Irreversibility in models of macroevolution

The canonical example of a self-organized critical system exhibiting power law properties is the sandpile model of Per Bak, and in its evolutionary ex tension, a model of macroevolution. Avalanches of events, be they sandslide s or mutational activities, ale caused by a domino effect. The system's eme rging new property, called self-organized criticality, is a time symmetric one. However, if one tries not only to explain certain mechanisms of extinc tion events, then models of macroevolution have to take into account an app arent tendency, at least for some species, toward growing complexity. How t o overcome the lime symmetric situation is discussed in the following possi ble mechanisms, thereby maintaining, nevertheless, the relevant systems pro perties described by power laws.