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Topic

Scalable Bayesian Multistate Capture–Recapture Models for Complex Demographic Processes

Department of Mathematics and Statistics

Date & location

• Friday, April 17, 2026
• 1:30 P.M.
• Clearihue Building, Room B017

Examining Committee

Supervisory Committee

• Dr. Laura Cowen, Department of Mathematics and Statistics, ̽��ϵ�� (Supervisor)
• Dr. Saman Muthukumarana, Department of Mathematics and Statistics, UVic (Co-Supervisor)
• Dr. Jason Fisher, School of Environmental Studies, UVic (Outside Member)

External Examiner

• Dr. Paul Conn, Marine Mammal Laboratory, National Oceanic and Atmospheric Administration

Chair of Oral Examination

• Dr. Timothy Iles, Department of Pacific and Asian Studies, UVic

Abstract

Quantitative understanding of population dynamics depends on reliable estimation of demographic parameters from ecological data. Capture–recapture studies play an important role in this context and serve as a primary source of such data based on repeated observations of individuals over time. However, statistical inference on these parameters often gets complicated by partial observation, individual heterogeneity, and missing information. In most cases, key biological processes, including survival, reproduction, and growth, are only intermittently observed or entirely unobserved, while individual capture histories are sparse and irregular. Ignoring missing information or using data-reductive approaches such as discretization techniques can lead to biased or unstable parameter estimates. We develop scalable Bayesian hierarchical capture–recapture models that explicitly represent latent processes and allow demographic inference in the presence of complex missing-data structures.

For my first contribution, we developed a Bayesian multistate capture–recapture model for estimating survival, capture, and reproductive state transition probabilities when reproductive condition (spawning or non-spawning) and sex are incompletely observed. Reproductive state is modelled as a latent process evolving over time, and sex is incorporated as a discrete individual-level covariate that may be partially unknown. This framework allows demographic parameters to vary by reproductive state and sex while accounting for uncertainty arising from sparse recaptures and missing state information. The model is motivated by the capture–recapture data of anadromous Dolly Varden (Salvelinus malma) populations in the western Canadian Arctic, and it reveals sex- and state-specific differences in survival and capture dynamics associated with intermittent spawning behaviour.

My second contribution addresses the challenge of incorporating individual growth into capture–recapture analyses when encounters are irregular and complete age or growth histories are unavailable. We develop a novel Bayesian hierarchical framework for modelling individual growth, for which length evolves through a stochastic, age-independent incremental process and is treated as a latent, time-varying covariate when observations are missing. Using simulation studies, we compare our newly proposed simple additive growth approach (SAGA) with the standard von Bertalanffy growth model (VBGM) under varying degrees of recapture sparsity. We then apply the model to capture–recapture data of anadromous Dolly Varden from two populations in the western Canadian Arctic. By embedding growth within a joint likelihood for growth, survival, and capture processes, this approach improves inference on growth dynamics in data-limited systems.

My third contribution relaxes the assumption of permanent individual identification by developing a novel tag-loss–retagging capture–recapture model for systems in which individuals are identified using external tags that can be lost and replaced multiple times. Tag retention is modelled as a stochastic process that evolves through retagging events and is directly linked to capture probability. To model tag loss while accounting for retagging, two alternative model formulations: a single-regime (homogeneous) and a multi-regime model, are proposed. These models are evaluated using simulation studies and applied to long-term capture-recapture data of Antarctic fur seals (Arctocephalus gazella) at Macquarie Island, Australia. By incorporating retagging information into the capture–recapture framework, this study demonstrates a practical approach for demographic inference under realistic field conditions where tag loss and retagging are common.

Together, these contributions advance Bayesian capture–recapture methodology for analysing demographic data characterised by latent biological processes, continuous individual heterogeneity, and evolving observation processes, with broad applicability across ecological systems.