The probability of permanence
type: Item
instance of: scholarly article
title: The probability of permanence
zbMATH Open document ID: 0778.92015
DOI: 10.1016/0025-5564(93)90007-W
author: Peter F. Stadler
author: Robert Happel
published in: Mathematical Biosciences
publication date: 1993-06-29T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 92D15
Mathematics Subject Classification ID: 65C20
Mathematics Subject Classification ID: 92D10
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 94C99
zbMATH DE Number: 219755
zbMATH Keywords: hypercycle-type interactions
zbMATH Keywords: genetic information
zbMATH Keywords: pure RNA world
zbMATH Keywords: conditions for permanence
zbMATH Keywords: systems of second-order replicator equations
zbMATH Keywords: Lotka-Volterra equations
zbMATH Keywords: natural selection
zbMATH Keywords: interacting species
zbMATH Keywords: random networks
zbMATH Keywords: probability of permanence
zbMATH Keywords: random autocatalytic networks
zbMATH Keywords: persistent networks
zbMATH Keywords: random additional species
zbMATH Keywords: cooperative network
Wikidata QID: Q47856630
reviewed by: Carlos A. dos Santos Braumann
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 219755