A fitness peak represents a regime of behavior within a system that once, arrived upon, cannot be moved smoothly away from without reducing fitness.
Example: Imagine that an agent can vary its behavior according to three different Variables. Perhaps the agent is an adjustable bed, embedded with sensors, and 'fitness' for the bed pertains to how little movement it detects from a sleeper. This 'smart' bed can adjust its temperature, its firmness, and the volume of soothing music it emits (the extent of adjustment possible are the bed's Degrees of Freedom ). One can imagine the bed randomly varying these three parameters, and receiving Feedback with each variation that begins to direct if a parameter needs to be turned 'up' (say, higher temperature) or down (say, lower music volume). As the sleeper begins to lay increasingly still in bed, the bed will arrive at a state at wherein (all other things being equal), any change to any parameter will result in the motion of the sleeper increasing rather than decreasing. The bed has now arrived at a fitness peak.
What is interesting about this example is that we can imagine a landscape where an agent is on a local peak, while remaining unaware of higher peaks within the landscape or Phase Space. So perhaps someone sleeps well EITHER with low music and a warm, firm bed, OR with loud music and a cool, soft, bed. The peak with louder music and a cooler bed might result in the sounder sleep of the two, but if the bed randomly adjusts and initially arrives at the first regime of behavior, it may not be able to arrive at the second without passing through states that decrease fitness prior to improving fitness. It will, therefore, be difficult to move to the higher peak without 'jumping' from one part of the fitness terrain to another.
These jumps can be assisted by what is called a system Perturbation, which disrupts the landscape in such a way as to jolt an agent away from the peak it has been inhabiting and thereby explore a different part of the potential landscape. Without these perturbations, agents are limited to exploring smooth variations in behavior that move into the what Stuart Kauffman describes as the 'adjacent possible'.
The idea of a fitness peaks is part of the broader concept of Fitness within a Complex System.
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