Kinetic roughening theory predicts properties of ecological fronts in a variety of systems and spatial scales
Advancing fronts are common in ecological systems at a variety of spatial scales, from clustered interactions within a field to range expansions of native or invasive species. Movement of a front is determined by local ecological interactions along the leading edge, whether through localized dispersal, competitive or facilitative interactions, or population-level processes (e.g., Allee effect). Despite the various biological properties, localized interactions cause correlations in advance along the front, so that the interface develops into a self-affine fractal. Kinetic roughening theory identifies scaling relationships along the front, so that studies of smaller sections of a front predict properties of the front as a whole. Kinetic roughening has been applied in systems as varied as crystal formation and tumor growth. Here, we aim to introduce these properties to ecology. First, we describe the results of a field experiment, where clonal growth produces an advancing front of white clover (Trifolium repens) into a perennial ryegrass (Lolium perenne) monoculture. Then, we use satellite imagery to examine “tiger stripe” vegetation bands found on sloped ground in arid ecosystems around the world. Water running down the hill collects in front of the bands, where reproduction occurs, and these bands advance uphill through time.
In our clover experiment, we found that localized interactions led to spatial correlations along the fronts. This led to scaling in both front roughness (variance in front position) and the front runner (furthest advanced individual) with front length. However, the scaling exponents differed from expectation, possible due to the morphology of clover clonal growth (e.g., bias towards forward rather than lateral growth).
Through driven by a completely different ecological process, we found these same correlations in advance along the vegetative bands. Scaling exponents in the leading (uphill) and trailing edge of these fronts were similar. This is interested as different biological processes drive variance in these edges: reproduction on the leading and mortality in the trailing edge.
We conclude that kinetic roughening theory can lead to a unifying understanding of ecological fronts in many systems at various spatial scales.