MATHEMATICAL MODEL OF DUNE GRASS (AMMOPHILA BREVILIGULATA) POPULATION DYNAMICS: TESTING A POSSIBLE MECHANISM FOR BLOWOUT INITIATION

Coastal dune blowouts develop when vegetation is removed from a stabilized dune surface, exposing bare sand to wind. Blowouts play a key role in dune formation and reactivation, because they can evolve into larger dune structures including massive parabolic dunes and nested dunes. It is thought that blowout initiation is largely dependent on disturbances such as wave action during high lake levels, fire, and human foot and vehicle traffic. In this talk we use mathematical models to explore the hypothesis that blowout initiation can arise as a consequence of plant population dynamics even in the absence of external disturbances.

Our work focuses on marram grass (Ammophila breviligulata), the dominant pioneer plant species in the coastal dune system along the southeast shore of Lake Michigan. Marram grass thrives under moderate sand burial, and exhibits low population densities after several years of low burial conditions. We modeled burial-dependent population dynamics of marram grass using a system of nonlinear integro-difference equations. The model incorporates a measure of soil quality that declines in the presence of plants and recovers with time and with influx of sand. The growth and spread of the plants is in turn dependent on the soil quality. This introduces a lag in the population dynamics that can result in expanding and contracting rings of high population densities. Most importantly, the model predicts the natural evolution of bare patches based solely on the population dynamics.