Phylogeny, genealogy and the Linnaean hierarchy: a logical analysis

Phylogenetic terms (monophyly, polyphyly, and paraphyly) were first defined in the context of a phylogenetic tree. However, reproduction is the background process that largely determines phylogeny. To establish a connection between genealogy and phylogeny, definitions of phylogenetic terms are presented and studied within a genealogical context. The correctness of the definitions is corroborated with results that show they satisfy the appropriate properties in the context of a phylogenetic tree. In an application of the definitions, a formal analysis shows why the monophyletic condition makes a Linnaean hierarchy entirely monotypic.