Size and Shape in Biology

Arguments based on elastic stability and flexure, as opposed to the more conventional ones based on yield strength, require that living organisms adopt forms whereby lengths increase as the ⅔ power of diameter. The somatic dimensions of several species of animals and of a wide variety of trees fit this rule well. It is a simple matter to show that energy metabolism during maximal sustained work depends on body cross-sectional area, not total body surface area as proposed by Rubner ( 1 ) and many after him. This result and the result requiring animal proportions to change with size amount to a derivation of Kleiber's law, a statement only empirical until now, correlating the metabolically related variables with body weight raised to the ¾ power. In the present model, biological frequencies are predicted to go inversely as body weight to the ¼; power, and total body surface areas should correlate with body weight to the ⅝ power. All predictions of the proposed model are tested by comparison with existing data, and the fit is considered satisfactory. In The Fire of Life, Kleiber ( 5 ) wrote "When the concepts concerned with the relation of body size and metabolic rate are clarified, . . . then compartive physiology of metabolism will be of great help in solving one of the most intricate and interesting problems in biology, namely the regulation of the rate of cell metabolism." Although Hill ( 23 ) realized that "the essential point about a large animal is that its structure should be capable of bearing its own weight and this leaves less play for other factors," he was forced to use an oversimplified "geometric similarity" hypothesis in his important work on animal locomotion and muscular dynamics. It is my hope that the model proposed here promises useful answers in comparisons of living things on both the microscopic and the gross scale, as part of the growing science of form, which asks precisely how organisms are diverse and yet again how they are alike.