A model of s interacting species is considered with two types of dynamical
variables. The fast variables are the populations of the species and slow
variables the links of a directed graph that defines the catalytic interactions
among them. The graph evolves via mutations of the least fit species. Starting
from a sparse random graph, we find that an autocatalytic set (ACS) inevitably
appears and triggers a cascade of exponentially increasing connectivity until
it spans the whole graph. The connectivity subsequently saturates in a
statistical steady state. The time scales for the appearance of an ACS in the
graph and its growth have a power law dependence on s and the catalytic
probability. At the end of the growth period the network is highly non-random,
being localized on an exponentially small region of graph space for large s.Comment: 13 pages REVTEX (including figures), 4 Postscript figure
