Файл:Bak sneppen model.pngSample of Bak–Sneppen model evolution: on the x-axis the population status, on the y-axis (from top to the bottom) the history of the population. Each discontinuity represents an evolution. The color codes the age of the species.
The model dynamics repeatedly eliminates the least adapted species and mutates it and its neighbors to recreate the interaction between species. A comprehensive study of the details of this model can be found in Phys. Rev. E53, 414–443 (1996). A solvable version of the model has been proposed in Phys. Rev. Lett.76, 348–351 (1996), which shows that the dynamics evolves sub-diffusively, driven by a long-range memory.
We consider N species, which are associated with a fitness factor f(i). They are indexed by integers i around a ring. The algorithm consists in choosing the least fit species, and then replacing it and its two closest neighbors (previous and next integer) by new species, with a new random fitness. After a long run there will be a minimum required fitness, below which species don't survive. These "long-run" events are referred to as avalanches, and the model proceeds through these avalanches until it reaches a state of relative stability where all species' fitness are above a certain threshold.[2]
↑Wei1, Li; Yang, Luo; YuanFang, Wang & AiPing, Cai. "A mean-field Bak-Sneppen model with varying interaction strength". Chinese Science Bulletin, 2011, p. 3639.
