Evolution on trees: a brief review about the extinctions of species, and the case of genocide in a Darwinistic punctuated equilibrium evolution model

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 fields, or intrinsic population density conditions have already been considered. An original genocide model is presented as a step towards describing effects due to the extinction of species. Critical exponents for (i) the avalanche distribution. (ii) the teady-state approach, and (iii) the tree size are given. A mean-field approximation is shown to be quite accurate for describing the critical state. The screening of species from the evolution process is not numerically studied.