Extremal dynamics and punctuated co-evolution

Extremal dynamics opens up a new way for understanding the coherence that is observed in some large non-equilibrium systems. Extremal dynamics is characterized by quasistatic motion where only one part of the large system is active at a given instant: the part where a local variable assumes a global extremum value. Extremal dynamics may apply when the parts of the system nearly always are caught in metastable states. Examples from physics may include earthquakes, fluid invasion in porous media and possibly also dynamical roughening of interfaces. We discuss a simple model of extremal dynamics and its application to biological macroevolution. The model can be formulated as an ecology of adapting interacting species. The environment of any given species is affected by other species; hence it may change with time. For low mutation rate the model ecology expands at a self-organized critical state where periods of statis alternate with avalanches of evolutionary changes.