Competition Among Limestone Depressions Leads to Self-Organized Regular Patterning on a Flat Landscape

Self-organized pattern formation is widespread and functionally significant. Scale-dependent feedback in space (short-distance positive feedback coupled with long-distance negative feedback) has been embraced as an arguably universal mechanism of ecological self-organization. Recently, intraspecific territorial competition has been proposed as a complementary mechanism contributing to spatial self-organization in ecology. In geomorphology, regular patterning is also widespread and has often been attributed to competition among geomorphic features. This mechanism has never been integrated into the framework of ecological pattern formation. Using the regularly patterned landscape of Big Cypress National Preserve in South Florida as a case study, we formalize a third mechanism of spatial self-organization: competition among pattern elements of finite amplitude stabilized by scale-dependent feedback in time. Depressions first accelerate their expansion rate via the positive feedback between depression volume and weathering rate. Later negative feedbacks become stronger, and eventually stabilize the size of depressions. While scale-dependent feedback in time provides a mechanism to stabilize individual depressions, it is the competition among depressions that induces spatial regularity. A relatively smaller depression could have a greater expansion rate than larger ones in its development. Higher weathering rate on the side of a divide toward the smaller depression causes migration of the divide to the larger depression. Consequently, the smaller depression expands its catchment area while the catchment area of the neighboring larger depression contracts, resulting in depressions achieving similar size and distance from each other. The diversity of regular patterns dictates the need to integrate perspectives from multiple disciplines. Plain Language Summary Regular patterns in ecosystems formed by self-organization are widespread and have significant ecological consequences. Coupled locally positive, distantly negative feedbacks (i.e., scale-dependent feedbacks) have been embraced in ecology as a unifying mechanism to explain formation of regular patterns. In geomorphology, regular patterns are also widespread, and many have been attributed to competition among geomorphic features. This geomorphic mechanism has not heretofore been integrated into the framework of ecological pattern formation. We demonstrated that it is competition, instead of scale-dependent feedbacks, that leads to the formation of the evenly spaced limestone depressions in the Big Cypress National Preserve in Florida. Growth of the size of limestone depressions requires water. As a depression grows, it holds more water, which extends the wet period, resulting in a higher weathering rate. Meanwhile, negative feedbacks triggered by ecohydrologic processes become stronger over time and eventually stabilize the size of depressions. During this process, depressions compete with each other for catchment area (proxy for water), by repeatedly moving the divide between the catchments caused by difference in their weathering rate. Such spatial interactions eventually result in similar depression size and distance of depressions to each other, giving rise to spatial regularity.

Automated summary

In this study, the authors explore the formation of regular patterns in ecosystems and geomorphology, proposing competition as a complementary mechanism contributing to spatial self-organization. By studying the patterned landscape of Big Cypress National Preserve in South Florida, they demonstrate that competition among pattern elements, rather than scale-dependent feedback, leads to spatial regularity such as evenly spaced limestone depressions.