Punctuated Equilibrium and the Validation of Macroevolutionary Theory 869
gradualism of microfossils in deep-sea cores must record a general pattern that
would be seen wherever stratigraphic sampling could attain such completeness.
Cheetham (1986) calculated 160,000 years for average spacing between
successively sampled populations in the intensely collected interval— for a
stratigraphic completeness of 0.63 by Sadler's (1981) criteria.
In Metrarabdotos (again see Fig. 9-18), 11 of the 17 species persist in stasis
for 2-6 million years, and all originate punctuationally within the limit of
resolution (at least in the intensely sampled interval) of 160,000 years—
undoubtedly in far less time for many branching events, since 160,000 years
represents a maximum figure based on the available unit of measurement. Again
for the intensely sampled interval, Cheetham writes (1986, p. 190) that "nine
comparisons of ancestor-descendant species pairs all show within-species rates of
morphologic change that do not vary significantly from zero, hence accounting for
none of the across-species difference. In all cases, the ratio of within-species
fluctuation to across-species difference is low enough to allow the punctuated
pattern to be distinguished with virtual certainty. In at least seven of the cases,
ancestor species persisted after giving rise to descendants, in conformity with the
punctuated equilibrium mode of evolution."
The morphometric details can only increase confidence in "the remarkably
clear-cut evidence for a punctuated evolutionary pattern in these Metrarabdotos
species" (1986, p. 201). The reported central tendencies of samples integrate data
from 46 measurements, providing a good assessment of general anatomical
distance (based on characters considered important in the taxonomy and functional
morphology of these organisms), and not on selected single characters (see
Cheetham, 1987, for affirmation of punctuated equilibrium from analyses of
temporal trends in individual characters as well). In supplementary affirmation,
Cheetham studied the fine-scale pattern of temporal variation by computing
autocorrelations between mean scores of stratigraphically successive pairs of
populations: "In all cases, the autocorrelations of mean scores of successive
populations are nonsignificant and near zero, and the autocorrelations of rate
deviations are negative and (except in one case) nonsignificant. These
autocorrelations clearly indicate that changes within species are fluctuations
around a near zero, otherwise unchanging rate" (1986, p. 201).
Finally, some authors (see Marshall, 1995) have challenged Cheetham's
phylogeny for its stratophenetic basis. But a purely cladistic analysis, as now
preferred by many researchers, not only changes the previous scheme in only
minor ways (Cheetham and Jackson, 1995, p. 192), but also—and the point
becomes almost amusingly obvious once one grasps the different criteria used by
the two methods—leads to an even stronger pattern of punctuated equilibrium, for
the stratophenetic phylogeny minimizes the mean morphologic distances between
putative ancestor-descendant pairs, while the cladistic phylogeny makes no such
assumption and must therefore yield a larger mean difference between species.
Since the documented stasis within species is not affected in either case, the
cladistic scheme must increase the average magnitude of punctuational events, thus
only decreasing the likelihood that between-species