The robustness of self-organized criticality against extinctions in a tree-like model of evolution

We investigate a so-called punctuated-equilibrium model of tree-like evolution containing extinctions for the weakest species with respect to a strength parameter r. Without extinctions (for r = 0), the model leads to self-organized criticality. For r not equal 0, a transition from growing trees to finite ones takes place at some critical r(c) = 0.48 +/- 0.01 value. For 0 less than or equal to r less than or similar to r(c), self-organized criticality is thus robust against extinctions of the weakest species. The size distribution of avalanches follows a power law behaviour with an exponent 3/2 which seems to be independent of the parameter r. The growing trees are found to be self-similar with a non-universal fractal dimension D-f non-trivially ranging from 2 to 1 depending on the parameter r. This constraint model opens up the field of description of various possible physical events for such an evolution model.