Optimization of skeletal structure in vertebrates.

Stresses due to bending moments generally predominate in long bones. They can be equalized along the length of the bone shaft if the bone tapers so as to make section modulus proportional to distance from the distal end. For marrow-filled bones, there is an optimum ratio of radius to wall thickness that minimizes mass for given strength, but different strength criteria give different optimum ratios. Increasing the strength of a bone reduces the probability of failure but increase the cost of growing the bone and the energy cost of moving it. A theory of optimum safety factors has been formulated but has not been used quantitatively because of the difficulty of expressing the cost of failure in the same currency as the other costs. A theory of optimum elastic stiffness successfully predicts the thicknesses of typical tendons. The possibility that the stiffness of bones is optimized, rather than their strength, is considered.