I recently discussed this over lunch with a colleague who has the strong conviction that this species concept is "wrong".
The idea behind it is as follows: There are many different species concepts for defining and delimiting species in the here and now, but regardless of that we all agree that the history of species is mostly tree-like, a process of separate lineages through time of interbreeding or asexual, but definitely reproducing individuals splitting into more such separate lineages.
Now Willi Hennig, the founder of phylogenetic systematics, suggested the following approach to delimiting species along a phylogenetic tree: the existence of each individual species is limited to one internodon, to the space between two nodes of the phylogenetic (species) tree. It comes into existence with a lineage splitting event and it ends either with true extinction of all its populations or with the next splitting event. That means if one of its populations becomes sufficiently distinct to be considered a different species B, the entire ancestral species A is considered "pseudo-extinct", and its remaining populations, although they may be completely indistinguishable from A, are considered to be a new species C. And this is precisely what my colleague does not like: C looks like A, so they must be the same.
Yes, Hennig's approach intuitively seems weird. To cite from his 1966 book, "such a statement appears paradoxical to the logical human mind, and obviously no systematist would be prepared, on the basis of such reflections, to give another name to the [indistinguishable descendant] species". However, names aside, there is logic to defining the temporal boundaries of species like this: From a historical, phylogenetic perspective, ancestral species A is not identical to C, but A is identical to C plus its other descendant B. Or in other words, what has happened is not that A has remained unchanged while B has poofed into existence from nowhere, but really that A has diversified. Diversifying is not remaining unchanged, obviously. And Hennig gave other arguments for his preference beyond this, which merely I personally find the most relevant.
I am not claiming, however, that Hennig was "right" and my colleague was "wrong". This is all pretty academic anyway (in the derogatory sense), a mere matter of definitions and labeling, and cannot be decided empirically. I am just saying that Hennig's position is a legitimate one. More importantly, my colleague was right to point out that the controversy over the Internodon Species Concept was an unnecessary distraction. It was once a big cause of controversy, but these days it is mostly irrelevant.
First, most systematists don't actually care about ancestral species anyway. The work of palaeobotanists, for example, is really cool (I have taken a course myself and marveled at how well preserved the cellular structure of Sphenophyllum stems from 300 million years ago can be), but most of us deal with living plants only, and even when we combine it all into one system we don't actually ever know a significant number of confirmed ancestral species, if any, so who cares?
It is even more irrelevant because phylogenetic systematics does not, in contrast to what some of its opponents are claiming, depend on it. Kornet & McAllister (2005) have developed the Composite Species Concept, basically a typological concept with a historical dimension, in case somebody needs a species concept for phylogenetic trees in a hurry. It sees species as paraphyletic, morphologically homogeneous groups of internodons and it works well with phylogenetic classification. Why? Because you can't infer clades in the absence of synapomorphies, and the fixation of a new apomorphy terminates a Composite Species. That guarantees that no Composite Species makes a supraspecific taxon non-monophyletic.
Hennig W, 1966. Phylogenetic Systematics. Urbana: University of Illinois Press.
Kornet DJ, McAllister JW, 2005. The Composite Species Concept: A rigorous basis for cladistic practice, pp. 95-127 in Teydon & Hemerik, Current Themes in Theoretical Biology, Springer.