Self-reproducing systems: structure, niche relations and evolution

A formal definition of a self-reproducing system is proposed using Petri nets. A potential self-reproducing system is a set of places in the Petri net such that the number of tokens in each place increases due to some sequence of internal transitions (a transition is called internal to the marked subset of places if at least one of its starting places and one of its terminating places belongs to that subset). An actual self-reproducing system is a system that compensates the outflow of its components by reproduction. In a suitable environment every potential self-reproducing system becomes an actual one. Each Petri net can be considered as an ecosystem with the web of ecological niches bound together with trophic and other relations. The stationary dynamics of the ecosystem is characterized by the set of filled niches. The process of evolution is described in terms of niche composition change. Perspectives of the theory of self-reproducing systems in biology are discussed.