Partitioned Frames in Bak Sneppen Models

In the first section we recall Bak Sneppen model and its evolutions. In this paper we wish to present some simplified cases in which explicit computations via Markov chains are possible, hence reaching a better understanding of some rather hidden phenomena of the general case: in particular “avalanches” can be read in terms of average return times and in terms of transitions between structures. A short comparison of the behaviour of different model of graphs of interaction is contained in section 2. The simple models allow us to introduce new frames that do not seem to have been considered in the previous literature, namely the case of partitioned Bak-Sneppen frames, that appear more realistic from the point of view of speed of evolution and do not present a unique criticality level, but a staircase tending towards a final equilibrium level. This is the object of section 3, while section 4 shows how this model clearly explains the overtaking of competitors with respect to species that seem to be well assessed and recalls some of our experimental data.