  Clonal interference, competition between multiple co-occurring beneficial
mutations, has a major role in adaptation of asexual populations. We provide a
simple individual based stochastic model of clonal interference taking into
account a wide variety of competitive interactions which can be found in
nature. In particular, we relax the classical assumption of transitivity
between the different mutations. It allows us to predict genetic patterns, such
as coexistence of several mutants or emergence of Rock-Paper-Scissors cycles,
which were not explained by existing models. In addition, we call into
questions some classical preconceived ideas about fixation time and fixation
probability of competing mutations.
