The Evolution of Diversity in Replicator Networks

Robert Happel and Peter F. Stadler

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 of mutation events. Surprisingly, replicator evolved by mutant incorporation are always permanent, despite the fact that permanence is in general a very rare phenomenon. In the second case, on the other hands, immigrants lead to frequent break-downs of the entire network and hence to complete extinction. In both cases individual species are short-lived, the distribution of survival times is exponential.

keywords: Replicator Equation - Meta-population Dynamics - Mutation - Immigration - Permanence

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