The Structure of Evolutionary Theory

by Stephen Jay Gould

  Empirical science has also contributed to this developing general move­ment by providing models and factual confirmations at several levels of anal­ysis and for several kinds of systems, with catastrophic mass extinction [Page 923] theory first seriously proposed in 1980 and then strongly promoted by in­creasingly firm evidence for bolide triggering of the late Cretaceous event, as an obvious input from paleontology. I take pride in the role that punctuated equilibrium has played as a spur for this larger intellectual transformation — for our 1972 proposal, formulated at one level of biological change, provided some general guidelines, definitions and terminology, and also provoked a good deal of interest in the application of this general style of change to other fields of study and other levels of causality. This extension has proceeded so far that some scientists and scholars from other disciplines (see Gersick, 1991; Mokyr, 1990; Den Tex, 1990; Rubinstein, 1995, for example) now use punctuated equilibrium as the general term for this style of change (while we would prefer that punctuated equilibrium retain its more specific meaning for the level of speciation, with punctuational change or punctuationalism used for the generality).

  Some recent mathematical work has explicitly tried to model punctuational change at the level and phenomenology of our original theory. Rand and Wil­son (1993, p. 137), for example, following Rand et al.'s (1993) “general mathematical” model for “Darwinian evolution in ecosystems,” applied their basic apparatus to the problem of speciation in individual taxa within ecosys­tems, primarily to test whether or not the pattern of punctuational equilib­rium would emerge. “We do not mean,” they write (1993, p. 137), “a large multispecies extinction event but rather the sudden disappearance of an evo­lutionary stable state causing a species to undergo very rapid evolution to a different state.”

  Under basic trade-off “rules” of bioenergetics and ecological interaction, which they call “constraints” (correlations, for example, between a prey's in­crease in population size and the exposure of individuals to a predator's attention), punctuated equilibrium emerges as a general pattern. Gradual change may prevail in systems without such constraints, but as the authors state, and to say the very least about nature's evident complexity!!), “the ab­sence of such constraints is biologically unrealistic” (1993, p. 138). More­over, they argue, reasonable features of the model's internal operation, and recognized properties of natural ecosystems, suggest a general status for punctuational change at all levels: “In this note,” Rand and Wilson write (1993, p. 137), “we wish to address the important issue of gradualism against punctualism in evolutionary theory. We discuss this in terms of a simple illus­trative example, but emphasize that . . . our results apply quite generally and are ubiquitous and wide ranging.”

  Explicit modelling of other levels has also yielded punctuational change as an expectation and generality under realistic assumptions. Elsewhere, I dis­cuss models for punctuational anagenesis within populations in ecological time (see p. 877), erroneously interpreted by some critics as a demonstra­tion that punctuated equilibrium emerges from ordinary microevolutionary dynamics and therefore embodies nothing original — although such studies should be interpreted as illustrating the potential generality of punctuational change by rendering the same pattern as an anticipated result of different [Page 924] processes (transformation of a deme rather than origin of a new species by branching) at a lower hierarchical level (intra rather than interspecific change).

  Punctuational change has been modelled more frequently at the most evi­dent level above punctuated equilibrium — coordinated and rapid change in several species (or the analogs of separate taxa in modelled systems) within communities or faunas. Per Bale's “sandpile” model of self-organized criticality (see Bak and Sneppen, 1993; Sneppen et al., 1994; and commentary of Maddux, 1994) have generated both particular interest and legitimate criti­cism. Maddux (1994, p. 197), noting the “minor avalanche of articles on the theme,” began his commentary by writing: “That physicists are itching to take over biology is now well attested . . . But surely only a brave physicist would take on Darwin on his home ground, the theory of evolution, let alone Gould and Eldredge on punctuated equilibrium.”

  Bak's models operate by analogy to metastable sandpiles, where grains may accumulate for long periods without forcing major readjustment (the analog of community stability), whereas, at a critical point, just one or a few added grains will trigger an avalanche, forcing the entire pile to a new and more sta­ble configuration (the analog of mass extinction and establishment of new faunas, not to mention the straw that broke the camel's back). In his basic model, Bak assigns random fitnesses, chooses the “species” with the smallest fitness, and then reassigns another random number both to this item and to the two neighboring species of its line (to stimulate interactions among taxa in communities). He also randomly selects a certain number of other points for similar reassignment (to acknowledge that interconnections among taxa need not link only the most obviously related or adjacent forms).

  This procedure often generates waves of rapidly cascading readjustments, propagated when some species receive small numbers in the reassignment of fitnesses, and then must change, taking their neighbors and also some distant forms with them, by the rules of this particular game — a play that admittedly cannot mimic nature closely (if only because the model includes no analogs of extinction or branching), but that may give us insight into expected rates and patterns of change within simple systems of partly, and largely stochastically, linked entities. In any case, Bak and his colleagues have formalized the gen­eral notion that small inputs (random reassignment of fitness to just one en­tity of lowest value) to simple systems of limited connectivity among parts (changes induced in a few other entities by this initial input) can lead to punctuational reformation of the entire system.

  In a similar spirit, the substantial research program known as Artificial Life (AL to aficionados) takes an empirical, if only virtual, approach to such ques­tions by generating and tracking evolving systems operating under simple rules in cyberspace. I regard such work as of great potential value, but often philosophically confused because researchers have not always been clear about which of two fundamentally different intentions they espouse: (1) to build systems that mimic life with enough fidelity to state something useful [Page 925] about actual evolution on earth; or (2) to construct alternative virtual worlds so explicitly unlike actual life in their minimality that we can ferret out some abstract properties, applicable to any genealogical system, by using models that permit perfect tracking of results and also operate with sufficient simplic­ity to identify the role of any single component.

  Ray (1992, a pioneer in these studies of “evolution in a bottle” or “syn­thetic life in a computer” (1992, p. 372), started his “Tierra” system by de­signing a block of RAM memory as “a 'soup' which can be inoculated with creatures” (1992, p. 374), and then beginning with a “prototype creature [that] consists of 80 machine instructions,” with “the 'genome' of the crea­tures consisting of the sequence of machine instructions that make up the creature's self-replicating algorithm.”

  “When the simulator is run over long periods of time, hundreds of millions or billions of instructions, various patterns emerge” (1992, p. 387). Obvi­ously, the results depend crucially on the human mental protoplasm that sets the particular rules and idiosyncrasies of the virtual system. Ray found, for example (and unsurprisingly), that “under selection for small sizes, there is a proliferation of small parasites and a rather interesting ecology.” Similarly, “selection for large creatures has usually led to continuous incrementally in­creasing sizes . . . This evolutionary pattern might be described as phyletic gradualism” (p. 387).

  But under the much more “reality mimicking” condition of no consistent directional selection for size, Ray found “a pattern which could be described as periods of stasis punctuated by periods of rapid evolutionary change, which appears to parallel the pattern of punctuated equilib
rium described by Eldredge and Gould” (p. 387). Ray then describes his frequently replicated and longest running results in more detail (pp. 387-390):

  Initially these communities are dominated by creatures with genome sizes in the 80's. This represents a period of relative stasis, which has lasted from 178 million to 1.44 billion instructions . . . The system then very abruptly (in a span of 1 or 2 million instructions) evolves into com­munities dominated by sizes ranging from about 400 to about 800. These communities have not yet been seen to evolve into communities dominated by either smaller or substantially larger size ranges. The com­munities of creatures in the 400 to 800-size range also show a long-term pattern of punctuated equilibrium. These communities regularly come to be dominated by one or two size classes, and remain in that condition for long periods of time. However, they inevitably break out of that stasis and enter a period where no size class dominates . . . Eventually the sys­tem will settle down to another period of stasis dominated by one or a few size classes which breed true.

  All models previously discussed have generated punctuational patterns at explicit and particular levels of evolutionary change (anagenetically within demes, for the origin of species by branching, and in coordinated behavior of [Page 926] groups of species within entire faunas and ecosystems). This range of success suggests that the apparent ubiquity of punctuational patterns at substantial, if not dominant, relative frequencies may be telling us something about gen­eral properties of change itself, and about the nature of systems built of in­teracting components that propagate themselves through history. Some pre­liminary work has attempted to formalize these regularities, or even just to identify them through a glass darkly (see, for example, Chau, 1994, on Bak's models).

  Bak has tried to specify two “signatures of punctuated equilibrium” in very general properties of systems: “a power-law distribution of event sizes where there is no characteristic size for events, but the number of events of a certain size is inversely proportional to some power of that size”; and a property that Bak calls 1/f noise, “where events are distributed over all time-scales, but the power or size of events is inversely proportional to some power of their fre­quency” (Shalizi, 1998, p. 9). Since we can document such inverse relation­ships between magnitude and frequency in many natural systems — indeed, R. A. Fisher (1930) began his classic defense of Darwinism with a denial of efficacy for macromutations based on their extreme rarity under such a regu­larity — punctuational change may emerge as predictably general across all scales if Bak's conditions hold.

  The intellectual movement dedicated to the study of complex dynamical systems and their putative tendencies to generate spontaneous order from ini­tial randomness — a prominent fad of the 1990's, centered at the Santa Fe In­stitute and replete, as all fashions must be, with cascades of nonsense, but also imbued with vital, perhaps revolutionary, insights — has identified punc­tuated equilibrium as a central subject of inquiry. A defining workshop, held in Santa Fe in 1990, specified three primary illustrations or consequences of this discipline's central principle, “the tendency of complex dynamical sys­tems to fall into an ordered state without any selection pressure whatsoever”: the origin of life, the “self-regulation of the genome to produce well defined cell types”; and “the postulated sudden waves of evolutionary change known as 'punctuated equilibrium.'”

  Stuart Kauffman, the leading biological theorist and mathematical modeler of this movement (see Chapter 11, pp. 1208–1214 for a discussion of his work on structuralist approaches to adaptive systems), stressed the generality of punctuational change by beginning with simple models of coevolution and then obtaining punctuational change at all levels as a consequence. Science magazine's report of this 1990 meeting linked Kauffman's multilevel work to the ubiquitous emergence of punctuated equilibrium from models of highly disparate systems and processes — all suggesting a generality and an intrinsic character transcending any particular scale or phenomenology: “This pattern of change and stasis itself evolves,” says Kauffman. “In the subtly shifting network of competition and cooperation, predator and prey, a fast-evolving species might suddenly freeze and cease to evolve for a time, while a formerly stable species might suddenly be forced to transform itself into something [Page 927] new. The fossil record of the latter process would then resemble 'punctuated equilibrium': a pattern of stasis interrupted by sudden change, which some paleontologists now believe to be the norm in real evolution . . . This same pattern of stasis punctuated by sudden change also showed up in a number of other ecosystem models presented at the workshop, even when those models seemed superficially quite different. Does this mean some more general mech­anism is at work, some theory that could account for the behavior of these models — and perhaps real life — no matter how they are structured?”

  A false and counterproductive argument has enveloped this work during the past few years. Bak, in particular, has noted that punctuations at the high­est level, corresponding to simultaneous extinction of a high percentage of components in a system, can be generated from internal dynamics alone, and require no environmental trigger of corresponding (or even of any) magni­tude. He and others then draw the overextended inference that because such large-scale punctuations can arise endogenously, the actual mass extinctions of the fossil record therefore need no exogenous trigger of environmental ca­tastrophe, or any other external prod. This claim, emanating from a theoreti­cal physicist with little knowledge of the empirical archives of geology and paleontology, and emerging just as persuasive evidence seems to have sealed the case for bolide impact as a trigger of at least one actual mass extinction (the end Cretaceous event 65 million years ago), could hardly fail to raise the hackles of observationally minded scientists who, for reasons both under­standable and lamentable, already bear considerable animus towards any pure theoretician's claim that success in modelling logically entails reification in nature.

  The obvious solution — if human emotions matched human logic in clarity, or the empirical world in complexity — would welcome the mathematical vali­dation of potential endogenous triggers (often of small initial extent) for punctuational change as a partner with well-documented exogenous triggers (of great extent in one well documented case, but perhaps also of potentially small magnitude as well). Instead of waging a false battle for preference or ex­clusivity of one alternative between two plausible arguments, we should rec­ognize instead the complementary and general theme behind both propos­als — their common role as sources for punctuational change (which then achieves higher status as a truly general pattern in nature), and in their mu­tual reinforcement for revising and expanding the Darwinian paradigm on all three supporting legs of its essential tripod. For the punctuational style of change — disfavored by Darwin, who recognized the necessary status of grad­ualism within the logic of his world view — now emerges as a primary conse­quence of repairs and reinforcements upon all legs of the tripod: the expan­sion beyond small uniformitarian inputs for the external triggers and causes of leg three (thus granting environment an even greater role than Darwin himself, who so brilliantly introduced the concept to defeat previous intern­alist theories of change, had envisioned); and the recognition that constraints of systems (leg two) — not only overt natural selection — acting at all levels of [Page 928] a causal and genealogical hierarchy (leg one) can also generate punctuations from within.

  Punctuational change at other levels and scales of evolution

  A PRELIMINARY NOTE ON HOMOLOGY AND ANALOGY IN THE CONCEP­TUAL REALM. The simple documentation of punctuational patterns at scales other than the speciational status of punctuated equilibrium (and, therefore, presumably attributable to different causes as well) gives us little insight into the key question of whether or not punctuated equilibrium, in ei­ther its observed phenomenology or its proposed mechanics, can lay claim to meaningful generality in evolutionary studies. Rather, the overt similarity in pattern must be promoted to importance through an additional
claim, akin in the world of ideas to the weight that an assertion of homology would carry in assessing the value of taxonomic characters. What, then, would make an example of punctuational change from another scale (where the immedi­ate speciational cause of punctuated equilibrium could not apply) effectively “homologous” to punctuated equilibrium — that is, sufficiently similar by rea­son of phenomenological “kinship” that the similar pattern across disparate scales may be read as revealing the shared components of a common expla­nation?

  We rank some similarities across scales as capricious enough to be deemed accidental, and therefore devoid of causal meaning. The appearance of a “face” on a large mesa on the surface of Mars — an actual case by the way, of­ten invoked by fringe enthusiasts of extraterrestrial intelligence — bears no such conceptual homology to faces of animals on earth. We label the similar­ity in pattern as accidentally analogous — even though the perceived likeness can teach us something about innate preferences in our neural wiring for reading all simple patterns in this configuration (a line below two adjacent circles) as faces. (An actual face and the accidental set of holes on the mesa top may stimulate the same pathway in our brain, but the two patterns can­not be deemed causally similar in their own generation — that is, as faces.)

  Identity of specific cause will rarely be available to provide a basis for asserting meaningful homology, rather than misleading analogy, between com­mon patterns at disparate scales. Punctuated equilibrium, for example, gains power and testability in proposing a particular scale-bound reason for an observed phenomenon — the expression of ordinary speciation in geological time, in this case. Since most theories win strength by such specificity, concep­tual homologies across scales must seek other definitions and rationales. A punctuational pattern below the scale of punctuated equilibrium (change within a single deme for example), or above (temporal clumping in the origin or extinction of many species within a fauna), could not, in principle, be ex­plained by the specific causes of punctuated equilibrium itself.