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Effective Fitness Landscapes for Evolutionary Systems

In evolution theory the concept of a fitness landscape has played an important role, evolution itself being portrayed as a hill-climbing process on a rugged landscape. In this article it is shown that in general, in the presence of other genetic operators such as mutation and recombination, hill-climbing is the exception rather than the rule. This descrepency can be traced to the different ways that the concept of fitness appears --- as a measure of the number of fit offspring, or as a measure of the probability to reach reproductive age. Effective fitness models the former not the latter and gives an intuitive way to understand population dynamics as flows on an effective fitness landscape when genetic operators other than selection play an important role. The efficacy of the concept is shown using several simple analytic examples and also some more complicated cases illustrated by simulations.