A graphical user interface (GUI) input-based algorithm to automate generation of multi-state models for release-recapture studies Adam C. Pope A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science University of Washington 2014 Committee: John R. Skalski Timothy E. Essington Program Authorized to Offer Degree: Quantitative Ecology and Resource Management University of Washington Abstract A graphical user interface (GUI) input-based algorithm to automate generation of multi-state models for release-recapture studies Adam C. Pope Chair of the Supervisory Committee: Professor John R. Skalski School of Aquatic and Fishery Sciences Release-recapture studies represent an important branch of population analysis and are the primary method used to investigate population survival and migration. As researchers seek to answer more detailed questions about the populations under study, and as the study designs themselves become increasingly complex, the models necessary to estimate survival and migration parameters must increase in complexity as well. Multi-state models are widely used for this purpose since they can accommodate multi-dimensional study designs and have a flexible parameterization. Model specification of a multi-state model for a complex release- recapture study design is far from trivial, and requires a thorough statistical understanding of these types of models. Additionally, multi-state models require specification of all possible capture histories for the study design in question. This task can be daunting when done manually as possible capture histories for some release-recapture studies can number in the tens of thousands. This thesis describes the creation and implementation of a computer program (Program BRANCH) capable of multi-state model specification and parameter estimation for complex release-recapture studies. The program is divided into three main elements: (1) Allow the user to draw a study design diagram on the screen as input, specifying releases and recapture opportunities and the structure of survival and migration routes through the study, (2) translate the study design diagram into a multi-state model specified by a product-multinomial conditional likelihood equation, and (3) provide estimates and standard errors for biologically meaningful migration and survival parameters from study data. The construction of Program BRANCH is developed from digraph and maximum likelihood theory and is illustrated using five diverse release-recapture studies as test cases. Acknowledgments I would like, first and foremost, to acknowledge my wife Amanda. Her emotional support, commitment, and understanding were essential to the completion of this research. I am unable to express the depth of gratitude her unwavering encouragement has inspired. Thanks honey! John Skalski served as my primary advisor and Thesis Committee Chair. His counsel was consistently invaluable and excellent, and his guidance enabled me to complete the daunting task of writing this thesis. To him and to my second committee member Tim Essington, who both provided their time and advice without reservation, I owe a huge debt of thanks. Additionally, Rebecca Buchanan, Richard Townsend, Cindy Helfrich and the rest of the staff at University of Washington’s Columbia Basin Research freely and consistently gave of their time and experience to answer the many questions I frequently needed help with. I will miss working with all of them and am grateful for their support. I would also like to thank my fellow graduate students in the Quantitative Ecology and Resource Management program. Academic research should always include the free exchange of ideas as a central tenet, and the brilliance of my fellow students often illuminated my own path to completion of this thesis. This work was supported by Bonneville Power Administration, Project 1989-107-00, Contract No. 267893. Table of Contents List of Figures .................................................................................................................................v List of Tables ................................................................................................................................vii Chapter 1: Introduction ................................................................................................................1 1.1 Cormack-Jolly-Seber models .......................................................................................1 1.2 Multi-state models ......................................................................................................2 1.3 Motivation ...................................................................................................................6 1.4 Objectives ....................................................................................................................8 Chapter 2: Developing Program BRANCH ...................................................................................10 2.1 Introduction ..............................................................................................................10 2.2 Algorithm development ............................................................................................11 2.2.1 Representation of a study design schematic ..............................................12 2.2.2 Diagram interpretation using digraph theory ............................................14 2.2.3 Traversing the digraph using recursive programming ................................18 2.2.4 Creating conditional likelihoods .................................................................19 2.2.5 Re-parameterization and estimability ........................................................23 2.2.6 Data and sufficient statistics ......................................................................26 2.2.7 System level parameter estimation ...........................................................27 2.3 Algorithm construction .............................................................................................28 2.4 Other types of multi-state models ............................................................................29 Chapter 3: Applying Program BRANCH .......................................................................................34 3.1 Introduction ..............................................................................................................34 i 3.2 CJS model for juvenile Chinook salmon in the Lower Columbia River .....................37 3.2.1 Introduction ...............................................................................................37 3.2.2 Study site ....................................................................................................37 3.2.3 Methods .....................................................................................................38 3.2.3.1 Tagging and data recovery ..........................................................38 3.2.3.2 Data analysis ................................................................................38 3.2.4 Results ........................................................................................................41 3.2.5 Discussion ...................................................................................................41 3.3 Multi-state model for juvenile fall Chinook salmon 2010 cohort .............................42 3.3.1 Introduction ...............................................................................................42 3.3.2 Study site ....................................................................................................43 3.3.3 Methods .....................................................................................................44 3.3.3.1 Tagging and data recovery ..........................................................44 3.3.3.2 Data analysis ................................................................................45 3.3.4 Results ........................................................................................................50 3.3.5 Discussion ...................................................................................................51 3.4 Multi-state model for Lost River and shortnose suckers in Clear Lake Reservoir .....53 3.4.1 Introduction ...............................................................................................53 3.4.2 Study site ....................................................................................................53 3.4.3 Methods .....................................................................................................55 3.4.3.1 Tagging and data recovery ..........................................................55 3.4.3.2 Data analysis ................................................................................56 ii 3.4.4 Results ........................................................................................................62 3.4.5 Discussion ...................................................................................................65 3.4.5.1 Ecology ........................................................................................65 3.4.5.2 Modeling .....................................................................................66 3.5 Multi-state model for juvenile Chinook salmon in the Sacramento-San Joaquin .....67 3.5.1 Introduction ...............................................................................................67 3.5.2 Study site ....................................................................................................67