  Phenotype of biological systems needs to be robust against mutation in order
to sustain themselves between generations. On the other hand, phenotype of an
individual also needs to be robust against fluctuations of both internal and
external origins that are encountered during growth and development. Is there a
relationship between these two types of robustness, one during a single
generation and the other during evolution? Could stochasticity in gene
expression have any relevance to the evolution of these robustness? Robustness
can be defined by the sharpness of the distribution of phenotype; the variance
of phenotype distribution due to genetic variation gives a measure of `genetic
robustness' while that of isogenic individuals gives a measure of
`developmental robustness'. Through simulations of a simple stochastic gene
expression network that undergoes mutation and selection, we show that in order
for the network to acquire both types of robustness, the phenotypic variance
induced by mutations must be smaller than that observed in an isogenic
population. As the latter originates from noise in gene expression, this
signifies that the genetic robustness evolves only when the noise strength in
gene expression is larger than some threshold. In such a case, the two
variances decrease throughout the evolutionary time course, indicating increase
in robustness. The results reveal how noise that cells encounter during growth
and development shapes networks' robustness to stochasticity in gene
expression, which in turn shapes networks' robustness to mutation. The
condition for evolution of robustness as well as relationship between genetic
and developmental robustness is derived through the variance of phenotypic
fluctuations, which are measurable experimentally.
