Species, Clusters and the 'Tree of Life': A graph-theoretic perspective

TL;DR

This paper explores how to mathematically define hierarchical structures of species based solely on genealogical relationships using graph theory, aiming to formalize the 'Tree of Life' concept.

Contribution

It introduces mathematically precise methods to derive nested hierarchical clusters from genealogical graphs, connecting biological classification with graph-theoretic concepts.

Findings

Defined collections of nested subsets based on ancestry graphs

Established relationships between genealogical clusters and traditional taxonomy

Provided mathematical frameworks for hierarchical species classification

Abstract

A hierarchical structure describing the inter-relationships of species has long been a fundamental concept in systematic biology, from Linnean classification through to the more recent quest for a 'Tree of Life.' In this paper we use an approach based on discrete mathematics to address a basic question: Could one delineate this hierarchical structure in nature purely by reference to the 'genealogy' of present-day individuals, which describes how they are related with one another by ancestry through a continuous line of descent? We describe several mathematically precise ways by which one can naturally define collections of subsets of present day individuals so that these subsets are nested (and so form a tree) based purely on the directed graph that describes the ancestry of these individuals. We also explore the relationship between these and related clustering constructions.