92-01-001
The Probability of Permanence
Robert Happel and Peter F. Stadler
Numerical experiments
suggest that cooperation is a very rare phenomenon in autocatalytic
networks with more than some 5 interacting species. There is strong
evidence that the probability for a cooperative behaviour in random
networks decreases at least exponentially and at most as
an2 with the number n of
interacting species.
The evolution of larger persistent networks
by subsequent incorporation of additional species into a cooperative
network is shown to be even less probable. This leads to the
conclusion that hypercycle-type interactions alone are not sufficient
to maintain the genetic information of more than a few interacting
species in a pure RNA world.
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