THE EVOLUTION OF DIVERSITY IN REPLICATOR NETWORKS

Novel species are introduced into a network of interacting replicators either (i) as mutants of members of the network or (ii) as unrelated immigrants. We consider the meta-population dynamics of such a system. In the first case the appearance of mutants leads to a slow growth of the replicator network, proportional to the logarithm of the number o f mutation events. Surprisingly, replicator evolved by mutant incorpor ation are always permanent, despite the fact that permanence is in gen eral a very rare phenomenon, In the second case, on the other hand, im migrants lead to frequent break-downs on the entire network and hence to complete extinction. In both cases individual species are short-liv ed and the distribution of survival times is exponential. (C) 1998 Aca demic Press.