Spatial competition: roughening of the ecological interface

Limited dispersal distance, whether due to vegetative growth or localized 2 reproduction, generates spatial clustering. Many invasive plants, in particular, propagate clonally and aggregate spatially. Local dispersal concentrates intraspecific interactions 4 within clusters, while most between-species interactions occur near cluster boundaries. Spread of a spatially clustered, invasive plant then becomes motion of an interface between 6 the invader and resident species, and competition along the interface produces random variation in the extent of invasive advance. Development of these growth fluctuations, 8 termed stochastic roughening, will often structure the ecological interface as a self-affine fractal. This property implies a series of scaling relationships for the statistics of spatial 10 growth. For many individual-based processes exhibiting both forward and lateral propagation, the extent of invader advance becomes spatially correlated along the interface, 12 and the width of the interface (where invader and resident compete directly) increases as a power function of time. Once roughening equilibrates, interface width and the location of 14 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 16 clover (Trifolium repens) invade ryegrass (Lolium perenne) experimentally. Spatial correlation developed as anticipated, and both interface width and the front-runner’s lead 18 scaled as a power law of length. However, the scaling exponents differed, plausibly an effect of clover’s growth morphology. Our results suggest that the theory of kinetic roughening 20 offers a framework for understanding causes and consequences of spatial pattern in between-species interaction. Although our analysis focuses on growth at the neighborhood 22 scale, the methods may be applied to invasive fronts at extended spatial scales.