  Cell populations are often characterised by phenotypic heterogeneity in the
form of two distinct subpopulations. We consider a model of tumour cells
consisting of two subpopulations: non-cancer promoting (NCP) and
cancer-promoting (CP). Under steady state conditions, the model has
similarities with a well-known model of population genetics which exhibits a
purely noise-induced transition from unimodality to bimodality at a critical
value of the noise intensity $\sigma^2$. The noise is associated with a
parameter $\lambda$ representing the system-environment coupling. In the case
of the tumour model, $\lambda$ has a natural interpretation in terms of the
tissue microenvironment which has considerable influence on the phenotypic
composition of the tumour. Oncogenic transformations give rise to considerable
fluctuations in the parameter. We compute the $\lambda-\sigma^2$ phase diagram
in a stochastic setting, drawing analogies between bifurcations and phase
transitions. In the region of bimodality, a transition from a state of balance
to a state of dominance, in terms of the competing subpopulations, occurs at
$\lambda=0$. Away from this point, the NCP (CP) subpopulation becomes dominant
as $\lambda$ changes towards positive (negative) values. The variance of the
steady state probability density function as well as two entropic measures
provide characteristic signatures at the transtion point.
