Extremal dynamics in random replicator ecosystems

• Extremal Dynamics organizes random replicator ecosystems to two phases in fitness space.
• Replicator systems show power-law scaling of activity.
• Species extinction interferes with Bak–Sneppen type mutation activity.
• Speciation–extinction dynamics does not show any critical phase transition.
• Biological macroevolution probably is not a self-organized critical phenomenon.

The seminal numerical experiment by Bak and Sneppen (BS) is repeated, along with computations with replicator models, including a greater amount of features. Both types of models do self-organize, and do obey power-law scaling for the size distribution of activity cycles. However species extinction within the replicator models interferes with the BS self-organized critical (SOC) activity. Speciation–extinction dynamics ruins any stationary state which might contain a steady size distribution of activity cycles. The BS-type activity appears as a dissimilar phenomenon in comparison to speciation–extinction dynamics in the replicator system. No criticality is found from the speciation–extinction dynamics. Neither are speciations and extinctions in real biological macroevolution known to contain any diverging distributions, or self-organization towards any critical state. Consequently, biological macroevolution probably is not a self-organized critical phenomenon.