Eur. Phys. J. B 16, 575-578 (2000)
https://doi.org/10.1007/s100510070175

An evolution theory in finite size systems

¹ Département d'Informatique, University of Geneva, 24 rue Général-Dufour, 1211 Genève 4, Switzerland
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

Received: 25 June 2000
Published online: 15 August 2000

Abstract

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.