926 THE STRUCTURE OF EVOLUTIONARY THEORY
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