When engineers set out to design a new structure, they make it to withstand loads and forces far beyond those experienced on a daily basis. For example, aeroplanes not only have to withstand routine take off and landings but also severe turbulence and other extreme events. In the natural world, natural selection, governed by various functional demands and constraints, has driven the development of a wide range of body forms, all superbly adapted to their individual niches. Åke Norberg from Gothenburg University, Sweden, is intrigued by the forces that shaped locomotor organs, such as the wings of birds or the limbs of mammals. Curious to find out whether bird and mammal bones are designed with respect to the body weight they must bear or the loads experienced during extreme manoeuvres, Norberg and his student, Björn Wetterholm Aldrin, began looking at the proportions of small bird and mammal bones relative to larger creatures' bones (p. 2873).

Norberg explains that one way of identifying the selective pressures that moulded animal body shapes is to compare a particular anatomical trait in animals over a wide range of body sizes, plot that trait against body mass to find the rate of change (gradient) of that trait, and see how it matches the predictions of how that trait changes relative to body mass derived from alternative theories. With this in mind, Norberg built a mathematical model of a mammal's leg and a bird's wing to see if he could calculate the rate of change of bone stress in animals ranging from tiny to large to find out which forces drove their evolution. Based on his models, he explains that among animals that have the same general shape, bone stress will increase with a gradient of 0.33 when bones are loaded by the body weight, but when bones are loaded by maximal manoeuvring muscle forces, the gradient will be 0; that is, bone stress will be the same regardless of animal size. So he decided to use measurements taken from animals and insert them into his models to find out whether, or how, stress experienced by mammal and bird bones might change when loaded by the body weight, or by maximal muscle forces in animals of increasing size.

Thinking first about the bending and twisting forces exerted on mammals' legs ranging from small crouched rodents up to large animals with more upright locomotion postures, Norberg, using measurements taken from animals, found that the gradient for bone stress across a wide range of mammals is 0.11 under loads due to the animal's body weight, rather than 0.33 (expected if animals of different sizes all had essentially the same shape). And when he considered the stress in leg bones at high speed or during manoeuvres, the scaling gradient is 0.17, instead of the expected 0 if animals were the same shape over the entire range of sizes.

Norberg says these values are compromises (0.11 and 0.17 instead of 0.33 and 0), and explains that they are due to the differences in the mammals' postures and leg muscles. He adds that the frequency with which animals experience extreme loads may affect the evolution of bone shape.

Moving on to scaling feather and bone proportions in birds, Norberg used measurements taken from animals, put them into his bird model and found that the gradient is 0.23 when the wing is loaded by body weight and −0.04 when the wing is subject to maximal muscle forces as the bird manoeuvres. This is very close to the gradient of 0 that Norberg expected, and shows that the safety factor against bone breakage during extreme manoeuvres is the same for birds across all size ranges. So wing bone dimensions seem to be adapted to maximal muscle forces rather than to the body weight.

R. Å.
Wetterholm Aldrin
B. S.
Scaling for stress similarity and distorted-shape similarity in bending and torsion under maximal muscle forces concurs with geometric similarity among different-sized animals
J. Exp. Biol.