The probability of permanence
After an introduction to known (mainly necessary) conditions for permanence in systems of second-order replicator equations or Lotka- Volterra equations (standard models for natural selection and interacting species, respectively), the authors perform numerical experiments on random networks described by such equations. The main purpose of the experiments is to estimate the probability of permanence. The experiments suggest that cooperation is a very rare phenomenon in random autocatalytic networks (except when there are only a few species). They also show that the evolution of larger persistent networks by subsequent incorporation of random additional species into a cooperative network is even less probable.
systems of second-order replicator equations
scientific article; zbMATH DE number 219755
scientific article