Highly optimized tolerance: A mechanism for power laws in designed systems

We introduce a mechanism for generating power law distributions, referred t o as highly optimized tolerance (HOT), which is motivated by biological org anisms and advanced engineering technologies. Our focus is on systems which are optimized, either through natural selection or engineering design, to provide robust performance despite uncertain environments. We suggest that power laws in these systems are due to tradeoffs between yield, cost of res ources, and tolerance to risks. These tradeoffs lead to highly optimized de signs that allow for occasional large events. We investigate the mechanism in the context of percolation and sand pile models in order to emphasize th e sharp contrasts between HOT and self-organized criticality (SOC), which h as been widely suggested as the origin for power laws in complex systems. L ike SOC, HOT produces power laws. However, compared to SOC, HOT states exis t for densities which are higher than the critical density, and the power l aws are not restricted to special values of the density. The characteristic features of HOT systems include: (1) high efficiency, performance, and rob ustness to designed-for uncertainties; (2) hypersensitivity to design flaws and unanticipated perturbations; (3) nongeneric, specialized, structured c onfigurations; and (4) power laws. The first three of these are in contrast to the traditional hallmarks of criticality, and are obtained by simply ad ding the element of design to percolation and sand pile models, which compl etely changes their characteristics. [S1063-651X(99)05908-5].