PhD proposal - Ecological Geometry

✦ Context

PhD Thesis Project – QUT Mathematical Sciences (IF49 Doctor of Philosophy)
Application submitted October 2024 – QUT Application ID: 7937703
Supervisor: Pr. Michael Bode (Mathematical Marine Ecology Lab / School of Mathematical Sciences) & Dr. Juliano Morimoto (School of Natural and Computational Sciences / Aberdeen University)

This research proposes a novel “Ecological Geometry” framework that moves beyond traditional ODE/PDE approaches to better capture high-dimensional, nonlinear ecological data. By integrating geometric and topological tools, the project aims to model complex species interactions, reveal hidden structural patterns in ecological networks, improve predictive power, and support more robust ecosystem management and conservation strategies.

Working title:
“Ecological Geometry: Applying geometric and topological concepts to model species interactions”

✦ Tools & Skills

Topological Data Analysis (TDA) Persistent homology Betti numbers Voronoi diagrams Delaunay triangulations Geometric modelling Graph theory & network robustness Joint Species Distribution Models (JSDM) R / Python algorithm development Spatial covariates & residual analysis Theoretical & integrative ecology

✦ Key Contributions (Thesis Proposal)

• Development of a comprehensive geometric-topological framework to overcome limitations of classical dynamical models in high-dimensional ecological systems
• Application of spatial geometry tools (Voronoi diagrams, Delaunay triangulations) to model species territories and distributions
• Integration of topological methods (persistent homology, Betti numbers) to detect higher-order connectivity patterns and hidden structures in ecological networks
• Enhancement of existing tools such as JSDM residuals through new geometric/topological spatial covariates
• Design of novel algorithms (R/Python) for geometric spatial analysis, topological data analysis (TDA), and graph-theoretic assessment of network stability and robustness
• Systematic validation against established theoretical frameworks in ecology
• Three-year timeline structured around literature review, model/framework development, algorithm implementation, simulations, validation, and manuscript preparation

✦ Outputs & Links

📄 Full research proposal (PDF) 🏛️ Queensland University of Technology (QUT)

Note: This PhD proposal was submitted in October 2024 for the IF49 PhD program. Full proposal (including detailed methods, 3-year timeline, references, and alignment with national priorities in mathematical biology) is attached above.