  Traveling fronts describe the transition between two alternative states in a
great number of physical and biological systems. Examples include the spread of
beneficial mutations, chemical reactions, and the invasions by foreign species.
In homogeneous environments, the alternative states are separated by a smooth
front moving at a constant velocity. This simple picture can break down in
structured environments such as tissues, patchy landscapes, and microfluidic
devices. Habitat fragmentation can pin the front at a particular location or
lock invasion velocities into specific values. Locked velocities are not
sensitive to moderate changes in dispersal or growth and are determined by the
spatial and temporal periodicity of the environment. The synchronization with
the environment results in discontinuous fronts that propagate as periodic
pulses. We characterize the transition from continuous to locked invasions and
show that it is controlled by positive density-dependence in dispersal or
growth. We also demonstrate that velocity locking is robust to demographic and
environmental fluctuations and examine stochastic dynamics and evolution in
locked invasions.
