A Symmetry-based Framework for Model Selection of Coral Reef Population Growth Models

TL;DR

This paper introduces a symmetry-based approach using Lie group theory to improve model selection for coral reef population growth, demonstrating its effectiveness on real and simulated data.

Contribution

It develops a novel framework leveraging Lie symmetries to distinguish between candidate models in population dynamics, including a method for optimizing parameters.

Findings

Symmetry analysis can effectively differentiate models using coral reef data.

The approach identifies trivial symmetries as key discriminators.

Method for locally optimizing multi-parameter symmetries is proposed.

Abstract

The problem of selecting a model given a set of candidates remains a challenging one that pervades many scientific fields. We employ techniques from the theory of Lie groups to analyse the symmetries in differential equation models of population growth, with the aim of informing the model selection problem. To illustrate the use of Lie symmetries in model selection, we apply them to simulated data and to coral reef data from the Great Barrier Reef, demonstrating that the trivial symmetries can distinguish between candidate models. A method for finding locally optimal parameters for multi-parameter symmetries is presented, and the paper concludes with related results, some open problems, and avenues of further research.