4.1 Time-Scales Of Incremental Innovations

In the context of fitness landscapes incremental innovations can be interpreted as gradient-following approach to a (local) minimum. The individual agent in the complex system senses the local gradient in the fitness landscape i.e. the direction of the steepest descent. Under the assumption that the landscape itself changes only slowly compared to the movement in the landscape the approach to the minimum will be exponential which implies a constant rate of improvement of the fitness parameter. The improvement rate itself is determined by the curvature of the landscape close to the minimum. It is higher if the minimum is deep and narrow and slower if it is wide and shallow. In a complex landscape, however, chances are very large that the minimum that was reached exponentially fast was not the global minimum. In other words: the system is stuck in a local optimum. Without change in the landscape or external perturbations the system would remain there forever.