  The fitness landscape metaphor plays a central role on the modeling of
optimizing principles in many research fields, ranging from evolutionary
biology, where it was first introduced, to management research. Here we
consider the ensemble of trajectories of the imitative learning search, in
which agents exchange information on their fitness and imitate the fittest
agent in the population aiming at reaching the global maximum of the fitness
landscape. We assess the degree to which the starting and ending points
determine the learning trajectories using two measures, namely, the
predictability that yields the probability that two randomly chosen
trajectories are the same, and the mean path divergence that gauges the
dissimilarity between two learning trajectories. We find that the
predictability is greater in rugged landscapes than in smooth ones. The mean
path divergence, however, is strongly affected by the search parameters --
population size and imitation propensity -- that obliterate the influence of
the underlying landscape. The learning trajectories become more deterministic,
in the sense that there are fewer distinct trajectories and those trajectories
are more similar to each other, with increasing population size and imitation
propensity. In addition, we find that the roughness of the learning
trajectories, which measures the deviation from additivity of the fitness
function, is always greater than the roughness estimated over the entire
fitness landscape.
