Evolution of Random Catalytic Networks

In this paper we investigate the evolution of populations of sequences on a random catalytic network. Sequences are mapped into structures, between which are catalytic interactions that determine their instantaneous fitness. The catalytic network is constructed as a random directed graph. We prove that at certain parameter values, the probability of some relevant subgraphs of this graph, for example cycles without outgoing edges, is maximized. Populations evolving under point mutations realise a comparatively small induced subgraph of the complete catalytic network. We present results which show that populations reliably discover and persist on directed cycles in the catalytic graph, though these may be lost because of stochastic effects, and study the effect of population size on this behavior. 1 Introduction Understanding evolutionary dynamics requires an understanding of the dynamics at a number of different levels--- the population dynamics which result from selection, the mechan..