Physica A 273 (1999) 33– 45 www.elsevier.com/locate/physa Evolution on trees: a brief review about the extinctions of species, and the case of genocide in a Darwinistic punctuated equilibrium evolution model M. Ausloos a ; ∗; 1; 2 , M. Kramer b , N. Vandewalle a a GRASP, and SUPRAS, Institut de Physique B5, Universit e de Li ege, B-4000 Li ege, Belgium b Minist ere de l’Education Nationale, Lyc ee Classique, Diekirch, Luxembourg Received 31 July 1999 Abstract Numerical and theoretical investigations of species evolution in presence of extinction rules are recalled in the framework of punctuated equilibrium evolution models. Previous results, on the Bak–Sneppen model are mentioned together with extensions taking into account a variable number of species. Conditions for limited growth due to species interactions, external elds, or intrinsic population density conditions have already been considered. An original genocide model is presented as a step towards describing eects due to the extinction of species. Critical exponents for (i) the avalanche distribution, (ii) the steady-state approach, and (iii) the tree size are given. A mean-eld approximation is shown to be quite accurate for describing the critical state. The screening of species from the evolution process is not numerically studied. c  1999 Elsevier Science B.V. All rights reserved. PACS: 05.65.+b; 87.23.-n; 05.40.-a; 5.45.Df Keywords: Evolution; Tree; Scaling laws * Corresponding author. Fax: +32-4-366-29-90. E-mail addresses: ausloos@gw.unipc.ulg.ac.be (M. Ausloos), nvandewalle@ulg.ac.be (N. Vandewalle) 1 Groupe de Recherche pour les Applications de la Statistique Physique, Group for Research in Applied Statistical Physics. 2 Services Universitaires Pour la Recherche et les Applications en Supraconductivit e, Services of the University Performing Research and Applications in Superconductivity. 0378-4371/99/$ - see front matter c  1999 Elsevier Science B.V. All rights reserved. PII:S0378-4371(99)00339-8