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An evolution theory in finite size systems
B. Chopard1, M. Droz2 and S. Galam3
Département d'Informatique, University of Geneva, 24 rue Général-Dufour, 1211 Genève 4,
2 Département de Physique Théorique, University of Geneva, 24 quai Ernest-Ansermet, 1211 Genève 4, Switzerland
3 Laboratoire des Milieux Désordonnés et HétérogènesLaboratoire associé au CNRS (UMR n° 800) et à l'Université P. et M. Curie - Paris 6., Tour 13 - Case 86, 4 place Jussieu, 75252 Paris Cedex 05, France
Published online: 15 August 2000
A new model of evolution is presented for finite size systems. Conditions under which a minority species can emerge, spread and stabilize to a macroscopic size are studied. It is found that space organization is instrumental in addition to a qualitative advantage. Some peculiar topologies ensure the overcome of the initial majority species. However the probability of such local clusters is very small and depend strongly on the system size. A probabilistic phase diagram is obtained for small sizes. It reduces to a trivial situation in the thermodynamic limit, thus indicating the importance of dealing with finite systems in evolution problems. Results are discussed with respect to both Darwin and punctuated equilibria theories.
PACS: 87.23.Kg – Dynamics of evolution / 05.50.+q – Lattice theory and statistics / 64.60.-i – General studies of phase transitions
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2000