Kauffman NK model

Kauffman NK model is model of evolution powered by  sorting from the standpoint of stability.   The basis of this model lies in abstract, randomly generated Boolean networks consisting of individual elements capable of transition between two states, on and off (true and untrue). The properties of these elements, i.e. the manner in which they respond to a combination of signals at their inputs, represent the individual functions of Boolean logics. For example, an element of the AND type is converted to the “on” state only if activation signal “turn on” is present at both its inputs, an element of the OR type is converted to the “on” state if the activation signal “turn on” is present on at least one of its inputs, and an element of the XOR type is converted to the “on” state if the “turn on” activation signal is present at just one of its two inputs. The individual networks differ in the number of their elements and the average number of bonds that connect these elements together, i.e. that transfer on-off signals from the outputs of one element to the inputs of another element. If an element is in the “on” state, the “on” signal is present at all its outputs; when it is in the “off” state, the signal “turn off” is present at all its outputs. At the beginning, one of the possible logical functions (e.g. NOT, OR, AND, XOR, etc.) and also a random state, i.e. on or off, is randomly assigned to each element. The system again gradually develops in discrete steps and, once again, complicated stable or unstable structures are formed in it. Kauffman showed that the system can “freeze”, i.e. stop developing, or pass to a state of chaos, or begin to develop in a direction towards increasing complexity of its structure. He showed that the third, most interesting alternative occurs at the edge of chaos, when there are a medium number of bonds between the individual elements, e.g. an average of two inputs and two outputs, and he simultaneously demonstrated that a great many biological systems occur in this state.

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The classical Darwinian theory of evolution can explain the evolution of adaptive traits only in asexual organisms. The frozen plasticity theory is much more general: It can also explain the origin and evolution of adaptive traits in both asexual and sexual organisms Read more