Microclimate feedbacks sustain power law clustering of encroaching coastal woody vegetation

Modeling the interaction of vegetation and sea level rise on barrier island evolution

Barrier islands provide a first line of defense against ocean flooding and storm surge. Biogeomorphic interactions are recognized as important in coastal system processes, but current barrier island models are primarily dominated by physical processes. Recent research has demonstrated different biogeomorphic states that influence response to sea level rise and other disturbance. Building on this understanding, we present a cellular model utilizing biotic and abiotic processes and their interactions for barrier island evolution. Using the literature and field derived parameters, we model barrier island evolution and compare to three decades of change for Smith Island, a Virginia Coast Reserve barrier island. We conduct simulations that show the impact of biogeomorphic states on island migration under different sea level rise scenarios. We find that migration is highest in areas with low topography and light vegetation cover (i.e. disturbance reinforcing) compared to areas with greater topographic complexity and high cover of woody vegetation i.e. disturbance resisting). This study demonstrates the importance of biogeomorphic interactions for barrier island evolution with sea level rise and will aid future predictions for these important ecosystems with climate change.

Emergence of power-law distributions in self-segregation reaction-diffusion processes

Many natural or human-made systems encompassing local reactions and diffusion processes exhibit spatially distributed patterns of some relevant dynamical variable. These interactions, through self-organization and critical phenomena, give rise to power-law distributions, where emergent patterns and structures become visible across vastly different scales. Recent observations reveal power-law distributions in the spatial organization of, e.g., tree clusters and forest patch sizes. Crucially, these patterns do not follow a spatially periodic order but rather a statistical one. Unlike the spatially periodic patterns elucidated by the Turing mechanism, the statistical order of these particular vegetation patterns suggests an incomplete understanding of the underlying mechanisms. Here, we present a self-segregation mechanism, driving the emergence of power-law scalings in pattern-forming systems. The model incorporates an Allee-logistic reaction term, responsible for the local growth, and a nonlinear diffusion process accounting for positive interactions and limited resources. According to a self-organized criticality (SOC) principle, after an initial decrease, the system mass reaches an analytically predictable threshold, beyond which it self-segregates into distinct clusters, due to local positive interactions that promote cooperation. Numerical investigations show that the distribution of cluster sizes obeys a power law with an exponential cutoff.