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Implementation of Bayesian Inference Techniques To Implementation of Bayesian inference technique to address data limited problems in ecology: A case study with Peary caribou in Canadian Arctic Archipelago By Samarth Kaluskar A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Department of Physical and Environmental Science University of Toronto © Copyright by Samarth Kaluskar 2021 ii Implementation of Bayesian inference technique to address data limited problems in ecology: A case study with Peary caribou in Canadian Arctic Archipelago Samarth Kaluskar Doctor of Philosophy Department of Physical and Environmental Science University of Toronto 2021 Abstract: In the present era, rates of decline in species’ abundance provide some of the most compelling evidence of biodiversity loss rates globally. To address the problem of biodiversity loss, a critical piece of knowledge is the understanding of species interactions with their environment, because environmental variables are generally better predictors of population integrity than intrinsic biological traits. Peary caribou (Rangifer tarandus pearyi), the smallest of all caribou subspecies, are endemic to the Canadian Arctic Archipelago (CAA) and a characteristic example of species at risk. Climate change can affect their habitat availability, as well as the makeup of the entire Arctic ecosystem. Logistical and financial constraints in the CAA often compromise the frequency and the spatial extent of Peary caribou surveys, and therefore inconsistent sampling, errors in measurements, or faults in data acquisition encumber the robust assessment of their population status. To remedy such data gaps in surveys and, improve the robustness of any modelling exercise, I first developed a regression-based imputation framework to reconstruct the Peary caribou time series. The model was able to capture more than 65% of the variability in the dataset. To date, little work has been done to evaluate the net impact of changes from the climate on Peary caribou population dynamics, as it has been argued that the net balance of limited forage accessibility due to severe weather conditions relative to that of increased forage biomass due to prolonged growing season will depend on local climate, floral abundance and composition, and iii landscape characteristics. Using a two-pronged modelling approach, I characterized the year-to- year variability of the habitat conditions across the CAA, using meteorological variables, landscape features, and resource competition. My dissertation also introduced a spatially explicit modelling framework to examine the strength and nature of the relationships of snow density and vegetation with Peary caribou populations. My dissertation concludes by identifying critical augmentations of the available scientific knowledge that necessitate to design the optimal management actions of Peary caribou populations across the Canadian Arctic Archipelago. iv Acknowledgement I would love to thank my ever loving, wife Akshata for her assurances and advices which helped me in good stead. Her enthusiasm and encouragement helped me get through the toughest part of my academic career. I express my whole hearted thanks to my family for their generosity, unwavering support and encouragement. Thank you for helping me to flourish. Thank you for supporting me through trying times, always believing in me, and for giving me strength. Siddharth, thank you for being my best friend. I would like to express deep sense of gratitude to Dr. George Arhonditsis. He is like a candle who has lit up my career path, so I can achieve my goals. Without his inspiring and instrumental role, this research would not have been possible. I consider myself very fortunate to have him as my supervisor. His dynamic approach and encouraging guidance boosted my moral which helped me to complete this research work to a great extent. I am very grateful for all the support that the supervisory committee (Dr. George Arhonditsis, Dr. Agnes Richards, Dr. William Gough and Dr. Péter K. Molnár) have extended to me during my time here at UofT. I deeply appreciate how you have been continuously encouraging and guiding me, and also how you have always been so friendly and supportive of all of my efforts and struggles. With immense pleasure, I take this opportunity to express my deep sense of gratitude and respect to my parents, professors, colleagues, friends & well-wishers. A very special gratitude goes out to all Ecological Modelling lab members. They have made time that spent working in the lab a much enjoyable and memorable experience. I also thank Dr. Cheryl-Ann Johnson for sharing meteorological and landscape feature dataset and habitat suitability estimates. I am highly indebted to her for the guidance and for providing necessary information regarding the project and also for the support in completing the v project. I would like to express my special gratitude and thanks to Dr. Johnson for giving me such attention and time. With gratitude, I would like to thank Dr. Alexander Langlois, who gave me the opportunity to learn SNOWPACK model and for his support in this project. I am grateful for the experience. Special thanks to Dr. Yuhong He from University of Toronto, Mississauga for sharing NDVI data. I am sincerely grateful for their contribution. This project was undertaken with the financial support of the Government of Canada provided through the Department of the Environment. I would also like to acknowledge the contributions with respect to data sharing and empirical/technical input from the Communities of Nuvanut (Resolute Bay, Grise Fiord, Gjoa Haven, Kugaaruk, Taloyoak, Cambridge Bay) and Northwest Territories (Sachs Harbour, Ulukhaktok, Paulatuk). Samarth Kaluskar vi Dedication I dedicate this dissertation to my wonderful family: To my parents, Rachna & Ramesh Kaluskar, and brother, Siddharth Kaluskar Who believe in the pursuit of academic excellence. Thanks for supporting me and encouraging me! To my wife, Akshata (A.K.A Bestie) … Life is NOT beautiful but you try to make it joyful. For that I dedicate this work to you vii Table of Contents Acknowledgement ....................................................................................................................................... iv List of Tables ............................................................................................................................................... ix List of Figures .............................................................................................................................................. xi List of Appendices Figures ........................................................................................................................ xiv List of Appendices Tables ......................................................................................................................... xvi Chapter 1 Introduction .................................................................................................................................. 1 1.1 Ecological services and importance of biodiversity ........................................................................... 1 1.2 Species extinction risk ......................................................................................................................... 2 1.3 Introduction to Peary caribou ............................................................................................................. 7 Chapter 2 Research Objectives ................................................................................................................... 11 Chapter 3 Connecting the Dots in Databases of Endangered Species: A Bayesian Hierarchical Imputation Strategy for Missing Peary caribou (Rangifer tarandus pearyi) Population Data ....................................... 15 3.1 Introduction ....................................................................................................................................... 15 3.2 Methods............................................................................................................................................. 18 3.2.1 Peary caribou population .......................................................................................................... 18 3.2.2 Study area .................................................................................................................................. 19 3.2.3 Modelling Framework................................................................................................................ 22 3.3 Results-Discussion ............................................................................................................................ 28 3.3.1 Data imputation and island-specific population sizes ............................................................... 28 3.3.2 Delineation of local population units and inter-island migration ............................................. 32 3.3.3 Peary caribou population trends across the Canadian Arctic Archipelago .............................. 35 Chapter 4 A stochastic modelling framework to accommodate the inter-annual variability of habitat conditions for Peary caribou (Rangifer tarandus pearyi) populations ........................................................ 54 4.1 Introduction ....................................................................................................................................... 54 4.2 Methods............................................................................................................................................
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