ON PHASE THREE OF THE SHIFTING-BALANCE THEORY.

A common conclusion in several recent publications devoted to the deterministic analysis of the third phase of Wright's shifting-balance theory is that under reasonable conditions phase three should proceed easily. I argue that the mathematical equations analyzed in these papers do not correspond to the biological situation they were meant to describe. I present a more appropriate study of the third phase of the shifting balance. My results show that the third phase can proceed only under much more restricted conditions than the previous studies suggested. Migration should be neither too strong not too weak relative to selection. The higher peak should be sufficiently dominant over the lower peak. Recombination can greatly reduce the plausibility of this phase or completely preclude peak shifts. A very important determinant of the ultimate outcome of the competition between different peaks is the topological structure of the network of demes. Peak shifts in two-dimensional networks of demes are more difficult than in one-dimensional networks. Phase three can be accomplished easiest if it is initiated in one of the peripheral demes.