Mean field theory for a simple model of evolution

A simple dynamical model for Darwinian evolution on its slowest time scale is analyzed. Its mean field theory is formulated and solved. A random neighbor version of the model is simulated, as is a one-dimensional version. In one dimension, the dynamics can be described in terms of a ``repetitious random walker'' and anomalous diffusion with exponent 0.4. In all cases the model self-organizes to a robust critical attractor.