Sampling large ecosystem network structures using ODEs and linear algebra: mathematically exploring the ecological "diversity-stability debate"

Overview

https://research.qut.edu.au/environment/https://research.qut.edu.au/environment/

Ecosystem networks in nature, in which all species coexist, are often simulated using generalised Lotka-Volterra (GLV) equations. The equilibria of GLV are readily calculated using linear algebra, but for large networks, this set of equations suffers from difficulty in sampling parameter values that yield coexisting species. Such theoretical work has contributed to the ecological "diversity-stability debate" which questions why large ecosystem networks can easily exist in nature?

A recently proposed model published in Science, the "sublinear model", suggests that this debate can be reconciled by considering an alternative mechanistic formulation for how species coexist in nature. The sublinear model is proposed to have parameter values that are easier to sample in high-dimensional networks, thus resolving the "diversity-stability debate". However, this model remains fairly unexplored so far.

This project will explore how the sublinear and GLV models differ in their abilities to simulate coexisting species in high-dimensional networks.

Research engagement

In this project the student will engage in mathematical ecology research using pen-and-paper mathematics and computer simulations. Some reading of the relevant literature will also be required (e.g. see links to papers provided in Background section).

Research activities

This project will involve numerical simulation of ODEs, steady state analysis, and statistical sampling, in MATLAB or similar software to explore the different models' predictions of ecological coexistence.

The student will work with Dr Matthew Adams and also have an opportunity to connect with several broader research groups including but not limited to: QUT Applied Mathematical Ecology Group; QUT Centre for Data Science; Securing Antarctica's Environmental Future; and QUT Centre for Resilience.

Outcomes

The aim will be new predictions of the sublinear model, and new evidence for or against its usage to simulate ecosystem networks.

Skills and experience

The ideal candidate will have some experience with ODEs, linear algebra and MATLAB is recommended, and an interest in merging statistics with applied and computational mathematics techniques.

Start date

1 November, 2024

End date

28 February, 2025

Location

QUT, Gardens Point Campus

Keywords

• ecosystem networks
• ordinary differential equations
• linear algebra
• statistical sampling
• species interactions

Contact

Dr Matthew Adams, mp.adams@qut.edu.au