The processes by which boundaries between ecosystems are formed are not well understood. The boundary is a byproduct of the underlying stress gradient and localized interactions among organisms, which are often facilitative, but can include complex scale-dependent feedbacks. Boundaries can be smooth, step-wise, or involving a catastrophic bifurcation; the latter two typically stemming from facilitative interactions. Based on criticality theory, the spatial structure of the boundary should always include fractal structures at the percolation point (classical criticality), but positive interactions can extend the fractal region far into the hostile environment (robust criticality) where the structures decay very predictably from a power-law distribution to power law with exponential tail and eventually to an exponential distribution. Here we present a study of alpine treeline spatial structure that exhibits a catastrophic bifurcation and robust criticality. Our 380m by 90m AOI was a diffuse treeline on Pikes Peak (CO). We utilized drone imaging to produce an orthomosaic and DSM of the site, allowing us to manually digitize tree, sapling, and seedling canopies in ArcGIS. We divided the AOI into zones and examined the patch size distribution and tree canopy cover for evidence of bimodality and robust criticality using the Spatial Warnings package in R.
Results/Conclusions
Our results showed that the ecotone structure is broadly consistent with catastrophic bifurcation and robust criticality. In agreement with catastrophic bifurcation we found a large area of bimodal distribution of tree cover across the transition zone from forest to tundra. The low tree cover mode corresponded to tundra with scattered saplings and the high tree cover mode corresponded to dense patches of adult trees. Tree cover was unimodal with high tree cover in the forest, bimodal at the transition, and unimodal with low tree cover in the tundra. Consistent with robust criticality, the patch size distribution in the forest exhibited a power law with an exponential tail (as expected for systems where positive interactions are less important). The transition zone exhibited a power law, followed by a power law with an exponential tail as it moved into the tundra. The upper regions of the tundra exhibited exponential patch size distribution. Other indicators of robust criticality (skewness, variance, and Moran’s I) had mixed results. As expected, skewness and variance decreased in patch size distribution with increasing elevation, where as the spike in Moran’s I was difficult to detect due to the high variability of the measure.