The Species Problem from the Modeler's Point of View.

How to define a partition of individuals into species is a long-standing question called the species problem in systematics. Here, we focus on this problem in the thought experiment where individuals reproduce clonally and both the differentiation process and the population genealogies are explicitly known. We specify three desirable properties of species partitions: (A) Heterotypy between species, (B) Homotypy within species and (M) Genealogical monophyly of each species. We then ask: How and when is it possible to delineate species in a way satisfying these properties? We point out that the three desirable properties cannot in general be satisfied simultaneously, but that any two of them can. We mathematically prove the existence of the finest partition satisfying (A) and (M) and the coarsest partition satisfying (B) and (M). For each of them, we propose a simple algorithm to build the associated phylogeny out of the genealogy. The ways we propose to phrase the species problem shed new light on the interaction between the genealogical and phylogenetic scales in modeling work. The two definitions centered on the monophyly property can readily be used at a higher taxonomic level as well, e.g., to cluster species into monophyletic genera.