Hi Richard, At the risk of sounding pompous, I'd like you to read The Nature of Diversity (Chicago, 2002), especially the sections on speciation and on evolutionary radiations (including adaptive radiations), and see what you think. Then we could perhaps move ahead. Deborah McLennan and I had no problems with multifurcations/explosive speciation events, whether due to rapid widespread climate change and associated dispersal or due to actual adaptive changes. The issue of over- or under-bifurcating in phylogenetic analyses (due to paucity of data or the nature of particular kinds of data) can be at least partly overcome by assessing the mode of speciation at particular nodes and the mode of radiation within a particular clade. Not perfect by any means - and when we published the book we had not yet understood the fundamental importance of taxon pulses as the null hypothesis for evolutionary radiations, as it encompasses both adaptive change associated with speciation and explosive episodes of species formation.

I personally have never thought of Hennig's depiction of phylogenetic analysis in bifurcating terms as an axiom, though he may have believed it. Rather, a completely dichotomous rendering is the most dissected picture we can get of diversifying evolution. As Deborah and I pointed out (citing other sources as well), both "extra bifurcations" and multifurcations can be the result of multiple speciation events involving the same ancestor. Our position, beginning with Phylogeny, Ecology and Behavior, has always been that the tree alone is not enough - trees are descriptions, not explanations. They are necessary but not sufficient for answering many evolutionary questions. In The Nature of Diversity, we made this point a core element and suggested field-based, lab-based, and model-based information that is essential to explain those phylogenetic patterns.

Whew, long-winded. Apologies in advance if needed. But you touch on multiple important issues, including the most critical one of distinguishing different kinds of evolutionary radiations, some of which may be adaptive radiations, many of which are not. - dan

The premiss - two out of three taxa being more closely related - is actually never hurt because the (mother) taxon before the first bifurcation is never identical (neither in terms of cladistic model assumptions nor in its ontic status) to the (daughter) taxon that was subject to the second bifurcation, even though they appear to be morphologically similar. Taxa that try to integrate representatives of the (pre-bifurcation) mother lineage and one (post-bifurcation) daughter lineage are usually not considered as valid (under conditions of a taxonomy consistent with cladistics).

Perhaps more figuratively spoken: A mother species splits up into two daughter species and no mother species is ever exactly the same as one of the daughter species (so they should not be given the same name).

Daniel Brooks: We are apparently approaching the under and over furcation problem from two poles. You from a fundamental (usually) dichotomously branching tree with unknown nodes, and myself from a Besseyan cactus of (usually) known taxa.

Yes, more than phylogenetically informative info must be addressed, I think we agree. One can think of evolutionary data as two sorts, those that do not change with speciation and preserve cladistic relationahips, and those that do and signal serial macroevolutionary transformations, whether adaptive or not. Focusing only on the former can give wrong results and focusing only on the latter loses a sense of evolutionary place. Kinds of adaptive changes are not particularly relevant to me since I lump adaptive changes and neutral or exaptive changes together as tranformational changes. In my own studies I find what are commonly centrirfugal transformations away from a generalized ancestor, either at hand (usually the case) or predictable.

My own book (Framework for a Post-Phylogenetic Systematics, Amazon) details the problems caused when all non-phylogenetically informative data are suppressed. And gives a solution based on both classical and phylogenetic methods of synthesis.

Not axiomatic? See the comment of Michael Buchwitz above.

Michael Buchwitz: Using your method you get a cladogram. A cladogram is indeed a phylogenetic analysis but may not necessarily represent evolutionary relationships, which may be serial.

Regarding splits, consider a species that generates two or three descendant species. The ancestral species continues to change molecularly with non-coding traits (or trivial genetic traits) and if the species are not generated all at once, they will have different molecular strain ancestors but the same taxon as ancestor. An ancestral taxon is never at rest mutation-wise, but unless you see speciation as divergence among molecular strains, you have no good grasp of the history of speciation.

I think many cladists feel that the cladogram is the end result of finding structure in evolution. And no more is needed. Actually eliminating non-phylogenetically informative data simply allows fancy statistical analysis because all the phylogenetically informative data are related to each other (being heirarchical), while data on serial transformations are not amenable to such. Both kinds of information are important, however, and must be combined, that is, branching with serial.

@ Richard Zander: No, I wanted to say that independent from the type of phylogenetic model buildung - e.g. cladistic analysis (on the basis of molecular or other data) or phenetic approaches or whatever else you might think of - the actual course of evolution offers no clear criteria to discriminate species in a way that they pass branching events.

Before a split you have got a population with a certain genetic and phenotypic inventory and after a split ("a new species develops from an ancestral taxon") you have got two populations, each with its own genetic + phenotypic inventory, neither completely or essentially identical to that of the ancestral population.

Thus the idea of an ancestral taxon, from which new species branch off successively, is arguably wrong, i.e. doesn't sufficiently fit the reality of evolution and cannot be falsifiably substantiated - independent from the question what cladists think about their models and model assumptions.

Michael Buchwitz:

Seems axiomatic to me. Like theorems and lemmas in mathematics, unlike hypotheses and theories in science. You say "the actual course of evolution offers no clear criteria to discriminate species in a way that they pass branching events." Sure it does. A "branching event" is a cladistic or phenetic idea, not an evolutionary idea. It is part of a METHOD of grouping taxa. Reifying a node as something is uncalled for unless you have an organism in mind that you can describe as such if not at hand then potentially discoverable. I repeat that changes in base pairs may not be genetic. Genetic means "of the genes" and usually involves dominant or recessive expressed changes in the phenotype. Sure enough, "the idea of an ancestral taxon, from which new species branch off successively, is arguably wrong" is true since you are arguing, but "doesn't sufficiently fit the reality of evolution and cannot be falsifiably substantiated" is nonsense. There is much in the evolutionary literature that documents living ancestral taxa of living daughter species, maybe not so much in the cladistic literature with seems to be your guide to evolution.

But arguably the diversity of life (millions of species instead of one) cannot be explained without branching. Or is that wrong? What can be described as 'branching event' actually happens from time to time and is not only part of a method of grouping taxa. The idea of an "ancestral taxon" and a "daughter species" at the same time slice (e.g. the present) also requires the existence of some kind of process in which one (only ancestral taxon) becomes two (ancestral + daughter taxon). So how can such a split be not real?

Considering an individual branching process in the tree of life as

"an ancestral taxon persisting and giving rise to one daughter species" (how you described it)" or

"an ancestral taxon fading away and giving rise to two daughter species" (as I described it)

you will find the that the latter has the (epistemic) advantage that it doesn't require all kinds of criteria (genetic, morphological or else) to match one of the lineages after the split with the ancestral lineage. (That there is much evolutionary literature that describes living ancestral taxa of living daughter species could also be due to lacking rigorousity when it comes to thinking about such concepts.)

Perhaps there is a misunderstanding (between us here or neontologists and palaeontologists) comes from the perspective and time scale of the processes we are looking at: If you are interested in extant taxa and evolutionary processes presently at action (and thus directly observable) or happening in youngest past it might be helpful to think about ancestral species as persisting and giving rise to one or several daughter species.

Looking at so-called 'deep time' processes, that take millions of years and happened tens to hundreds of millions of years ago, the ancestry of some taxon to some other taxon usually becomes completely vague (for various reasons) and thus phylogenetic model-building tries to avoid any such statements about direct ancestry (because they appear to be virtually untestable). But that does not mean that you can't study character evolution in 'deep time' using 'nodes' as a concept that (more or less well) describes branching in the tree of life. Instead of trying to infer character evolution from changes that happen from (ancestral) taxon A to (daughter) taxon B to (granddaughter) taxon C you are (mediately) looking at changes that happen from node to node.