Continuous Evolution in the NK Treadmill Model

Abstract

The NK fitness landscape is a well-known model with which to study evolutionary dynamics in landscapes of different ruggedness. However, the model is static, and genomes are typically small, allowing observations over only a short adaptive period. Here we introduce an extension to the model that allows the experimenter to set the velocity at which the landscape changes independently from other parameters, such as the ruggedness or the mutation rate. We find that, similar to the previously observed complexity catastrophe, where evolution comes to a halt when environments become too complex due to overly high degrees of epistasis, here the same phenomenon occurs when changes happen too rapidly. Our expanded model also preserves essential properties of the static NK landscape, allowing for proper comparisons between static and dynamic landscapes.