Speciations and extinctions in a self-organizing critical model of tree-like evolution

We study analytically a simple model of a self-organized critical evolution. The model considers both extinction and speciation events leading to the growth of phylogenetic-like trees. Through a mean-field like theory, we study the evolution of the local configurations for the tree leaves. The fitness threshold, below which life activity takes place through avalanches of all sizes is calculated. The transition between speciating (evolving) and dead trees is obtained and is in agreement with numerical simulations. Moreover, this theoretical work suggests that the structure of the tree is strongly dependent on the extinction strength.