24 January 2011

Solutions of relative growth

I have been reading Julian Huxley's 1932 classic* Problems of relative growth. It is all about the growth of different body parts relative to each other and the consequences of such growth. But what exactly are we talking about?

Generally speaking, an animal's body may be taken to be compartmentalized. Compartments may be the individual organs, such as the nose, the heart and the penis, or different parts of the body, such as the head, the torso and the appendages.

The growth of all the compartments during the ontogeny of an animal at the same rate is called isometric growth. Isometric growth does not change the shape of the animal; the adult has more or less the same shape as the baby or even the late-stage embryo.

The growth of the compartments at different rates relative to each other is called allometric growth. Allometric growth changes the shape of the animal; the adult is not only bigger than the baby but it also has different proportions.

Here is a crude drawing that contrasts isometric and allometric growths. The terms in parentheses, isogonic and heterogonic, were what Huxley used for isometric and allometric, respectively. Huxley's terminology has since fell into disuse.

The "animal" in the drawing consists of 4 compartments. If it undergoes isometric growth, all compartments grow at the same rate and the overall shape stays the same. If it undergoes allometric growth, on the other hand, compartments, and even different regions of some compartments, grow at different rates. For example, the orange and the yellow compartments grow faster in one direction than in the other. That process eventually changes their shapes. At the same time, the yellow compartment grows at an equal rate in every direction, while the blue compartment grows at a very slow rate. The net result of all these growth processes is that the overall shape of the adult animal is different than that of the baby.

How do we apply these ideas to the growth of snail shells? That will be the subject of a future post.

*Actually, the 1972 Dover edition.

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