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Backbone length (cm)

Figure 6.4 Tests of allometry in the ichthyosaur Ichthyosaurus. (a) Plot of orbit length against skull length, and (b) plot of skull length against backbone length. The Somerset embryo (Fig. 6.3b) is indicated by a solid circle. Both graphs show negative allometry (orbit diameter = 0.355 (skull length)0987; skull length = 1.162 (backbone length)0933), confirming that embryos and juveniles had relatively large heads and eyes. (Courtesy of Makoto Manabe.)

ratio of eye diameter to body length diminishes as the animal approaches adulthood. This is an example of allometric ("different measure") growth. If there is no change in proportions during growth, the feature is said to show isometric ("same measure") growth.

Allometric growth is commoner than isometric. Positive allometry is when the organ or feature of interest increases faster than the isometric expectation, and negative allometry is when growth of the structure of interest is slower than isometry. Head and eye size usually show negative allometry, starting relatively large in the juvenile, and becoming relatively smaller in the adult. An example of positive allometry is in the antlers of the Irish deer (Box 6.2), and indeed in many other sexually selected features that are minute or absent in the juvenile, but very large in the adult.

Allometry is commonly considered only in the context of ontogeny, the growth from egg or embryo through juvenile to adult. But studies of form may compare species, and shape variation can be accounted for in an evolutionary context too. For example, a comparison of species of antelope would show positive allometry in leg width: scaled against body length, the sturdiness or width of the leg increases positively allometrically. This is because of the well-known biological scaling principle: some organs and functions relate to the mass of an animal (a three-dimensional measure), whereas others relate to body length or body outline (one- and two-dimensional measures). As body mass (three-dimensional) increases, the diameter of the legs (two-dimensional) increases in proportion to support the added weight. So, in body outline, small antelope have extremely slender legs, and larger ones have relatively more massive legs.

These aspects of allometry may be understood in terms of the allometric equation, y = kxa where y is the measurement of interest (e.g. head length, eye diameter), x is the standard of comparison (e.g. body length), k is a constant and a is the allometric coefficient. The constant k is calculated using the allometric equation for each particular case. The allome-tric coefficient a defines the nature of the slope: if a = 1, the slope is at 45° and this defines a case of isometric growth; if a > 1, we have positive allometry, and if a < 1, we have negative allometry (see Fig. 6.4).

After the nature of any allometric change of parts or organs has been established quantitatively, it is possible to investigate why such changes might occur. The large eyes and small noses of babies are said to make them look cute so their parents will look after them, and feed them. But the fundamental reason is presumably because the eye is complex and is at nearly adult size in the baby for functional reasons, and the relatively large head of a human baby is to accommodate the large

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