The inheritance of phenotypes: an adaptation to fluctuating environments.

We discuss simple models for the evolution of rates of spontaneous and induced heritable phenotypic variations in a periodically fluctuating environment with a cycle length between two and 100 generations. For the simplest case, the optimal spontaneous transition rate between two states is approximately 1/n (where n is the cycle length). It is also shown that selection for the optimal transition rate under these conditions is surprisingly strong. When n is small, this means that the heritable variations are produced by non-classical inheritance systems, including non-DNA inheritance systems. Thus, it is predicted that in genes controlling adaptation to such environments, non-classical genetic effects are likely to be observed. We argue that the evolution of spontaneous and induced heritable transitions played an important role in the evolution of ontogenies of both unicellular and multicellular organisms. The existence of a machinery for producing induced heritable phenotypic variations introduces a "Lamarckian" factor into evolution.