The Fruitful Facets of Galton's Polyhedron 347
be effective because regression toward the mean precludes accumulation in
favored directions. Galton introduces the term "transilience" (literally "going
between," and recently revived by Templeton, 1982, for a different mechanism in
the same spirit) to describe his favored concept of non-Darwinian saltatory
variation, or facet flipping:
No variation can establish itself unless it be of the character of a sport, that
is, by a leap from one position of organic stability to another, or as we may
phrase it, through "transilient" variation. If there be no such leap the
variation is, so to speak, a mere blend or divergence from the parent form,
towards which the offspring in the next generation will tend to regress; it
may therefore be called a "divergent" variation.... I am unable to conceive
the possibility of evolutionary progress except by transiliences, for, if they
were merely divergences, each subsequent generation would tend to regress
backwards towards the typical center (p. 368).- Internal factors establish a hierarchy of stabilities, discontinuous in origin,
and explaining differing degrees of divergence among typical forms.
The nonhomogeneity of morphospace seems so "obviously" intrinsic to nature
(lions close to tigers, with a big jump separating all cats from dogs and wolves)
that we rarely consider the puzzles thereby raised. Once evolution itself becomes
paradigmatic, simple inheritance and descent become the obvious, first-level
reason for ordering the resemblances portrayed in our taxonomic hierarchies. But
simple descent does not solve all problems of "clumping" in phenotypic space; we
still want to know why certain forms "attract" such big clumps of diversity, and
why such large empty spaces exist in conceivable, and not obviously
malfunctional, regions of potential morphospace. The functionalist and
adaptationist perspective (see Dobzhansky, 1958, quoted herein on p. 527, for a
particularly striking metaphor of this view) ties this clumping to available
environments, and to shaping by natural selection. Structuralists and formalists
wonder if some clumping might not record broader principles, at least partly
separate from a simple history of descent with adaptation—principles of genetics,
of development, or of physical laws transcending biological organization.
Galton proposed his polyhedron to explain a hierarchy of stabilities as in-
ternally generated, not externally shaped by gradual natural selection. As the long
quotation (p. 345) and figure indicate, Galton purposely shaped his model to
encompass both small islands of stability within species ("subtypes" in his terms,
and easily subject to reversion by tipping back to the primary type—as in facet BC
of Fig. 5-1, which easily falls back to AB, but can move onward to a new type only
by a much bigger push), and also to cover the origin of new taxa that cannot revert
(the push from facet CD to any position across the long axis and its major facet
AB). Of course, Galton's polyhedron does include a role for external forces like
natural selection: something must push, or the polyhedron can't move at all. But
selection, in this model, provides only an impetus: both discontinuity and
directionality of change follow