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Related Experiment Video

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Experimental Protocol for Manipulating Plant-induced Soil Heterogeneity
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Model of pattern formation in marsh ecosystems with nonlocal interactions.

Sofya Zaytseva1,2, Junping Shi3, Leah B Shaw3

  • 1Department of Applied Science, William & Mary, Williamsburg, VA, 23187-8795, USA. szaytseva@uga.edu.

Journal of Mathematical Biology
|October 14, 2019
PubMed
Summary

Smooth cordgrass (Spartina alterniflora) modifies tidal marshes by creating feedbacks between vegetation and sediment. This scale-dependent interaction shapes marsh shorelines, leading to erosion troughs and accretion zones.

Keywords:
CooperationMarsh ecosystemNonlocal interactionsPattern formationReaction–diffusionSteady state

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Area of Science:

  • Ecology
  • Environmental Science
  • Mathematical Biology

Background:

  • Smooth cordgrass (Spartina alterniflora) is a key ecosystem engineer in tidal marshes.
  • Marsh vegetation influences sediment dynamics through localized hydrodynamic energy attenuation and accretion.
  • Complex feedbacks between vegetation and sediment can lead to large-scale spatial patterns in shorelines.

Purpose of the Study:

  • To develop a mathematical framework modeling grass-sediment dynamics.
  • To investigate the role of scale-dependent feedback in shoreline formation.
  • To identify conditions leading to spatially varying marsh shorelines.

Main Methods:

  • A reaction-diffusion system with a nonlocal term was formulated.
  • A Mexican-hat kernel function was used to represent scale-dependent interactions.
  • Steady-state biharmonic approximation was applied to derive pattern formation conditions.

Main Results:

  • The model captures short-range positive and long-range negative grass-sediment interactions.
  • Emergence of spatial patterns, indicative of shoreline variation, was analyzed.
  • Pattern formation is contingent on the spatial scale and strength of feedback, defined by the Mexican-hat kernel.

Conclusions:

  • Scale-dependent feedback is crucial for generating complex marsh shoreline patterns.
  • Mathematical modeling provides insights into ecological engineering processes.
  • The study highlights the importance of spatial scale in ecosystem dynamics.