl i n e a r r i n g = [ ] # Th i s w i l l ho ld t h e x−y t u p l e s f o r t h ev e r t i c e s o f a g i v e n polygon p a r tf o r p n t i n ArcGISFea tu re . g e t P a r t ( par tnum ) :i f p n t :xy =[ p n t . X, p n t .Y]l i n e a r r i n g . append ( xy )e l s e :l i n e a r r i n g s . append ( l i n e a r r i n g )l i n e a r r i n g = [ ]l i n e a r r i n g s . append ( l i n e a r r i n g )M u l t i p o l y g o n . append ( l i n e a r r i n g s )par tnum += 1# p r i n t ( M u l t i p o l y g o n )po lygonRegion = ee . Geometry . M u l t i P o l y g o n ( M u l t i p o l y g o n )r e t u r n po lygonRegiond e f t e m p o r a l E x t r a c t ( t empFea t ) :s t a r t = tempFea t . g e t ( ’ s t a r t U n i x ’ )end = tempFea t . g e t ( ’ endUnix ’ )c o l l e c t i o n = ee . I m a g e C o l l e c t i o n ( col l_Name ) . f i l t e r D a t e ( s t a r t , end )b a n d Co l l = c o l l e c t i o n . map ( selectBAND )t i l e C o u n t = b a n d C o l l . a g g r e g a t e _ c o u n t ( " sys tem : i d " )reducedImage = b a n dC o l l . r e d u c e ( imgStackReducer )r e d u c e d P o l y = reducedImage . r e d u c e R e g i o n ( po lyAreaReducer , t empFea t .geomet ry ( ) , p o l y A r e a R e d u c e r S c a l e )198r e t u r n tempFea t . s e t ( { ’ imgVal ’ : r e d u c e d P o l y . g e t ( reducedCalcName ) , ’ count’ : t i l e C o u n t } )# Cycle t h r o u g h each of t h e f e a t u r e s i n t h e Polygon F e a t u r e C l a s s ande x t r a c t t h e s t a t i s t i c s from images f a l l i n g w i t h i n t h e t ime framedesc = a r c p y . D e s c r i b e ( i n f c )s h a p e f i e l d n a m e = desc . ShapeFieldName # Shape f i e l d nameOIDFieldName = desc . OIDFieldName #OID f i e l d namerows = a r c p y . S e a r c h C u r s o r ( i n f c )t o t a l r o w c o u n t = a r c p y . GetCount_management ( i n f c )c o u n t =0# Se tup t h e o u t p u t CSV f i l ef = open ( outputCSV , ’w’ )f . w r i t e ( ’ OID , Name , ImgVal , S t a r t D a t e , EndDate , ImgCount \ n ’ )f o r row i n rows :s u c c e s s = F a l s ec o u n t = c o u n t +1w h i l e s u c c e s s == F a l s e :t r y :p r i n t ( ’ P r o c e s s i n g f c : ’ + s t r ( c o u n t ) + ’ o f ’ + s t r (t o t a l r o w c o u n t ) )#OIDo i d = row . g e t V a l u e ( OIDFieldName )# S t a r t D a t es t a r t D a t e = row . g e t V a l u e ( ’ S t a r t D a t e ’ )s t a r t D a t e U n i x = i n t ( ( s t a r t D a t e −epoch ) . t o t a l _ s e c o n d s ( ) *1000)# EndDateendDate = row . g e t V a l u e ( ’ EndDate ’ )endDateUnix = s t a r t D a t e U n i x + 1000 #Add 1 second t o t h e s t a r tv a l u e so t h a t t h e GEE d a t e f i l t e r on ly r e t u r n s one image#Namename=row . g e t V a l u e ( ’ ID ’ )# Shapef e a t = row . g e t V a l u e ( s h a p e f i e l d n a m e )po lygonRegion = Bui ldGEEFea tu reFromArcGISFea tu reClas s ( f e a t )t h i s F e a t u r e = ee . F e a t u r e ( polygonRegion , { ’ s t a r t U n i x ’ :s t a r t D a t e U n i x , ’ endUnix ’ : endDateUnix } )f t =ee . F e a t u r e C o l l e c t i o n ( t h i s F e a t u r e )# Per fo rm t h e image s t a t s e x t r a c t i o nmeanResu l t s = f t . map ( t e m p o r a l E x t r a c t ) . g e t I n f o ( )# E x t r a c t t h e r e s u l t sf o r i i n r a n g e ( l e n ( meanResu l t s [ ’ f e a t u r e s ’ ] ) ) :imgCount = meanResu l t s [ ’ f e a t u r e s ’ ] [ i ] [ ’ p r o p e r t i e s ’ ] [ ’ count’ ]meanVal = ’−999 ’t r y :meanVal = meanResu l t s [ ’ f e a t u r e s ’ ] [ i ] [ ’ p r o p e r t i e s’ ] [ ’ imgVal ’ ]e x c e p t :p r i n t ( ’ An e r r o r o c c u r r e d ’ )o u t S t r i n g = s t r ( o i d ) + ’ , ’ + name + ’ , ’ + s t r ( meanVal ) +’ , ’ + s t a r t D a t e . s t r f t i m e ( ’%Y−%m−%d %H:%M:%S ’ ) + ’ , ’ +endDate . s t r f t i m e ( ’%Y−%m−%d %H:%M:%S ’ ) + ’ , ’ + s t r (199imgCount ) + ’ \ n ’f . w r i t e ( o u t S t r i n g )s u c c e s s = Truee x c e p t :p r i n t ( ’ An e r r o r o c c u r r e d . . . re− t r y i n g . . . ’ )f . c l o s e ( )p r i n t ( ’ F i n i s h e d . ’ )200
Thesis/Dissertation
eng
Geography
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivs 2.5 Canada
Graduate
Geospatial analysis of African elephant movement (Loxodonta africana and L. cyclotis)
Text