Kaneko, Kunihiko, and Takashi Ikegami. “Homeochaos: dynamics stability of a symbiotic network with population dynamics and evolving mutation rates.” Physica D: Nonlinear Phenomena 56, no. 4 (1992): 406-429.
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Evolution of mutation rates is studied, in a population model with mutation of species coded by bit sequences and mutation rates. Even without interaction among species, the mutation rate is initially enhanced to search for fitted species and then is lowered towards zero. This enhancement opens a possibility of automatic simulated annealing. With the interaction among species (hosts versus parasites), high mutation rates are sustained. The rates go up with the interaction strength abruptly if the fitness landscape is rugged. A large cluster of species, connected by mutation, is formed by a sustained high mutation rate. With the formation of this symbiotic network resolved is the paradox of mutation rates; paradox on the stability of a rule to change itself. Population dynamics of each species shows high-dimensional chaos with small positive Lyapunov exponents. Stability of our symbiotic network is dynamically sustained through this weak high-dimensional chaos, termed “homeochaos”.