biology zoology blog frog Growing Older and Bigger isometrically or allometrically

Growing Older and Bigger: isometrically or allometrically?

Are we growing isometrically or allometrically?

Meeting old classmates at reunions can be enormously interesting, especially if one hasn’t seen one’s former classmates for decades. In my case it was 50 years that I hadn’t seen the “little boys” who as 10 and 11-year olds had been my buddies. Alex, who used to be one of the smallest had grown into a really big and strong man; Lindeman, who was a good swimmer even at age 10 seemed to have grown less upward than sideways and Thomas, who used to have such wonderfully shiny black hair, now was snow white; some of the others had no hair at all. A few had retained their childish features and proportions and even after 50 years were recognizable, but the majority had changed in size and proportions.

Obviously, human bodies change with age. Compared with adults and in relation to the lengths of their appendages, newborns have, relatively speaking, quite long arms and very short legs; they also have relatively big heads. As they get older the legs seem to grow faster and get proportionately longer than the arms, while the head grows the least. It shows us that different body parts grow at different speeds and that the proportions between structures of the body change with age: such kind of growth is called allometric. If there were no such changes, then as the baby grows, the external form of the baby would not change at all and plotting, for example, the growths or weights of various organs or perhaps the lengths of arms and legs against height increase of an individual would result in a straight line with a slope of 1. Such growth would be called isometric. In reality, however, the legs grow faster and the slope would be greater than 1 (called positive allometry). The head, on the other hand, grows less and its growth slope versus body height would be less than 1 (that is negative allometry). There have been suggestions that people in which fully grown adults exhibit features like shorter legs, relatively long arms and big heads retain juvenile features and that that contributes to a greater longevity, as for example in many East Asians, who in addition develop grey hair much later in life than Europeans or Indians.

Even in humans, however, not all growth is allometric. If we were to plot a person’s change of body mass against the mass of the liver, we would get a slope of close to 1 and would therefore have an example of isometry. Although the height of a person reaches its maximum usually at between 17 and 21 years of age, some parts of the body continue to grow, one could think of fingernails perhaps. Such continual growth, however, cannot be called isometric as the body itself has already stopped to grow. But the situation for some lower vertebrates and many invertebrates is different and there we find examples of isometry.

A garden snail that carries a shell: if you measure the shell’s height or horizontal width and plot that against the length of the snail’s foot as the snail grows and ages, you’d find a very nice isometric relationship with a straight line and a slope of 1. Locust hoppers growing into adults show the same. Newts and salamanders are another famous examples of isometric growth and from plants comes the example of an oak tree’s height and trunk diameter. I haven’t measured that, but it is supposed to nicely show isometric growth. Obviously, if all parts of a body remain equally important as the organism grows, allometry is not required. But if allometry were indeed a token of a structure’s importance, which organs of the human body would then qualify as important? The legs, sure, but what else? Think about it.

© Dr V.B. Meyer-Rochow and, 2018.
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