  Stem cells have the potential to produce lineages of non-stem cell
populations (differentiated cells) via a ubiquitous hierarchal division scheme.
Differentiation of a stem cell into (partially) differentiated cells can happen
either symmetrically or asymmetrically. The selection dynamics of a mutant
cancer stem cell should be investigated in the light of a stem cell
proliferation hierarchy and presence of a non-stem cell population. By
constructing a three-compartment Moran-type model composed of normal stem
cells, mutant (cancer) stem cells and differentiated cells, we derive the
replicator dynamics of stem cell frequencies where asymmetric differentiation
and differentiated cell death rates are included in the model. We determine how
these new factors change the conditions for a successful mutant invasion and
discuss the variation on the steady state fraction of the population as
different model parameters are changed. By including the phenotypic
plasticity/dedifferentiation, in which a progenitor/differentiated cell can
transform back into a cancer stem cell, we show that the effective fitness of
mutant stem cells is not only determined by their proliferation and death rates
but also according to their dedifferentiation potential. By numerically solving
the model we derive the phase diagram of the advantageous and disadvantageous
phases of cancer stem cells in the space of proliferation and dedifferentiation
potentials. The result shows that at high enough dedifferentiation rates even a
previously disadvantageous mutant can take over the population of normal stem
cells. This observation has implications in different areas of cancer research
including experimental observations that imply metastatic cancer stem cell
types might have lower proliferation potential than other stem cell phenotypes
while showing much more phenotypic plasticity and can undergo clonal expansion.
