Studying evolution of species on large time scale, one can observe large periods of equilibrium punctuated by short periods of great changes. Each of these revolutions can be explained by climatic changes, cosmic accidents: this is the catastrophism theory. These events look cyclic, and it has been suggested that they might be caused by a comete, reentering regularly earth wherabouts. Another explanation is the "punctuated equilibrium theory", stating that this behavior is induced by the own dynamics of the ecosystem. Most theories take as a start a change in the environment, consider the selection of the fittest, and suggest the evolution of the species. This does not take into account the action of the species changing its environment while evolving. Bak Sneppen model has been submitted by physicists to take this into account and justify another possible explanation. It models a food chain, associating to each species an adaptation coefficient. At each step the species of minimal adaptation coefficient is removed and replaced by a new one, with a new adaptation coefficient. The adaptation coefficients of its neighbors in the food chain are also replaced, as their environment is being changed. The physicist have been simulating this model and found that it justified the theory. I analyzed with Claire Kenyon a variant and proved it behaved in the same way. Meester and Znamenski completed the analysis of the variant AND of the original model and proved some phase transition in these models. I will try to end my talk with a span of these results and the conclusion that can be drawn from those.

Reference: P Bak and S Boettcher. (1997) Self-Organized Criticality and Punctuated Equilibria. cond-mat/9701157.

The paper is available at http://xxx.lanl.gov/abs/cond-mat/9701157