Internodons as equivalence classes in genealogical networks: Building-blocks for a rigorous species concept

Among the options suggested in phylogenetic systematics to solve the species problem is the Hennigian or internodal species concept. This concept interprets species as parts of the genealogical network of individual organisms between two successive permanent splits or between a permanent split and an extinction event. Though this option is at present not favoured by phylogeneticists, we believe that, to solve the species problem, there is no alternative to finding a satisfactory partition of the genealogical network. In previous work a formal definition has been developed of Hennigian or internodal species (called internodons here), based on a logical relation between individual organisms. In this paper, we prove that this definition indeed partitions genealogical networks exhaustively into mutually exclusive entities, by showing that the defining relation is an equivalence relation. Although internodons should not themselves be seen as species, they are essential building-blocks for any satisfying species concept.
KEYWORDS: Genealogical network; Permanent splits; Species definition; Hennigian or internodal species concept; Equivalence relation; Internodon

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