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Data Integration Methods for Studying Animal Population Dynamics

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Data Integration Methods for Studying Animal Population Dynamics Data integration methods for studying animal population dynamics by Audrey Béliveau M.Sc., Université de Montréal, 2012 B.Sc., Université de Montréal, 2010 Dissertation Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in the Department of Statistics and Actuarial Science Faculty of Science c Audrey Béliveau 2015 SIMON FRASER UNIVERSITY Fall 2015 All rights reserved. However, in accordance with the Copyright Act of Canada, this work may be reproduced without authorization under the conditions for “Fair Dealing.” Therefore, limited reproduction of this work for the purposes of private study, research, criticism, review and news reporting is likely to be in accordance with the law, particularly if cited appropriately. Approval Name: Audrey Béliveau Degree: Doctor of Philosophy (Statistics) Title: Data integration methods for studying animal population dynamics Examining Committee: Chair: Gary Parker Professor Richard Lockhart Senior Supervisor Professor Carl Schwarz Co-Supervisor Professor Steven Thompson Supervisor Professor Rick Routledge Internal Examiner Professor Paul Conn External Examiner Research Mathematical Statistician National Marine Mammal Laboratory NOAA/NMFS Alaska Fisheries Science Center Date Defended: 22 December 2015 ii Abstract In this thesis, we develop new data integration methods to better understand animal pop- ulation dynamics. In a first project, we study the problem of integrating aerial and access data from aerial-access creel surveys to estimate angling effort, catch and harvest. We pro- pose new estimation methods, study their statistical properties theoretically and conduct a simulation study to compare their performance. We apply our methods to data from an annual Kootenay Lake (Canada) survey. In a second project, we present a new Bayesian modeling approach to integrate capture- recapture data with other sources of data without relying on the usual independence assump- tion. We use a simulation study to compare, under various scenarios, our approach with the usual approach of simply multiplying likelihoods. In the simulation study, the Monte Carlo RMSEs and expected posterior standard deviations obtained with our approach are always smaller than or equal to those obtained with the usual approach of simply multi- plying likelihoods. Finally, we compare the performance of the two approaches using real data from a colony of Greater horseshoe bats (Rhinolophus ferrumequinum) in the Valais, Switzerland. In a third project, we develop an explicit integrated population model to integrate capture- recapture survey data, dead recovery survey data and snorkel survey data to better under- stand the movement from the ocean to spawning grounds of Chinook salmon (Oncorhynchus tshawytscha) on the West Coast of Vancouver Island, Canada. In addition to providing spawning escapement estimates, the model provides estimates of stream residence time and snorkel survey observer efficiency, which are crucial but currently lacking for the use of the area-under-the-curve method currently used to estimate escapement on the West Coast of Vancouver Island. Keywords: Aerial-access; Capture-recapture; Creel surveys; Independence assumption; Integrated population modeling; Oncorhynchus tshawytscha iii Acknowledgements First and foremost, I am very grateful to my supervisors Richard Lockhart and Carl Schwarz for their time, advice, financial support and the collaboration opportunities offered through- out my doctoral program. I would like to thank my collaborators: Steve Arndt for providing insight on the creel survey data; Roger Pradel for hosting me at the CEFE and introducing me to integrated population modeling; Michael Schaub and Raphaël Arlettaz for providing the bats data and insight; and finally Roger Dunlop for hosting me during the 2014 Burman River survey and for the numerous discussions that have followed. I can say without a doubt that those PhD years were the best of my life so far, for the most part thanks to the incredibly friendly atmosphere in the Department and the amazing people I met there. I would like to thank Derek Bingham for hosting me in his lab and providing access to computing resources. I am also grateful to Gary Parker for his support in a wide array of instances. To my fellow graduate students and friends Ararat, Biljana, Elena, Huijing, Mike, Ofir, Oksana, Ruth, Shirin, Zheng and many others, thank you for cheering up my days and for the many dinners, concerts, tennis matches and more! A very special mention goes to Shirin and Ofir for their support in difficult times. I would like to say a big thank you to all my dancing friends and teammates for all the fun times that helped maintain a good balance in my life. I am also thankful to David Haziza for always believing in me! Finally, I gratefully acknowledge the financial support from the Natural Sciences and Engineering Research Council of Canada. iv Table of Contents Approval ii Abstract iii Acknowledgements iv Table of Contents v List of Tables vii List of Figures ix 1 Introduction 1 2 Adjusting for undercoverage of access-points in creel surveys with fewer overflights 3 2.1 Introduction . 3 2.2 Sampling Protocol . 5 2.3 Statistical Methods . 6 2.3.1 Inference Framework . 7 2.3.2 Study of the Bias . 8 2.3.3 Study of the Variance . 9 2.3.4 Optimal Allocation . 10 2.3.5 Stratification . 11 2.4 Simulation Study . 12 2.5 Application . 15 2.6 Discussion . 21 3 Explicit integrated population modeling: escaping the conventional as- sumption of independence 23 3.1 Introduction . 23 3.2 Background and notation . 24 3.2.1 Capture-recapture survey . 24 v 3.2.2 Population count survey . 26 3.2.3 Integrated population modeling via likelihood multiplication . 27 3.3 Integrated population modeling based on the true joint likelihood . 28 3.3.1 Capture-recapture and count data . 28 3.3.2 Model variations . 32 3.4 Simulation Study . 33 3.5 Application . 38 3.6 Discussion . 43 4 Integrated population modeling of Chinook salmon (Oncorhynchus tshawytscha) migration on the West Coast of Vancouver Island 45 4.1 Introduction . 45 4.2 Sampling Protocol . 47 4.3 Notation . 48 4.4 A Jolly-Seber approach to estimate escapement . 49 4.5 Integrated population modeling . 53 4.6 Analysis of the 2012 data . 57 4.6.1 Assessment of the integrated population model . 64 4.7 Discussion . 66 Bibliography 67 Appendix A Supplementary materials for Chapter 2 70 A.1 First-order Taylor expansions . 70 A.2 Assumptions, propositions and proofs for the study of Errparty . 70 A.2.1 Assumptions . 70 A.2.2 Study of Errparty for the estimators CbR and CbDE . 71 A.2.3 Study of Errparty for the estimator Cb1 . 72 A.2.4 Study of Errparty for the estimator Cb2 . 74 A.3 Proof of the Optimal Allocation . 76 A.4 Monte Carlo measures . 77 A.5 Figures . 78 Appendix B Supplementary materials for Chapter 3 81 B.1 Monte Carlo measures used in the simulation study . 81 B.2 Plots of the results of the simulation study . 83 B.3 Bats data analysis . 93 Appendix C Supplementary materials for Chapter 4 94 C.1 Analysis of the 2012 capture-recapture data using the software MARK . 94 vi List of Tables Table 2.1 Values of αi and βi for the variance formulas . 10 Table 2.2 Parameter values used to generate the data for the simulation study. 13 Table 2.3 Monte Carlo measures for the simulation with µb = 130. Numbers are expressed in %. 16 Table 2.4 Allocation of sample size in the 2010-2011 Kootenay Lake Creel Survey. 18 Table 2.5 Optimal values of no/ng for each month and day type combination for the number of rainbow trout kept. Note that we do not present results for the double expansion estimator because in that case the optimal allocation is no = ng. ........................... 20 Table 2.6 Seasonal combined estimates (Est) of total number of rainbow trout kept along with approximate 95% confidence intervals (Low,Upp). The last column is computed as a separate total estimate over the three seasons. 21 Table 3.1 Changes in the population size per state over time for a study with K = 3 periods. The table follows the timeline in Figure 3.1. Starting in the upper left corner of the table, the population is comprised of N1 unmarked individuals at the beginning of period 1. Then, the count survey occurs (which does not affect the state nor size of the popula- tion). Then, B1 births occur resulting in N1 + B1 unmarked individu- als in the population. Then, C1 individuals are captured, marked and released which leaves N1 +B1 −C1 unmarked individuals in the popula- u m tion. Then, D1 unmarked individuals die and D11 marked individuals u die. When period 2 begins, there are respectively N1 + B1 − C1 − D1 m and C1 −D11 unmarked and marked individuals in the population. The table goes on like this until the study is finished. Note: C & R is used to abbreviate “captures and recaptures”. 30 Table 3.2 Monte Carlo measures comparing the performance of the true joint likelihood approach (L) and the composite likelihood approach (Lc) in the simulation study, across scenarios and parameters. Each Monte Carlo measure is based on 250 simulated datasets. 35 vii Table 3.3 Monte Carlo estimates of P (WL ≤ WLc ), where W stands for either the absolute error (AE), the standard deviation of the posterior sample (SD) or the length of the 95% HPD credible interval (LCI). Each Monte Carlo measure is based on 250 simulated datasets. 36 Table 4.1 Notation for the data collected at Burman River. The subscript s can take the values m (males) and f (females). 49 Table 4.2 Notation for the parameters used in the Jolly-Seber model and/or the integrated population model. The subscript s can take the values m (males) and f (females).
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