Distinguishing among populations in terms of their lack of sharing of direct ancestors.
Two populations are different phylogenetic species if, operationally, they both descended from different individuals. These populations in particular must be true populations as typically defined in terms of gene flow rather than simply small groups of individuals that happen to have the same individual as an ancestor (e.g., such as having a grandmother that is common to a group). Populations, in other words, tend to be well established for relatively long periods and do not display substantial gene exchange with other, similarly defined populations.
Implied in this idea is that those two populations therefore cannot be hybridizing together since if that were the case then the members of the populations could not be distinguished in terms of their ancestors, at least not absolutely. That is, a hybrid possesses the ancestors of both populations it is a descendant of. Thus, two distinct populations that truly are distinct populations, versus, e.g., subpopulations, could be described also as phylogenetic species.
The phylogenetic species concept is a means of visualizing species in more macroevolutionary terms, though the problems of figuring out whether hybridization is occurring is equivalent to that seen also with the morphological and ecological species concepts as, indeed, also with the biological species concept.