924 THE STRUCTURE OF EVOLUTIONARY THEORY
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