Evolution in Time-dependent Tness Landscapes Evolution in Time-dependent Tness Landscapes

Evolution in changing environments is an important, but little studied aspect of the theory of evolution. The idea of adaptive walks in tness landscapes has triggered a vast amount of research and has led to many important insights about the progress of evolution. Nevertheless, the small step to time-dependent tness landscapes has most of the time not been taken. In this work, some elements of a theory of adaptive walks on changing tness landscapes are proposed, and are subsequently applied to and tested on a simple family of time-dependent tness landscapes, the oscillating NK landscapes, also introduced here. For these landscapes, the parameter governing the evolutionary dynamics is the fraction of static tness contributions f S. For small f S , local optima are virtually non-existent, and the adaptive walk constantly encounters new genotypes, whereas for large f S , the evolutionary dynamics reduces to the one on static tness landscapes. Evidence is presented that the transition between the two regimes is a 2nd order phase transition akin a percolation transition. For f S close to the critical point, a rich dynamics can be observed. The adaptive walk gets trapped in noisy limit cycles, and transitions from one noisy limit cycle to another occur sporadically.