  Tumors initiate when a population of proliferating cells accumulates a
certain number and type of genetic and/or epigenetic alterations. The
population dynamics of such sequential acquisition of (epi)genetic alterations
has been the topic of much investigation. The phenomenon of stochastic
tunneling, where an intermediate mutant in a sequence does not reach fixation
in a population before generating a double mutant, has been studied using a
variety of computational and mathematical methods. However, the field still
lacks a comprehensive analytical description since theoretical predictions of
fixation times are only available for cases in which the second mutant is
advantageous. Here, we study stochastic tunneling in a Moran model. Analyzing
the deterministic dynamics of large populations we systematically identify the
parameter regimes captured by existing approaches. Our analysis also reveals
fitness landscapes and mutation rates for which finite populations are found in
long-lived metastable states. These are landscapes in which the final mutant is
not the most advantageous in the sequence, and resulting metastable states are
a consequence of a mutation-selection balance. The escape from these states is
driven by intrinsic noise, and their location affects the probability of
tunneling. Existing methods no longer apply. In these regimes it is the escape
from the metastable states that is the key bottleneck; fixation is no longer
limited by the emergence of a successful mutant lineage. We used the so-called
Wentzel-Kramers-Brillouin method to compute fixation times in these parameter
regimes, successfully validated by stochastic simulations. Our work fills a gap
left by previous approaches and provides a more comprehensive description of
the acquisition of multiple mutations in populations of somatic cells.
