2. Patterns of changing variation through a “dissected” punctuation may reveal a cladogenetic mode of direct filiation. Empirical patterns of variation may permit distinction between punctuational incursion from elsewhere (a migrational event of uncertain interpretation) and cladogenesis in situ. To contrast two studies previously reported, Heaton (1993) found consistent and unaltered bimodality in a vertical sequence of Oligocene rodents, with an appearance of overall gradualism arising as an artifact of directionally changing relative abundances. Such a pattern — while confirming stasis and showing the utility of punctuated equilibrium as a generator of alternative hypotheses — cannot resolve the descendant's mode of origin, for the new species enters the fossil record in full and complete distinction. In Williamson's study of African lake mollusks (1981), however, a distinctive pattern of variation (see previous discussion on page 769) implicates cladogenesis in situ — for Williamson's fine-scale vertical resolution allowed him to discern an initial period of expanded intrapopulational variation followed by a reduction back to ancestral levels, but now centered about the altered mean of the new species.
3. Comparison of within- and between-species variation as a test of extrapolationism. If new species arise by gradualistic anagenesis, then the direction of selection within populations and the pattern of temporal variation during the life of a species should mirror the morphological changes between species in a geological trend. But Shapiro (1978) estimated natural selection in the Miocene scallop Chesapecten coccynelus by comparing specimens that died as juveniles to those that survived to adulthood. He measured the direction of implied change as not only different from, but actually orthogonal to, the distinction between this species and its descendant, Chesapecten nefrens. [Page 854] Shapiro could not resolve the tempo or mode of the cladogenetic event itself, but he showed that its direction cannot be extrapolated from an inferred pattern of change by natural selection within the ancestral species.
Kelley (1983, 1984) then conducted a more extensive study of all molluscan species with sufficiently rich vertical records in these classical and well-studied Miocene beds of Maryland. She found trending within species for only 16 of 90 cases (17.8%) as defined by well-determined rank correlation coefficients between a shell measurement and stratigraphic position. But for the majority of positive coefficients, she found that the trend within a species is “oriented opposite to the direction of the succeeding species's morphology, indicating a decoupling of macroevolution from microevolution in those cases” (1983, p. 581).
PROPER AND ADEQUATE TESTS OF RELATIVE FREQUENCIES: THE STRONG EMPIRICAL VALIDATION OF PUNCTUATED EQUILIBRIUM
The indispensability of data on relative frequencies
As stated before (p. 823), proponents of punctuated equilibrium have always recognized that the theory cannot be proven, and can win only two minimal validations — proof of plausibility and promise of testability — from documentations, however rigorous and complete, of individual cases (as presented in the last two sections). As its primary claim, therefore, punctuated equilibrium must assert a dominant role for stasis within species and rapid cladogenesis between species in the construction of macroevolutionary patterns at the appropriate scale of speciation and trends across species within clades. This assertion requires that punctuated equilibrium maintain a dominant relative frequency in the origin of new paleospecies. Tests of the theory must therefore focus upon percentages of occurrence in exhaustive, or at least statistically definitive, surveys of particular taxa, faunas, and times.
Species cannot be conceptualized as indistinguishable beans in the conventional bag of our standard metaphor for problems in probability — for the nature of history grants uniqueness to times and taxa, and therefore precludes any simple tabulation by global enumerative induction. We may, however, assess relative frequencies for well-bounded situations restricted to taxa of a given fauna, species within a monophyletic clade, or representatives of a particular time or geological formation. Several such studies have been carried out, and effectively all have found the clear signal of a dominant relative frequency for stasis and punctuation, as predicted by the theory of punctuated equilibrium. I regard these data as our most convincing indication of the validity and importance of punctuated equilibrium as a primary generator of pattern in the history of life. I am also surprised that this clear signal has not been more widely appreciated as the most decisive result in a quarter century of research and debate about punctuated equilibrium.
For reasons previously discussed under the heading of “publication bias” or “Cordelia's dilemma” (see pp. 763–765), proper tests of relative frequencies cannot be made by a “catch as catch can” style of simple enumeration [Page 855] based on previously published studies done for other reasons. Until quite recently in paleontology, strong and pervasive biases equated evolution with gradual change, and regarded stasis as “no data,” and therefore not worth recording. Tabulations of older literature will inevitably favor gradualism both because no other style of evolution attracted study, and (even more problematically) because paleontologists, expecting only gradualism, tended to misread other patterns in this conventional light. Proper (and noncircular) testing — as in any statistical study — requires that the items chosen for sampling display no bias (imposed by human choice or preference) away from their relative frequencies in nature. When this ideal cannot be realized in natural experiments, which necessarily lack the rigor of laboratory controls, we should at least insist that unavoidable biases be directed against the hypothesis under test.
Thus, one cannot achieve a reliable relative frequency for punctuated equilibrium by tabulating cases from an existing literature, where strong biases in favor of gradualism may reasonably be suspected (or, to put the issue more accurately, virtually guaranteed). May I simply restate Tony Hallam's comment to me on why evolutionary studies of mollusks in English Liassic beds have concentrated with near exclusivity on Gryphaea (which, ironically, does not, after all, display the kind or direction of gradualism that initiated this literature in Trueman's famous (1922) paper — see Hallam, 1968; Gould, 1972; Jones and Gould, 1999): “Why hasn't anyone ever examined any of the 100 or so other molluscan species, many with equally good records, in the same strata?” Hallam then answered his own rhetorical question: “Because they seem to show stasis, and were therefore regarded as uninteresting “(see Johnson's (1985) affirmation of this stasis).
As an example of major differences between adequate and biased modes of sampling, two contrasting studies were presented at the North American Paleontological Convention, Boulder, Colorado, 1986. Barnovsky calculated the relative frequency of punctuated equilibrium vs. anagenetic transformation for Pleistocene mammals based exclusively on previously published reports in the literature. The two modes were supported at close to equal frequency.* Prothero then reported his field study for all mammalian lineages in Oligocene rocks of the Big Badlands of South Dakota. (See pages 861–865 for a full discussion of Prothero's refined and extended results — an even more impressive validation of punctuation equilibrium by well-established relative frequencies.) Nearly all lineages remained in stasis, and all new forms entered the record with geological abruptness. Prothero found very few cases of gradual anagenesis. Of course the differences might be real; perhaps the Pleistocene [Page 856] 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 significan
t 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 [Page 857] one lineage, the famous oyster Gryphaea, showed a corresponding gradual change in shape as well — a consequence of heterochronic linkage to phyletic variation in size (see affirmation of Jones and Gould, 1999). Hallam concluded, in persuasive support of punctuated equilibrium by the proper criterion of relative frequency, and with explicit attention to important and potentially confounding issues of geographic variation and missing data due to gaps in the geological record (1978, p. 17):
The results of my analysis of 329 European Jurassic species provide, with an important exception, overwhelming support for the punctuated equilibria model. Species whose morphology appears to persist unchanged for long periods are abruptly terminated usually with one or more species of the same genus succeeding the older species with marked morphological discontinuity. The species ranges are long compared with the ammonites that allow fine stratigraphic subdivision and can be used to eliminate the possibility of significant stratigraphic gaps in the rock succession. Geographic variation within Europe is negligible, and more cursory examination of data from other continents provides no encouragement for the view that gradualistic events linking the “punctuated equilibria” in time took place outside Europe.
I trust, however, that Tony Hallam, one of my best friends in science, will not think me fractious or ungrateful if I point out that he then devoted the empirical content of his paper to documenting phyletic size increase in several species and, especially, to tracing gradual evolutionary changes within Gryphaea — in other words to the 1 lineage among 329 that illustrated phyletic gradualism. He presented no morphometric data for the overwhelming majority of species that remained in stasis throughout their existence. He wrote (1978, p. 17): “The succeeding sections of this paper are devoted primarily to this aspect of phyletic gradualism [size increase] and its implications in the broader context of environmental control of speciation, starting with the detailed analysis of Gryphaea.”
The unconsciously imbibed power of gradualism thus remained so strong during these early years of the punctuated equilibrium debate, that Hallam could declare “overwhelming support for the punctuated equilibria model” as his primary conclusion and the focus of his study — and then follow conventional practice in applying morphometric methods only to rare examples of gradualism within his sample, even though the predominant signal of stasis could be validated just as rigorously by the same methods. For all the theoretical uncertainties that still animate the punctuated equilibrium debate, at least we have made substantial headway on this operational issue since the 1970's. Any similar study, done now, would almost surely include the documentation of stasis.
Kelley (1983, 1984) studied all molluscan lineages with adequate samples over sufficiently long ranges in one of the most famous and widely studied of all fossil faunas: the Miocene deposits of the Chesapeake Group in Maryland (Shattuck, 1904, for the classic statement; Schoonover, 1941, for [Page 858] the standard stratigraphic study). In an initial study of rank correlations between stratigraphic position and values of unit characters at a standard shell length estimated from bivariate regressions, she found no directional change for 82 percent of characters within species of 8 lineages. Of the 18 percent showing significant rank correlations with time, most directional changes either become reversed later in the same sequence, or run in a direction opposite to the net transformation between the measured species and its descendant. In other words, such changes, however genuine, should be read either as mild fluctuations within a pattern of stasis, or as intraspecific temporal variation unrelated to the trend of the larger lineage. For example, shells of the bivalve Lucina anodonta become gradually less inflated from the Calvert into the overlying Choptank Formation. But the same species then regains its ancestral degree of inflation in the succeeding St. Mary's Formation (p. 587). Kelley (1983, p. 596) concluded with both substantive and methodological comments: “Within these middle Miocene mollusc species, then, changes are more commonly oscillatory than unidirectional . . . Most variables follow a pattern of fluctuation within a narrow range of values through time ... In order to approach the goal of unbiased assessment of entire faunas, I examined all taxa of the mollusc faunas which were abundant enough for statistical analysis. Because no other bias controls the taxa chosen for study, these data provide strong evidence for punctuated equilibria.”
Kelley's subsequent study (1984) affirms these patterns from a multivariate perspective based on discriminant analysis of 10 characters through 14 to 20 stratigraphic levels. Figure 9-23 (from Kelley, 1984, p. 1247) shows the stratigraphic distribution of centroids for each lineage at each level, as projected upon the first discriminant axis. Stasis prevails within most species (shown as unbroken vertical plots), while the four lineages composed of two or more successional species through the sequence generally show a stairstep pattern across transitions, and stasis within the bounds of species. In a very few cases, notably the transition from the lower to the middle species of Anadara, a trend within an ancestral species does move gradually towards the descendant's mean value. But even in this case, the third and uppermost species of the lineage then reverses the trend and moves back towards the beginning value.
Kelley (1984) also used patterns of misclassification for individual specimens to illustrate the character of predominant stasis. In the three successive species of Astarte, for example, 96.7 percent of specimens fall nearest the centroid of their own species — thus indicating sharp and clear division between successive species. But vari
ation within species showed the opposite pattern. Only 42.1 percent of specimens fell nearest the centroid for their own stratigraphic level. Most remarkably, only 36.7 percent of misidentified specimens fall closest to centroids for samples of either the same or an immediately adjacent stratigraphic level. In other words, nearly % of misidentified specimens stood closer to the centroids of stratigraphically distant populations than to the centroids for samples adjacent to their own time. This pattern of nondirectional [Page 859] distribution throughout the full vertical range of species — compared with sharp divisions between species — illustrates the strength and character of stasis in these well-known fossil lineages.
Perhaps the most impressive and definitive study of pervasive stasis in molluscan faunas has been presented by Stanley and Yang (1987) for Neogene bivalves from the Western Atlantic region. They studied 24 variables (normalized for shell size) in 19 lineages, for a total of more than 43,000 measurements. Stanley and Yang followed a comprehensive sampling method, unbiased with respect to likelihood of punctuation and stasis, and including all species within four bivalve taxa (Lucinidae, Tellinacea, Veneridae and Arcticacea) with shells sufficiently large and geometrically tractable (flat to only weakly convex) for their measurement protocol, and with adequate numbers of well-preserved specimens (almost always more than 20 per sample, with a minimum of 16) over a sufficient range of time (at least 4 million years from early Pliocene to Recent).
The Structure of Evolutionary Theory Page 136