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. R4sum4. Nous 4tudions analytiquement un modAle simple d'4volution auto-organis6e critique. Le modAle considAre des extinctions et des sp4ciations conduisant h une croissance d'arbres phylog4n4tiques. Nous 4tudions ici par une th40rie de champ moyen l'4volution des configurations des extr4mit4s de l'arbre. Le seuil critique de "fitness" en-dessous duquel des explosions d'activit6 biologique de toutes tailles se produisent est calculi. La transition entre arbres croissants et arbres 6teints est 4galement obtenue en accord avec les simulations. En outre, ce travail