A theory of mixed chains applied to safety factors in biological systems

The skeleton of a leg is a chain of bones, breakage of any one of which makes the whole leg useless. The oxygen-transport system of mammals is a chain of processes, any one of which may limit the rate of use of oxygen. The simple argument that a chain is as strong as its weakest link suggests that chains both of structures and of processes would be best designed to have the strengths or capacities of all their links matched. However, this paper shows that if the performance of a link built to a given design is to some extent unpredictable, it may be better to design links for unequal performance. In chains of structures, links made from less expensive or more variable materials should be designed to be somewhat stronger than others. In chains of processes, the plant for less expensive or more predictable processes should be designed for higher maximum rates of working. These conclusions offer possible explanations for some observations regarding frequencies of fracture in horse leg bones and the diffusing capacities of mammalian lungs.