Some concepts and terms are often misunderstood, confused or conflated, and it seems useful to illustrate them in a concise way for later reference.
Examples for systems that show a phylogenetic structure are groups of:
- homologous sequence copies / alleles / haplotypes / chromosomes, with some reticulation possible due to a process that allows recombination between alleles (crossover)
- chloroplasts and mitochondria
- cells within one organism
- individuals that belong to the same asexually reproducing species
- biological species, with some reticulations possible due to allopolyploid speciation
The red area in the above phylogeny shows a monophyletic group. It covers an entire branch of a phylogeny.
With the same content of extant species, it can be either paraphyletic or polyphyletic depending on whether the orange part is included or not, which in turn depends only on the ancestral character state of the character used to define the group. That shows quite nicely that there is hardly any difference between paraphyletic and polyphyletic groups, a fact one should perhaps take into consideration when discussing the proposal that paraphyletic groups be given formal recognition, or even just when discussing the attempt by evolutionary systematists to redefine monophyletic to mean either monophyletic or paraphyletic. (This is often justified with the observation that paraphyletic groups also have a common ancestor, but well, the same is true of any two species on this planet, even Homo sapiens and Escherichia coli.)
Memo to evolutionary systematists: Please reconsider justifying the acceptance of paraphyletic taxa with polytomies, uncertainties or low bootstrap support; in those cases, the groups you want to circumscribe may even be monophyletic!
Examples for systems that show a tokogenetic structure are groups of:
- individuals that belong to sexually reproducing species
- (well, that is it as far as biological systematics is concerned, unless allopolyploid speciation were a good deal more frequent than can be made plausible)
Memo to evolutionary systematists: Please reconsider justifying paraphyletic taxa with reticulation. If reticulation is rare enough, monophyletic taxa work fine. If it is frequent enough for monophyletic taxa to become problematic, there aren't any paraphyletic ones either.
Memo to cladists who think that the sentence "this species is monophyletic" makes any sense whatsoever: This is why it doesn't. Unless you are talking about asexually reproducing species, of course, because groups of individuals from those do have phylogenetic structure.
So is there a name for a group like the one in the last illustration? I am not sure if somebody has already bothered to invent these terms, but paratoketic sounds about right as a counterpart to the terms ending in -phyletic. A group containing all descendants of the common ancestor would then obviously be monotoketic.
Finally, consider the big picture: You have gene copies forming a phylogenetic structure within individuals, within populations, within species. You have organelle genomes forming a phylogenetic structure within individuals, within populations, within species. You have cell lines forming a phylogenetic structure within an individual. You have individuals and populations of sexually reproducing species forming tokogenetic structures, and individuals and populations of asexually reproducing species forming phylogenetic structures. And finally, you have all the species on the planet forming a (mostly) phylogenetic structure. All intertwined, on top of or within each other in a picture that is breathtakingly complex. But phylogenetic systematics is only about the last of all of these: discovering and naming monophyletic groups of species. Not monophyletic groups of gene copies, not monophyletic groups of individuals, and so on.