Autocatalytic Sets and the Growth of Complexity in an Evolutionary Model

Details Autocatalytic Sets and the Growth of Complexity in an Evolutionary Model Autocatalytic Sets and the Growth of Complexity in an Evolutionary Model

1998-09-17

arxiv.org/abs/adap-org/9809003v1

Physics

Condensed Matter

13 pages REVTEX (including figures), 4 Postscript figures

Scientific paper

10.1103/PhysRevLett.81.5684

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 $s$.

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