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.
Replicator Equation - Meta-population Dynamics
- Mutation - Immigration - Permanence
Return to 1997 working papers list.