Computer symbiosis-emergence of symbiotic behavior through evolution

Symbiosis is cooperation between distinct species. It is one of the most effective evolutionary processes, but its dynamics are not well understood as yet. A simple model of symbiosis is introduced, in which we consider interactions between hosts and parasites and also mutations of hosts and parasites. The interactions and mutations form a dynamical system on the populations of hosts and parasites. It is found that a symbiotic state emerges for a suitable range of mutation rates. The symbiotic state is not static, but dynamically oscillates. Harmful parasites violating symbiosis appear periodically, but are rapidly extinguished by hosts and other parasites, and the symbiotic state is recovered. The relation between these phenomena and "TIT for TAT" strategy to maintain symbiosis is discussed.