  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.
