  Sewall Wright's adaptive landscape metaphor penetrates a significant part of
evolutionary thinking. Supplemented with Fisher's fundamental theorem of
natural selection and Kimura's maximum principle, it provides a unifying and
intuitive representation of the evolutionary process under the influence of
natural selection as the hill climbing on the surface of mean population
fitness. On the other hand, it is also well known that for many more or less
realistic mathematical models this picture is a sever misrepresentation of what
actually occurs. Therefore, we are faced with two questions. First, it is
important to identify the cases in which adaptive landscape metaphor actually
holds exactly in the models, that is, to identify the conditions under which
system's dynamics coincides with the process of searching for a (local) fitness
maximum. Second, even if the mean fitness is not maximized in the process of
evolution, it is still important to understand the structure of the mean
fitness manifold and see the implications of this structure on the system's
dynamics. Using as a basic model the classical replicator equation, in this
note we attempt to answer these two questions and illustrate our results with
simple well studied systems.
