  Limited dispersal distance, whether associated with vegetative growth or
localized reproduction, induces spatial clustering and, in turn, focuses
ecological interactions at the neighborhood scale. In particular, most invasive
plants are clonal, cluster through vegetative propagation, and compete locally.
Dispersal limitation implies that invasive spread occurs as advance of an
ecological interface between invader and resident species. Interspecific
competition along the interface produces random variation in the extent of
invasive growth. Development of these random fluctuations, termed stochastic
roughening, will often structure the interface as a self-affine fractal; a
series of power-law scaling relationships follows as a result. For a diverse
array of local growth processes exhibiting both forward and lateral
propagation, the extent of invader advance becomes spatially correlated along
the interface, and the width of the interface (the area where invader and
resident compete directly) increases as a power function of time. Once
roughening equilibrates statistically, interface width and the location of the
most advanced invader (the "front-runner") beyond the mean incursion should
both increase as a power function of interface length. To test these
predictions, we let white clover (Trifolium repens) invade ryegrass (Lolium
perenne) experimentally. Spatial correlation developed as anticipated, and both
interface width and the front-runner's lead scaled as a power law of length.
However, the scaling exponents differed, likely a consequence of clover's
growth morphology. The theory of kinetic roughening offers a new framework for
understanding causes and consequences of spatial pattern in between-species
interaction, and indicates when interface measures at a local scale predict
properties of an invasive front at extended spatial scales.
