Dispersal limitation and roughening of the ecological interface
  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. 
Andrew J. Allstadt, Jonathan A. Newman, Jonathan A. Walter, G.   Korniss, and Thomas Caraco
q-bio.PE