  Biological systems are modular, and this modularity evolves over time and in
different environments. A number of observations have been made of increased
modularity in biological systems under increased environmental pressure. We
here develop a quasispecies theory for the dynamics of modularity in
populations of these systems. We show how the steady-state fitness in a
randomly changing environment can be computed. We derive a fluctuation
dissipation relation for the rate of change of modularity and use it to derive
a relationship between rate of environmental changes and rate of growth of
modularity. We also find a principle of least action for the evolved modularity
at steady state. Finally, we compare our predictions to simulations of protein
evolution and find them to be consistent.
