Testing the biomechanical optimality of the wall thickness of limb bones in the red fox (Vulpes vulpes)

The optimum for the ratio K of the internal to external diameter of a marrow-filled tubular bone with minimum mass designed to withstand a given type of strength (yield/fatigue, stiffness, fracture or impact) depends on Q=ρm/ρb only, where ρm and ρb are the densities of marrow and bone. With computer-assisted evaluation of radiographs of 62 femurs in the red fox (Vulpes vulpes) we measured the values of K. The mean and standard deviation of K are 0.68 and 0.036, and K changes in the rather wide range from 0.59 to 0.74. Accepting the assumption of earlier authors that Q=0.50 or 0.44, our data would support the hypothesis that the fox femurs are optimized to withstand yield, fatigue or stiffness strengths. However, since the Q-values are unknown, the possibility cannot be excluded that any studied fox bone with an appropriately selected Q-value is optimized for any strength type. Assuming Q=0.50 or 0.44, the relative mass increments μ of the investigated fox bones are smaller than 5% under all four mechanical conditions. The evolutionary relevance of such tiny μ-values is questionable.