Bayesian Hierarchical Models for Spatial and Temporal data from Ecological Surveys

Globally, biodiversity is declining at an unprecedented rate, with an increasing number species threatened by human actions and natural environments significantly altered. These declines are reinforcing the need for accurate wildlife monitoring to detect changes in species abundances and distributions and to identify the environmental and anthropogenic drivers underlying these. This thesis develops novel Bayesian hierarchical models tailored to both established and emerging ecological survey technologies (environmental DNA (eDNA), transect, and camera trap surveys). In each survey, the latent ecological process being targeted, such as species distribution or density, is temporally and/or spatially correlated. However, ecological surveys only provide imperfect indicators of latent ecological states. They are subject to imperfect detection (in the form of false negatives and false positives), measurement error or equipment failure (such as sample contamination or camera battery failure), and observation noise (such as observation heteroscedasticity). Traditional models often fail to appropriately propagate these errors and bias inference of spatial-temporal trends and drivers. Bayesian hierarchical frameworks allow for the separation of ecological and observation processes, enabling robust inference on latent states for conservation management. Chapter 2 develops a novel spatio-temporal Bayesian framework for inferring environmental DNA concentration from qPCR data. The approach accounts for contamination and inhibition in lab analyses, addressing biases particularly notable at low DNA concentrations, and for the inherent stochasticity in the corresponding data. Additionally, the model incorporates heteroscedasticity in qPCR output, recognizing the increased variance of qPCR data at lower DNA concentrations. We show that statistical frameworks ignoring these sources of error and noise have increased bias in inferred DNA concentrations, and make actionable recommendations to survey design to ensure robust inference. Chapter 3 develops a unified statistical framework for transect occupancy models and shows that different detection protocols produce structurally distinct models with varying parameter identifiability. Through algebraic analysis and data cloning, we demonstrate that single replicate detection/non-detection observations often fail to be practically identifiable, which can undermine inference. We introduce a novel data-based diagnostic for detecting identifiability issues and use simulations to assess how survey design and model choice affect statistical performance, providing actionable guidance for more reliable inference. Chapter 4 develops a modelling framework to infer the latent working state of cameras in camera trap surveys in the presence of several forms of common camera malfunction (namely battery depletion and sensor malfunction). Discrete-time HMMs and continuous-time MMMPPs infer latent camera states, effective effort, and detection rates. We show that the continuous-time framework reduces bias but raises computational costs and misspecification risks, highlighting complex comprises with the equivalent discrete-time frameworks. Overall, the statistical frameworks developed throughout the thesis advance Bayesian hierarchical models for inferring spatial and temporal dynamics in ecological processes whilst accounting for novel errors generated by emerging technologies and provide interpretable outputs for conservation managers.