$\beta$-diversity and Graph Sheaf Laplacians

TL;DR

This paper introduces a novel graph sheaf Laplacian-based measure for $eta$-diversity in ecological systems, providing a more informative and computationally efficient scalar quantity compared to traditional methods.

Contribution

It proposes a new $eta$-diversity measure derived from graph sheaf Laplacians, enhancing ecological data analysis with a linear algebra approach.

Findings

Energy measure outperforms traditional $eta$-diversity metrics in examples

Scalar quantity is easy to compute using linear algebra techniques

New approach offers more informative insights into ecological diversity

Abstract

We suggest a new approach to $\beta$-diversity in ecological systems, based on the energy of the graph sheaf Laplacian associated with the sample data. This scalar quantity is easily computable using methods of linear algebra. We show using simple examples that the energy is much more informative than the generally accepted definitions of $\beta$-diversity