  We consider a general class of Markovian models describing the growth in a
randomly fluctuating environment of a clonal biological population having
several phenotypes related by stochastic switching. Phenotypes differ e.g. by
the level of gene expression for a population of bacteria. The time-averaged
growth rate of the population, $\Lambda$, is self-averaging in the limit of
infinite times; it may be understood as the fitness of the population in a
context of Darwinian evolution.
  The observation time $T$ being however typically finite, the growth rate
fluctuates. For $T$ finite but large, we obtain the variance of the
time-averaged growth rate as the maximum of a functional based on the
stationary probability distribution for the phenotypes. This formula is
general. In the case of two states, the stationary probability was computed by
Hufton, Lin and Galla \cite{HufLin2}, allowing for an explicit expression which
can be checked numerically.
