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Adaptive landscape has been a fundamental concept in many branches of modernbiology since Wright's first proposition in 1932. Meanwhile, the generalexistence of landscape remains controversial. The causes include the mixed usesof different landscape definitions with their own different aims andadvantages. Sometimes the difficulty and the impossibility of the landscapeconstruction for complex models are also equated. To clarify these confusions,based on a recent formulation of Wright's theory, the current authors constructgeneralized adaptive landscape in a two-loci population model with non-gradientdynamics, where the conventional gradient landscape does not exist. On thegeneralized landscape, a population moves along an evolutionary trajectorywhich always increases or conserves adaptiveness but does not necessarilyfollow the steepest gradient direction. Comparisons of different aspects ofvarious landscapes lead to a conclusion that the generalized landscape is apossible direction to continue the exploration of Wright's theory for complexdynamics.

Landscape construction in non-gradient dynamics: A case from evolution