Brent D. Mishler and Edward C. Theriot.
A species is the least inclusive taxon recognized in a formal phylogenetic classification. As with all hierarchical level of taxa in such a classification organisms are grouped into species because of evidence of monophyly. Taxa are ranked as species rather than at some higher level because they are the smallest monophyletic groups deemed worthy of formal recognition, because of the amount of support for their monophyly and/or because of their importance in biological process operating on the lineage in question
Sensu Mishler and Theriot, there is no species problem per se in systematics. Rather, there is a taxon problem. Once one has decided what taxon names are to represent in general, then species taxa should be the same kinds of things, just the least inclusive. Evolution is real, as are organisms (physiological units), lineages (phylogenetic units), and demes (interbreeding units), for example. On the other hand, our classification systems are obviously human constructs, meant to serve certain purposes of our own: communication, data storage and retrieval, and predictivity. These purposes are best served by classification systems that reflect our best understanding of natural processes of evolution, and the field of systematics in general has settled on restricting the use of formal taxonomic names to represent phylogenetically natural, monophyletic groups.
A phylogenetic systematic study of a previously unknown group of organisms involves three major temporal, logical phases:
1. In the precladistic phase the elements of a cladistic data matrix are assembled. These elements include OTUs (operational taxonomic units), characters, and character states. OTUs are assembled initially from grouping together of individual specimens that are homogeneous for the characters then known. Here is important to stress that there is no obvious, theory-free way to individuate species. The process must involve analysis, and that analysis must be explicitly phylogenetic.
2. Cladistic analysis involves translation of the data matrix into a cladogram. Reciprocal illumination is often involved here as well because incongruence between characters or odd behaviour of particular OTUs may lead to a return to phase 1, a re-examination of OTUs and characters, primarily to check for fit to the assumptions of the cladistic method.
3. Classifications based on an assessment of the relative support for different clades provide a basis for evolutionary studies. Formal taxa (including species) are named here on the basis of clear support for their existence as monophyletic cross sections of a lineage and for their utility in developing and discussing theories.
Any cladistic analysis that fails to take into account the possibility of reticulation may not be realistic. Not all lineages may have evolved apomorphic characteristics, and so they may not be identifiable through character analysis. That is, there may be monophyletic groups for which there is no direct evidence. This is a general problem for cladistic analysis and is not special to the species problem.