  Adaptive landscape has been a fundamental concept in many branches of modern
biology since Wright's first proposition in 1932. Meanwhile, the general
existence of landscape remains controversial. The causes include the mixed uses
of different landscape definitions with their own different aims and
advantages. Sometimes the difficulty and the impossibility of the landscape
construction for complex models are also equated. To clarify these confusions,
based on a recent formulation of Wright's theory, the current authors construct
generalized adaptive landscape in a two-loci population model with non-gradient
dynamics, where the conventional gradient landscape does not exist. On the
generalized landscape, a population moves along an evolutionary trajectory
which always increases or conserves adaptiveness but does not necessarily
follow the steepest gradient direction. Comparisons of different aspects of
various landscapes lead to a conclusion that the generalized landscape is a
possible direction to continue the exploration of Wright's theory for complex
dynamics.
