Point Pattern Analysis of Tropical Tree Populations Developing Flexible Spatial Models with Complex Boundary Structures

Ecological models to estimate species distributions, population size and habitat associations often rely on statistical assumptions that are unrealistic in the domain of application. Standard point process models in particular rely on assumptions of perfect detectability and independence that are unlikely to hold. These assumptions can be relaxed by incorporating models for detection and for structured random effects that account for unobserved causes of heterogeneity. The current status quo often involves a 2-stage approach, fitting detectability separately from spatial models and a spline approach for the structured random effect.

This PhD builds on recent developments in approximate Bayesian inference (Integrated Nested Laplace Approximation) and the approximation of Gaussian Markov random fields (GMRF) to develop 1-stage point process models that simultaneously account for unobserved heterogeneity and the detection process. There is also scope to include the GMRF developments in other types of spatial models common in ecological applications such as spatial capture-recapture models, which share similar assumptions about independence that are hard to meet in practice.