Criticality in Simple Models of Evolution
  We consider two, apparently similar, models of biological evolution which have been claimed to exhibit self-organized critical behaviour. A careful reanalysis of these models, including several new analytic results for one of them, suggests that they are qualitatively different. We demonstrate the limitations of the mean field description of these systems. We argue that a more precise definition of self-organized criticality is desirable and establish several criteria in this connection. 
Jan de Boer, A.D. Jackson, and Tilo Wettig