  Braneworld scenarios are motivated by string/M-theory and can be
characterized by the way in which they modify the conventional Friedmann
equations of Einstein gravity. An alternative approach to quantum gravity,
however, is the loop quantum cosmology program. In the semi-classical limit,
the cosmic dynamics in this scenario can also be described by a set of modified
Friedmann equations. We demonstrate that a dynamical correspondence can be
established between these two paradigms at the level of the effective field
equations. This allows qualitatively similar features between the two
approaches to be compared and contrasted as well as providing a framework for
viewing braneworld scenarios in terms of constrained Hamiltonian systems. As
concrete examples of this correspondence, we illustrate the relationships
between different cosmological backgrounds representing scaling solutions.
