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 a^n² 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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