Introduction - An Invariant Approach to Statistical Analysis of Shapes - page 4

Sneath's (1967) application of least-squares superimposition by over
60 years.
Julian Huxley also figures prominently in the study of biological
shape change because of his generalization of allometry to the study of
brain-body relationships (Gould, 1977). Many phenomena of metabo-
lism, biochemistry, morphogenesis, and evolution are governed by the
allometric equation in which one characteristic (e.g., length or weight
of an organ) can be expressed as a power function of another charac-
teristic (e.g., the length or weight of another organ or of the organism
as a whole). Allometric studies usually consist of collapsing measures
taken from biological organisms onto two-dimensional, bivariate plots.
Most often allometric analysis involves a regression of some biological
measure onto another biological variable, the latter being a represen-
tative of body size. The projection of measures from individual organ-
isms onto these plots can provide information about the relationship of
one organism to another, the relationship of one body part to another
part or to the whole, or the change in such relationships over phylo-
genetic and ontogenetic time.
When used in the study of morphology or morphogenesis, allometry
is the study of the relationship between parts, or the proportional rela-
tionship of parts to the whole, during either ontogenetic or evolution-
ary time. In its most general usage, these relationships are often
referred to as the relationship between size and shape. Since size and
shape are the vocabulary of allometry, allometric studies are closely
allied with morphometrics. In allometry, measures are chosen to act as
surrogates for body size, and the relationships among these and other
variables are interpreted as indicators of shape differences among the
organisms. The allometry literature is immense and it is clear that
important relationships have been delineated using this approach.
Allometry is really a study of proportions, however, and does not carry
with it information on the two- or three-dimensional geometry of the
organism.
Fred Bookstein's 1978 contribution, The Measurement of Biological
Shape and Shape Change brought geometry back to the modern study
of biological form. Though Bookstein's earliest work (1978) deals sole-
ly with two-dimensional data, his intention is to “redefine and recon-
struct morphometrics — the measurement of shapes, their variation
and change — as a branch of applied modern geometry (ibid: 3).” This
definition of morphometrics does not include the term biology, but
Bookstein's emphasis is clearly on biological applications. By the early
1980's, morphometrics was redefined as “the empirical fusion of geom-