  We propose here a new model to describe biological invasions in the plane
when a strong diffusion takes place on a line. We establish the main properties
of the system, and also derive the asymptotic speed of spreading in the
direction of the line. For low diffusion, the line has no effect, whereas, past
a threshold, the line enhances global diffusion in the plane and the
propagation is directed by diffusion on the line. It is shown here that the
global asymptotic speed of spreading in the plane, in the direction of the
line, grows as the square root of the diffusion on the line. The model is much
relevant to account for the effects of fast diffusion lines such as roads on
spreading of invasive species.
