that the average Lilliputian was about the same size as Gulliver’s index finger, Kleiber calculated that Gulliver was 26 times higher than a Lilliputian and so weighed 263, or 17,600 times more than him or her; 1,724 is 17,600 to the power of 0.76.
The relationship between metabolic rate and body weight is an example of a biological pattern called allometry, which compares how the value of any biological trait, such as metabolic rate or leg length, changes with the total size of a plant or animal. It shows whether, as things get bigger, they become proportionately bigger or smaller—in other words, if their shape changes. For example, baby humans have big heads relative to their bodies. But as they grow up, their heads grow more slowly than their bodies, bringing about adult proportions. Other features get proportionately bigger as an animal’s size increases. Deer antlers show this trend: The biggest British species, the red deer, is about 4 feet tall at the shoulder, and its antlers span about 3 feet. The largest deer that ever lived, the extinct Irish Elk, was less than twice as tall, standing at about 7 feet. But its antlers were 12 feet across. In other words, big deer have really big antlers. But although the Irish Elk’s antlers might seem freakish, the allometric comparison across all deer species shows that they are as big as we should expect for a deer of that size. The power of allometry is that it allows us, literally, to put things in proportion. The examples of babies and deer show that allometric comparisons can be made within species, between species, at different times during an individual’s growth, or across a population of animals of the same age. Allometry can be applied to fossils, to study a species’ changes in shape through time. It can also show when something is anomalously small or large. Perhaps no other theory in biology can match its sheer usefulness: The data for allometry studies are usually easy to collect and interpret; the analysis is transparent—biologists are not generally good at mathematics, but anyone can understand the allometric equation—and its results can be presented in a visual fashion. Allometry is one of the most powerful techniques for revealing patterns in biology.