Gould, Trends as Changes in Variance: A New Slant on Progress and Directionality in Evolution

322 JOURNAL OF PALEONTOLOGY, V. 62, NO. 3.1988

small-brained species present at all times. The evolution of enlarged brains, though generally a route to success and survival of new species, was not universal even among progressive orders.

In his latest work, Jerison adds that periods of expansion are confined to relatively short segments in the histories of most clades (1985, p. 124):

When there have been advances in grade in a broad spectrum of species ... the advance occurred over at least several million years, but when an appropriate grade was achieved there was no further advance. The prosimians appeared to have reached their present grade of encephalization by the end of the Oligocene. Steady states such as the Neogene stasis in prosimian encephalization are the rule. The picture is, therefore, more consistent with a punctuational than with a gradualist model.

In one of the most important dicoveries of modern paleoecology, several colleagues have demonstrated a strong and repeated tendency in the origin and spread of marine invertebrate clades: taxa tend to appear first in shallow waters and spread differentially to greater depths as new clades originate near shore (Sepkoski and Sheehan, 1983; Sepkoski and Miller, 1985; Jablonski and Bottjer, 1983). Many commentators have subtly misinterpreted this pattern as a directional trend mediated by the conventional Darwinian forces of competition and wedging-as advanced forms "push" a discrete and coherent entity into deeper waters. In most cases, the pattern should be read as a consequence of increasing variance, not as the shoving of an entity anywhere. If groups originate nearshore, and cannot invade the land by constraints of physiology, then where else can their mean and median position move as their taxic representation increases? Only one potential direction exists for expansion-farther offshore. Sepkoski and Sheehan (1983, p. 705-707) report that their best example of this onshore-to-offshore pattern occurred during a major episode of increase in the number of taxa: "The Ordovician radiations effected one of the largest and most rapid increases in taxonomic diversity that occurred during the Phanerozoic. In the first 50 m.y. of the Ordovician, the number of animal families in the oceans tripled".

We have often focused on the wrong phenomenon in judging the importance of this discovery. As Sepkoski and Shechan recognize, the "trend" offshore is a simple, almost trivial, result of expansion in taxa given the asymmetrical distribution of possibilities around a starting point in shallow waters. The profound issue is our need to understand why starting points tend to be nearshore; the later "trend" is a much less interesting consequence.

Cope's rule forms the locus classicus for this theme of increased variance misinterpreted as anagenetic trend. We all know the panoply of traditional explanations framed in terms of selective advantage for larger-bodied individuals--competitive success, greater efficiency in metabolism, larger foraging range, among many others. Although Stanley's seminal paper (1973) properly reinterpreted this phenomenon as an expansion away from small-bodied starting points mediated by increasing numbers of taxa within clades, purely anagenetic, explanations continue to prosper. In a paper titled "Body size, ecological dominance and Cope's rule," Brown and Maurer (1986, p.250)write, for example:

Presumably the ecological advantage of monopolizing resources provides the selective pressure that promotes evolution of greater size. Individuals of large size are favored by intraspecific natural selection, because they can dominate resource use and consequently leave more offspring than their smaller relatives.

Brown and Maurer do acknowledge a species-level effect of greater probability for extinction in small populations of specialized large-bodied creatures; but they view this differential only as a device to clear some space so that yet another lineage can begin its anagenetic march towards the personally advantageous realm of bulk.

I do not deny that size increase (or, rather, change of size in general) has often been documented as the most common of truly anagenetic trends within unbranched lineages (Bown and Rose, 1987; Malmgren and Kennett, 1981). But most clade-level trends to increasing body size are products of species sorting (Vrba and Gould, 1986), not a lockstep march to greater bulk by most species in parallel. Cope's real insight lay in his other, often neglected "law of the unspecialized" (see Stanley, 1973, p. 10-11)--the principle that morphologically "simple" creatures (generalized in form and ecology, not just plesiomorphic per se) act as starting points to most clades, and that such generalists tend to be small in body size. If originators usually lie near the lower end of a potential range in size, then Cope's more famous "law" of size increase follows as an automatic consequence once we view such trends at the proper level of species sorting. Where else can large numbers of successful species be added? Cope's rule arises from an asymmetry of possibilities about a starting point. The position of the starting point itself is the phenomenon demanding explanation; all else follows automatically from an increase in variance.

We owe this elegant reversal of perspective to Stanley (1973), and should really speak of "Stanley's rule" of increase by species sorting from small size. Stanley also provided a means for distinguishing true anagenesis from expansion of variance around asymmetrical starting points. He recommends that we establish the histograms of size within clades through time, rather than the geological excursion of central tendencies or extreme values. If we find a coupling between increased variance and increasing right skew, then the revised explanation holds.

Jablonski (1987) has studied all Late Cretaceous bivalve and gastropod genera with durations greater than 4 million years in the Gulf and Atlantic Coastal Plain. He recorded temporal change in range of variation, rather than excursions of central tendency. Of 58 bivalve genera, for example, 33 did follow Cope's rule in the "broad" (I would say inappropriate) sense that the largest late genus exceeds the largest early genus m size. But this extraction of extremes from complete systems is misleading. Only 11 of these genera showed a corresponding increase for the smallest species through time--the lockstep shift of the entire range that anagenetic interpretations require. For the other 22 genera with increase at the right extreme, size of the smallest species either remained stable or decreased. Jablonski concludes that "Cope's rule is driven by an increase in variance rather than a simple directional trend m body sizes."

Using data kindly supplied to me by Richard Norris, I present a fuller example from a history long interpreted as a canonical example of Cope's rule--trends in size for planktonic foraminifera. This case possesses the particular virtue of repetition, for latest Cretaceous and Paleogene extinctions provide three cycles of evolution from a limited number of ancestral forms.

Raw data for maximum test diameter (mm) of first appearances for 377 species against time (133 Cretaceous, 103 Paleogene, 141 Neogene) are shown in Figure 3. The basis for invoking Cope's rule is clear enough; each of the three phases shows a steady increase through time for its largest member (the Paleogene curve peaks before the end and then declines, but Creta-

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