The term allometry was coined by Julian Huxley and Georges Tessier in 1936 (Huxley & Tessier 1936), when it was applied to the phenomenon of relative growth. Huxley had been studying the extraordinarily large claw (or chela) of the male fiddler crab, Uca pugnax, and was interested in how the crab grew to produce such an exaggerated trait (Figure 1; Huxley 1924). He measured the body size and chela size of crabs at different developmental stages and plotted the relationship between the two on a chart. The result was a curvilinear relationship that, remarkably, was linearized when the data were re-plotted onto a log-log scale (Figure 1). Even more interesting was the fact that the slope of this line was steeper than 1. This meant that for any unit increase in body size through time there was a proportionally larger increase in chela size. Thus Huxley deduced that the reason the chela was exaggerated in the fiddler crab was because it was growing at a faster rate than the rest of the body.



Figure 1: The allometric relationship between chela (claw) size and body size in growing male fiddler crab (Uca pugnax) The red lines show the measurements made on the crab. When the data are displayed on a scatter plot, the relationship between chela and body size is curve-linear (A), which becomes linear when plotted on a log-log scale (B) and can therefore be described using a simple linear equation. The equation for the linear relationship indicates that its slope (which is the allometric coefficient α) is 1.57. Thus the relationship between chela and body size is hyperallometric. The blue line illustrates the allometric relationship if it were isometric and had a slope of 1. (Data from Miller 1973; illustration adapted from Cooper 1890)



Figure 2: The brain and heart grow at different rates relative to the body. Growth of the heart is more or less isometric to body size, with an allometric coefficient (α) of 0.98. In contrast growth of the brain is initially hypoallometric to body size, with an allometric coefficient (α) of 0.73, before growth stops once the body reaches a certain size, at about age 6. Consequently, head size becomes proportionally smaller as individuals grow to their final body size. Illustrations show body proportions at birth, 2, 5 and 20 years of age. (Adapted from Moore 1983; Data from Thompson 1917)

Huxley was not the first to examine scaling relationships between organ size and body size in growing animals. Several researchers had observed a similar phenomenon in other organs in other species, each researcher producing their own nomenclature to describe it (Gayon 2000). In an attempt to unify these studies into a cohesive concept and to avoid confusion, Huxley worked with Georges Tessier to propose an agreed terminology that described such scaling relationships. They recognized that many scaling relationships, when plotted on a log-log scale, were linear. Consequently these relationships could all be described using the simple linear equation:

log y = α log x + log b

where x is body size, y is organ size, log b is the intercept of the line on the y-axis and α is the slope of the line, also known as the allometric coefficient. When x and y are body and organ sizes at different developmental stages, the allometric coefficient captures the differential growth ratio between the organ and the body as a whole. When the organ has a higher growth rate than the body as whole, for example, the chela of male fiddler crab, α > 1, which is called positive allometry or hyperallometry. When the organ has a lower growth rate than the body as whole, α < 1, which is called negative allometry or hypoallometry. Organs that have negative allometry include the human head, which grows more slowly than the rest of the body after birth and so is proportionally smaller in adults than in children (Figure 2). When an organ grows at the same rate as the rest of the body, α = 1, a condition called isometry. Such an organ maintains a constant proportionate size (but not absolute size) throughout development.

