The screening of species in a Darwinistic tree-like model of evolution

Numerical and theoretical investigations of a tree-like model of self-organized critical evolution are presented. The screening of species from the evolution process is numerically studied. Critical exponents for (i) the avalanche distribution, (ii) the correlation function, (iii) the order parameter and (iv) the fraction of unscreened species are given. A mean-field approximation is developed. This theory is quite accurate for describing the critical state but is not able to describe the transient regimes, i.e. the self-organized slowing down of both order parameter and fraction of unscreened species towards the critical state.