Bayesian methods for interpretable and scalable modelling of population dynamics

The work in this thesis presents novel Bayesian methods for enhancing wildlife monitoring, a critical component in addressing climate change due to the regulatory role of species and their habitats in the climate system. Given the consistent decline in biodiversity, marked by shifts in life history events, the importance of effective wildlife monitoring is underscored. The thesis highlights the significance of understanding species behavior for better management, utilizing time-series monitoring and speciesborne devices like GPS and acoustic recorders to gather detailed behavioral data. These studies focus on latent behavioral states with Markovian dependence, for which Hidden Markov Models (HMMs) are frequently employed. Monitoring population dynamics is also emphasized, as population size is a key measure for assessing biodiversity loss and informing conservation policies. Depending on survey duration and species characteristics, populations can be closed or open. Common models like Jolly-Seber (JS) and Cormack-Jolly-Seber (CJS) are used, with temporary emigration (TE) models accommodating species with seasonal patterns. The thesis addresses the critical role of sampling schemes in population dynamics studies. Capture-Recapture (CR) is extensively used but when infeasible, Batch-Mark (BM) sampling serves as an alternative, providing accurate inference in open population models. Employing parametric and non-parametric hierarchical Bayesian models, the thesis uses Bayes’ Theorem to update prior beliefs based on observed data. The non-parametric approach, particularly using the P´olya Tree prior, offers flexibility by allowing data to shape the distribution. Markov Chain Monte Carlo (MCMC) methods are used to sample from posterior distributions for behavioral states and population parameters, demonstrating the robust application of these Bayesian methods in ecological datasets.

Chapter 2 develops a parametric Bayesian model to infer species behavior over time using Bayesian HMMs. The model addresses the challenge of selecting latent states by employing a Reversible Jump MCMC algorithm and repulsive priors to prevent overfitting. Extensive simulations and real case studies on muskox and Cape gannets demonstrate the model’s utility. Chapter 3 introduces a non-parametric Bayesian model for population dynamics using JS models for BM data, leveraging the P´olya Tree Prior. The model is computationally efficient and exact, accommodating various survey designs and incorporating capture losses. Robustness is demonstrated through simulations and case studies on weather loaches and golden mantella frogs. Chapter 4 addresses the complexity of TE models with Approximate Bayesian Computation (ABC), using Sequential Monte Carlo (SMC) ABC for efficient posterior sampling. The method’s f lexibility is shown through simulations and a case study on alpine common toad. Overall, this thesis advances Bayesian methods for wildlife monitoring, providing robust tools for understanding species behavior and population dynamics, ultimately contributing to biodiversity conservation and climate change mitigation.