  Genetically identical cells in the same population can take on phenotypically
variable states, leading to differentiated responses to external signals, such
as nutrients and drug-induced stress. Many models and experiments have focused
on a description based on discrete phenotypic states. Here we consider the
effects of selection acting on a single trait, which we explicitly link to the
variable number of proteins expressed by a gene. Considering different
regulatory models for the gene under selection, we calculate the steady-state
distribution of expression levels and show how the population adapts its
expression to enhance its fitness. We quantitatively relate the overall fitness
of the population to the heritability of expression levels, and their diversity
within the population. We show how selection can increase or decrease the
variability in the population, alter the stability of bimodal states, and
impact the switching rates between metastable attractors.
