Biology Reference
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stage. For example, the descendant adult could have the ancestral juvenile shape and size.
If growth is dissociated from morphogenesis and maturation, then the descendant adult
would have the ancestral adult shape at a different size. It might, for example, have the
ancestral adult shape at the ancestral juvenile size. Finally, if morphogenesis is dissociated
from growth and maturation, then the descendant adult would have the shape found in
the ancestral ontogeny at a different age and size.
The purpose of the clock model (
Figure 11.11
) was to reveal the modifications of
growth, morphogenesis and maturation because the same morphological outcome could
arise from different modifications of life-history. Thus, to understand the links between
ecology and heterochrony, we need to distinguish between the modifications of develop-
ment that produce the same morphological outcomes. Although the clock model is rarely
used now, understanding it is important because it supplied the context for the scheme
that replaced it. The face of the clock contains two arcs and one bar. One arc is a shape
axis, the other is a size axis and the bar is the age axis. The values of the ancestral shape
are plotted along the arc, with the values for the youngest age on the left. The ancestral
sizes are plotted on the size axis, lining up the ages at which the ancestor has that size,
and also lining up the shape at that size. The entire ontogeny of the ancestral shape is
represented on the clock, but the descendant is analyzed at one single stage. Not surpris-
ingly, the need to single out one stage for comparison prompted much discussion about
what that stage should be and whether it should be chosen according to chronological age,
developmental age, or even size. Whatever standard is used, the objective is to find the
matching ancestral size and shape at that point. When found, the hands of the clock are
arranged to point to it; if the matching shape occurs at an earlier stage in the ancestor, the
“shape hand” of the clock will point to the left. Similarly, if the matching size occurs at an
earlier stage in the ancestor, the “size hand” also points to the left. Differences between
ancestor and descendant in chronological age at the developmentally comparable stages
are indicated by the filled portion on the age bar.
The clock, and the terms defined by it, proved confusing and the scheme was
soon replaced by the one devised by Alberch and colleagues, whose intent was to clarify
the terminology of heterochrony. To that end,
Alberch et al. (1979)
redesigned Gould's
formalism, using a more conventional representation of a three-dimensional space: three
mutually orthogonal axes (
Figure 11.12
). They also replaced Gould's static comparative
framework by a dynamic one; the descendant ontogeny (not just one point along it) is
analyzed in conjunction with the ancestral ontogeny. Each ontogeny is represented as a
vector in the three-dimensional space defined by the ancestral values of size and shape.
The comparisons are made with respect to four parameters: (1)
α
, the age at the onset
of development; (2)
β
, the age at offset of development; (3) k
, the rate of development
σ
FIGURE 11.11
Gould's (1977)
clock model. The descendant's size,
shape and age at one developmental stage are compared to the ances-
tor's ontogeny of shape, size and age. The hands of the clock show the
change from ancestral to descendant values pointing from the descen-
dant's age-specific shape and size to the corresponding ancestral values
(no hand is shown if there is no change). The shape hand points to the
left, so the descendant adult has the morphology of a younger stage in
the ancestral ontogeny.
