  We consider energy relaxation of the long-range spin glass model with sparse
couplings, the so-called dilute Sherrington-Kirkpatrick (SK) model, starting
from a random initial state. We consider the effect that modularity of the
coupling matrix has on this relaxation dynamics. In the absence of finite size
effects, the relaxation dynamics appears independent of modularity. For finite
sizes, a more modular system reaches a less favorable energy at long times. For
small sizes, a more modular system also has a less favorable energy at short
times. For large sizes, modularity appears to lead to slightly more favorable
energies at intermediate times. We discuss these results in the context of
evolutionary theory, where horizontal gene transfer, absent in the Glauber
equilibration dynamics of the SK model studied here, endows modular organisms
with larger response functions at short times.
