Biological functions are generated as a result of developmental dynamics that
form phenotypes governed by genotypes. The dynamical system for development is
shaped through genetic evolution following natural selection based on the
fitness of the phenotype. Here we study how this dynamical system is robust to
noise during development and to genetic change by mutation. We adopt a
simplified transcription regulation network model to govern gene expression,
which gives a fitness function. Through simulations of the network that
undergoes mutation and selection, we show that a certain level of noise in gene
expression is required for the network to acquire both types of robustness. The
results reveal how the noise that cells encounter during development shapes any
network's robustness, not only to noise but also to mutations. We also
establish a relationship between developmental and mutational robustness
through phenotypic variances caused by genetic variation and epigenetic noise.
A universal relationship between the two variances is derived, akin to the
fluctuation-dissipation relationship known in physics