  Evolution is a dynamic process. The two classical forces of evolution are
mutation and selection. Assuming small mutation rates, evolution can be
predicted based solely on the fitness differences between phenotypes.
Predicting an evolutionary process under varying mutation rates as well as
varying fitness is still an open question. Experimental procedures, however, do
include these complexities along with fluctuating population sizes and
stochastic events such as extinctions. We investigate the mutational path
probabilities of systems having epistatic effects on both fitness and mutation
rates using a theoretical and computational framework. In contrast to previous
models, we do not limit ourselves to the typical strong selection, weak
mutation (SSWM)-regime or to fixed population sizes. Rather we allow epistatic
interactions to also affect mutation rates. This can lead to qualitatively
non-trivial dynamics. Pathways, that are negligible in the SSWM-regime, can
overcome fitness valleys and become accessible. This finding has the potential
to extend the traditional predictions based on the SSWM foundation and bring us
closer to what is observed in experimental systems.
