  A model of population growth and dispersal is considered where the spatial
habitat is a lattice and reproduction occurs generationally. The resulting
discrete dynamical systems exhibits velocity locking, where rational speed
invasion fronts are observed to persist as parameters are varied. In this
article, we construct locked fronts for a particular piecewise linear
reproduction function. These fronts are shown to be linear combinations of
exponentially decaying solutions to the linear system near the unstable state.
Based upon these front solutions, we then derive expressions for the boundary
of locking regions in parameter space. We obtain leading order expansions for
the locking regions in the limit as the migration parameter tends to zero.
Strict spectral stability in exponentially weighted spaces is also established.
