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$β$-diversity and Graph Sheaf Laplacians

Peter Davidson, Michael Grinfeld

Abstract

We suggest a new approach to $β$-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 $β$-diversity

$β$-diversity and Graph Sheaf Laplacians

Abstract

We suggest a new approach to -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 -diversity
Paper Structure (6 sections, 7 equations)

This paper contains 6 sections, 7 equations.

Table of Contents

  1. Introduction
  2. Defining a sheaf Laplacian
  3. Examples
  4. Chains
  5. $K_3$
  6. Discussion