856 THE STRUCTURE OF EVOLUTIONARY THEORY
did witness a much higher frequency of gradualism. But I suspect that Barnovsky's
result records a bias in older literature, when paleontologists tended to publish only
when they found "interesting" lineages in the midst of change. But Prothero
studied all lineages for a time and place, without preconception about modes or
tempos—and his relative frequencies matched the predictions of punctuated
equilibrium.
Proper empirical tests of relative frequencies impose two crucial
requirements: first, that cases be sampled without any preselection in favor of one
outcome or the other; and second, that cases be sufficiently numerous to establish a
statistically significant relative frequency for a totality. The "totalities,"
"universes," or "populations" that inspire studies of relative frequencies for testing
punctuated equilibrium constitute the "usual suspects" of evolutionary research: all
species in a monophyletic taxon (genealogical criterion), or all species (perhaps of
restricted taxonomic scope) in a given biota over a specified time and area
(temporal and geographic criteria).
Relative frequencies for higher taxa in entire biotas
I previously cited the admittedly subjective testimony of many leading experts
about the overwhelming predominance of punctuated equilibrium among all
lineages in the group of their lifelong expertise and specialization (not just those
featured in published studies)—see pages 752-755. Some paleontologists have
tried to provide a rough quantification for this "feel." For example, Fortey (1985)
states that, for graptolites and trilobiles, "the gradualistic mode does occur
especially in pelagic or planktonic forms, but accounts for 10% or less of
observations of phyletic change, and is relatively slow." J. Jackson (cited in Kerr,
1995, p. 1422) attempted to separate out only the most persuasive cases of
unbiased sampling in faunal studies of relative frequencies. Of this subset, he
remarked: "I'm imposing pretty strict criteria, but in the few cases I know [that
meet these criteria], it's perhaps 10 to 1 punctuated." Later, and after a more
rigorous attempt to compile best documented cases for the time and general
environment best suited for supplying the requisite density of data—Neogene
benthonic species of macroinvertebrates— Jackson concluded (in Jackson and
Cheetham, 1999, p. 75): "Overall, 29 out of 31 species of Neogene benthos for
which phylogenetic data are available exhibited punctuated morphological change
at cladogenesis that is consistent with the theory of punctuated equilibria. Cases of
punctuation more than double if we include extended morphological stasis ... Thus,
most but not all cases of speciation in the sea are punctuational."
The most persuasive studies have applied morphometric methods to large
numbers of species in exhaustive (or at least statistically well validated) tabulations
for the full diversity of higher taxa within particular faunas or spans of time.
Hallam (1978), for example, tabulated data for all adequately defined European
Jurassic bivalve species, forming a compendium of 329 taxa. He found
"overwhelming support" (p. 17) for punctuated equilibrium, with the single
exception that 15 to 20 percent of his species showed phyletic size increase—but
no changes in shape—during their geological tenure. Only