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.
