Tiers of Time and Trials of Extrapolationism 1323
Fractal iconoclasm scaled down
In evolutionary theory, the canonical observation of inverse relationship between
frequency of occurrence and intensity of effect has generally been used to deny the
force, or even the existence, of the largest pulses as too rare to matter, even in the
amplitude of geological time. (Fisher's citation, invoked to privilege small events by
their overwhelming frequency, opens the general argument in his Genetical Theory of
Natural Selection (see pp. 508-514), and remains the classical example in Darwinian
literature.) Interestingly, the application of this inverse relationship to assess the
range of catastrophic models had proceeded in precisely the opposite manner—from
accepting the magnitude of a proven single event (the K-T extinction) at maximal
scale, and then extrapolating down to ask whether much more common small events
of the same type could yield enough oomph and frequency to provide an alternative
account for our Darwinian preferences at the ecological scale of natural selection's
supposed and undoubted domination.
My dearest paleontological colleague David M. Raup has delighted me
throughout my career, and kept an entire profession on its collective toes, by acting as
Peck's Bad Boy to express outrageous and unthinkable ideas in the form of testable
hypotheses. I confess that I have never quite figured out whether Dave believes in, or
would place more than a minuscule probability upon, the hypotheses behind several
of his tests; or whether he just loves to play the role that the Church wished to assign
to Galileo—that is, to present the almost surely untrue as a hypothetical claim in
mathematical form, thereby to sharpen our empirical and logical skills in finding best
arguments for truthful propositions. Only once did I ever win an argument against
one of his null hypotheses, or "beans in a bag" models, for random worlds composed
of identical objects. Raup held for several years (before the Alvarez data convinced
him of the reality of a K-T event) that mass extinctions might be entirely artifactual,
representing only an occasional extreme in sampling from an actual set of equally
sized extinction pulses. "But Dave," I would say in frustration, "perhaps the Permo-
Triassic granddaddy of all extinctions can be rendered statistically as no more than an
extreme sample from a uniform pool. Still, you can't deny that, on Earth, the Triassic
organisms that actually reappear are so different from their Permian forebears.
Something 'real' must have happened then." I think that he finally acquiesced to this
point!
Raup developed his extreme model as a thought experiment because mass
extinction by bolide impact might, at least in principle, be regarded as random in both
of Eble's (1999) senses previously called, in this particular context, the "random" and
"different rules" models (see p. 1314)—that is, either truly so in the formal statistical
sense, or only so in the vernacular sense that reasons for differential success in such
catastrophically altered moments must be exaptive with respect to Darwinian bases
for evolving the relevant features in the first place, and in background times. Raup
therefore posed the following sly question: if this broad sense of randomness applies
to the largest event, and if the famous inverse curve of frequency vs. effect implies a
continuity in causality as well, then maybe we should extrapolate down and
reconceptualize