Evolution in time-dependent fitness landscapes

TL;DR

This paper develops a theoretical framework for adaptive walks on time-dependent fitness landscapes, specifically oscillating NK landscapes, revealing a phase transition and complex dynamics near critical points.

Contribution

It introduces a theory for evolution on changing fitness landscapes and applies it to oscillating NK landscapes, highlighting a phase transition and novel dynamic behaviors.

Findings

Transition between regimes is a second-order phase transition.

Adaptive walks exhibit noisy limit cycles near the critical point.

For small static contributions, the landscape has no local optima.

Abstract

Evolution in changing environments is an important, but little studied aspect of the theory of evolution. The idea of adaptive walks in fitness 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 fitness landscapes has most of the time not been taken. In this work, some elements of a theory of adaptive walks on changing fitness landscapes are proposed, and are subsequently applied to and tested on a simple family of time-dependent fitness landscapes, the oscillating NK landscapes, also introduced here. For these landscapes, the parameter governing the evolutionary dynamics is the fraction of static fitness 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 fitness 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.