Mutation–selection dynamics and error threshold in an evolutionary model for Turing machines

We investigate the mutation–selection dynamics for an evolutionary computation model based on Turing machines. The use of Turing machines allows for very simple mechanisms of code growth and code activation/inactivation through point mutations. To any value of the point mutation probability corresponds a maximum amount of active code that can be maintained by selection and the Turing machines that reach it are said to be at the error threshold. Simulations with our model show that the Turing machines population evolve toward the error threshold. Mathematical descriptions of the model point out that this behaviour is due more to the mutation–selection dynamics than to the intrinsic nature of the Turing machines. This indicates that this result is much more general than the model considered here and could play a role also in biological evolution.