Fitness Landscapes That Depend on Time

Abstract

Landscapes whose fitness values change with time occur in several contexts. A first is that the evolutionary process takes place in a dynamic environment. Dynamics may be connected to optimization problems with changing objective functions, or generally that conditions apart from the genetic makeup of the population, but massively influencing the evolutionary outcome, are not constant. Mathematically, such dynamic fitness landscapes can be described either by static landscapes that are externally driven to change with time, or by spatially extended dynamical systems which internally and simultaneously define topology and dynamics of the landscape. Another setting for time-dependent fitness are coevolutionary processes where the fitness of a given individual depends on the fitness and the genotype of other individuals in a temporal or spatial fashion. This is known to create coupled, interactive, tunable or deformable landscapes. Such coevolutionary processes induce time-dependence that is population-based and produce landscapes that are codynamic. In this chapter we intend to give an unified overview about issues in and problems of time-dependent fitness landscapes and particularly highlight several types of mathematical descriptions and their properties, similarities and differences.