Extinction Events and Species Lifetimes in a Simple Ecological Model

A model for large-scale evolution recently introduced by Amaral and Meyer is studied analytically and numerically. Species are located at different trophic levels and become extinct if their prey becomes extinct. It is proved that this model is self-organized critical in the thermodynamic limit, with an exponent of 2 characterizing the size distribution of extinction events. The lifetime distribution of species, cutoffs due to finite-size effects, and other quantities are evaluated. The relevance of this model to biological evolution is critically assessed.