820 THE STRUCTURE OF EVOLUTIONARY THEORY
best test for distinguishing the bifurcating model of speciational gradualism from
the cladogenetic model of punctuated equilibrium. In this case, the impediment
may be clear, but I can offer no legitimate excuse for my opacity—and I
congratulate Wagner and Erwin on their formulation.
The solution lies in the distribution and frequency of "hard" polytomies in
cladogenetic topologies. I failed to appreciate the following point: under
punctuated equilibrium, new species branch off from unchanged and persisting
ancestors. The successful ancestor remains in stasis and may live for a long time.
Therefore, these "stem" species may generate numerous descendants during their
geological tenure, while remaining unchanged themselves. Now what cladistic
pattern must emerge from such a situation? A group of species branching at
different times from an unchanged ancestor must yield a cladistic polytomy.
Cladograms cannot distinguish different times of origin from an unaltered ancestor,
and can therefore only record the phenetic constancy of the common and
unchanging ancestor as a polytomy, for all branches emerge from an invariant
source. Bifurcation, on the other hand, can produce a range of cladistic topologies
(Wagner and Erwin, 1995, p. 92), but not domination of the overall pattern by
polytomies. Thus, gradualistic vs. punctuational models of speciation should be
distinguishable by distributions of polytomies in the resulting cladogram.
I suspect that many of us never recognized this point because we have been
trained to view polytomies negatively as an expression of insufficient data to
resolve a true set of ordered dichotomies. (Shades of our profession's former
failure to conceptualize punctuated equilibrium because we had been trained to
view geologically rapid appearances as artifacts of an imperfect fossil record!)
Thus, we never recognized that polytomies might also be denoting a positive and
resolvable pattern—multiple branching through time of several species from an
unaltered ancestral source. Of course—and, again, just as with punctuated
equilibrium itself—polytomy can also result from imperfection, and we need
criteria to separate "real" polytomies representing a signal from the history of life
from polytomies that only record artifact of an imperfect record. Wagner and
Erwin (1995) develop such a criterion by distinguishing between "hard"
polytomies that include the persisting ancestor and "soft" polytomies that arise
from an inability to resolve true sets of ordered dichotomies.
Wagner and Erwin's modelling demonstrates the translation of punctuational
speciation to a cladistic pattern of predominant polytomies. (Wagner and Erwin
used my own model of punctuational phylogenies, done with D. M. Raup in the
1970's (Raup and Gould, 1974), to show this mapping of punctuational phylogeny
to a polytomous cladogram—see Figure 9- 13 —but I had never made the
connection myself.)
Wagner and Erwin then applied their modelled differences to cladograms for
two well resolved, but maximally different (in taxon and time) species-level
phylogenies in the fossil record: two Neogene clades of planktonic foraminifers
(Globigerinidae and Globorotaliidae), and Ordovician representatives of the
gastropod family Lophospiridae. In both cases, the cladograms indicated