Controversies have continued as to the range of applicability of neo-Darwinian and non-Darwinian view of evolution, since Kimura proposed the neutral theory of molecular evolution. By the former view evolution rate v is regulated by environment independent of mutation rate m, whereas by the latter view it is regulated by mutation independent of environment change rate. To understand the population genetical conditions for demarcating the two views, inducibility&khgr;=&dgr;v/&dgr;&mgr;of evolution rate is studied for simple dynamical model and Markovian model. For neo-Darwinian evolution the inducibility is almost 0, whereas for non-Darwinian evolution it is significantly positive. Among non-Darwinian evolution, the inducibility is nearly equal to 1 for neutral evolution. The critical selection intensitysCdemarcating neo-Darwinian and non-Darwinian evolution is obtained. There exists another demarcation selection intensitysC−such that in the range(sC−,sC)the evolution is non-Darwinian but not neutral. This transition region corresponds to Ohta’s nearly neutral evolution. Estimating its relative widthsC−/sC,it is argued that so long as the effect of selection is significant for polymorphism, neo-Darwinian evolution will be more frequent in nature than the nearly neutral evolution. ©2000 American Institute of Physics.