Evolution produces complex and structured networks of interacting components
in chemical, biological, and social systems. We describe a simple mathematical
model for the evolution of an idealized chemical system to study how a network
of cooperative molecular species arises and evolves to become more complex and
structured. The network is modeled by a directed weighted graph whose positive
and negative links represent `catalytic' and `inhibitory' interactions among
the molecular species, and which evolves as the least populated species
(typically those that go extinct) are replaced by new ones. A small
autocatalytic set (ACS), appearing by chance, provides the seed for the
spontaneous growth of connectivity and cooperation in the graph. A highly
structured chemical organization arises inevitably as the ACS enlarges and
percolates through the network in a short, analytically determined time scale.
This self-organization does not require the presence of self-replicating
species. The network also exhibits catastrophes over long time scales triggered
by the chance elimination of `keystone' species, followed by recoveries.Comment: 8 pages, 4 figure
