814 THE STRUCTURE OF EVOLUTIONARY THEORY
the recognition) of species without autapomorphies. Such species arise frequently
in the modelled system as a necessary consequence of the chosen rules of
generation and the general logic of cladistic analysis. But, in neontological
practices of naming, a species without autapomorphies represents an oxymoronic
concept, and such taxa could never be designated at all. Lemen and Freeman
recognize this point in writing about their various forms of gradualistic modelling
(p. 1551): "When distinctness of species is demanded the lack of autapomorphies
may not be the most expected condition."
- Under punctuated equilibrium, "as the number of characters used in the
analysis increases, the distribution of the number of autapomorphies per species
becomes bimodal. Under gradualism, the distribution of autapomorphies remains
unimodal under all conditions" (1538). This situation, a spinoff from their second
criterion, arises because each branch, in an event of punctuated equilibrium,
produces one changed descendant and one persisting ancestor—and the more
characters you measure, the more you pick up the differences between stasis on
one branch and change on the other. Under gradualism, total change correlates
only with elapsed time; so accumulating autapomorphies should form a unimodal
distribution so long as species duration remains unimodal as well.
Lemen and Freeman found no bimodal distributions in real data, and therefore
concluded again in favor of gradualism. But, once more, the differences between
idealized modeling and data from real organisms scuttles this conclusion. In the
models, we know for sure that long arms without branching are truly so
constituted, for we have perfect information of all simulated events. These
unbranched arms, under punctuated equilibrium, should accumulate no
autapomorphies—and the low mode of the bimodal distribution arises thereby.
But, in real data of cladograms based on living organisms, long unbranched arms
usually (I would say, virtually always) record our ignorance of numerous and
transient speciational branchings that quickly became extinct and left no fossil
record. (Moreover, since Lemen and Freeman's cladograms only include living
organisms, even if successful and well-represented fossil species existed, they
would not be included.) When we note a long arm without branches on a modern
cladogram, and then assume (as Lemen and Freeman did) that accumulated
autapomorphies between node and terminus must have arisen gradually and
anagenetically, we commit a major blunder. We have no idea how many
unrecorded speciation events separate node and terminus, and we cannot assert that
recorded autapomorphies did not occur at these (probably frequent) branchings. In
other words, Lemen and Freeman's bimodality test assumes that unbranched arms
of their cladograms truly feature no speciation events along their routes, whereas
numerous transient and extinct species must populate effectively all of these
pathways.
Other applications of this method—modeling of alternative outcomes and
testing of contrasting predictions against patterns of real data—have yielded results
favorable to punctuated equilibrium. In a path breaking paper, Stanley (1975—see
elaboration in Stanley, 1979 and 1982) first proposed this style of testing and
developed four putative criteria, all affirming punctuated equilibrium.