Adaptation on rugged fitness landscapes

Abstract

We introduce some basic terms pertinent to our work and define the quantities that shall be used in later calculations. For the sake of Figure 1: Schematic representation of a rugged fitness landscape with many fitness peaks. Here A and C are local fitness peaks which are fitter than all their nearest neighbours while B is the fittest sequence and hence the global peak. The arrows represent the change in the sequence and fitness of the population. The population (shown by dot) climbs the fitness landscape during adaptation. simplicity, we work with binary sequences which can replicate and mutate. The replication rate of each sequence is given by its fitness and all possible sequences along with their associated fitness comprise the fitness landscape which encodes information about the environment. For example, when the carbon source of a E.coli population is composed of glucose there is only a single metabolism pathway and as expected, the fitness landscape is smooth with a single fitness peak but becomes rugged with many local peaks when the medium is a complex mixture of carbon sources which can be metabolised in multiple ways [3]. The ruggedness of the fitness landscape is determined by the correlations between fitness of the sequences: decreasing correlations produce increasing ruggedness with the completely correlated fitness landscape being smooth.