M.V. Volkenstein, evolutionary thinking and the structure of fitness landscapes.

High dimensional fitness landscapes are robustly dominated by saddle points, not isolated peaks. We present an argument to this effect that is reminiscent of May's complexity stability analysis and trace out the significance for the dynamics of speciation, the connection between the neutral and punctuated aspects of evolution and evolution on moving landscapes. The paper is written in honor of M.V. Volkenstein (October 23rd, 1912-February 18th, 1992), who devoted his last papers to uniting dynamics with evolutionary thinking.