Allometry

Allometry is the study of how biological traits scale with body size. The term comes from Greek allos, meaning other, and metron, meaning measure, reflecting how different parts of an organism grow at different rates as size changes. Mathematically, a common description uses a power law: y = a x^b, where y is a trait, x is body size, a is a constant, and b is the allometric exponent. If b equals 1, the trait scales isometrically with size; if b is greater than 1, the trait grows faster than size (positive allometry); if b is less than 1, the trait grows more slowly (negative allometry).

Allometry can be studied from several angles: static allometry compares individuals of the same species at a given life stage; ontogenetic allometry examines growth trajectories within an individual over time; evolutionary allometry compares scaling patterns across species. Analysts typically use log-transformed data to estimate the exponent b through regression and may apply phylogenetic methods to account for shared ancestry when comparing related species.

Common examples include metabolic rate, which has historically been described by Kleiber’s law as scaling roughly with body mass to the 3/4 power. Brain size often shows negative allometry with body size, meaning larger animals have proportionally smaller brains. Allometry has broad applications in physiology, ecology, paleobiology, and evolutionary biology, aiding in the interpretation of energy needs, ecological roles, and functional constraints.

Limitations include variation among taxa, temperature effects, developmental stage, and measurement error. While a powerful organizing principle, allometric relationships are not universal and can vary with phylogeny, environment, and life history.