Patchy landscapes in arid environments: Nonlinear analysis of the interaction-redistribution model

Area of Science:

• Ecological modeling
• Vegetation dynamics
• Landscape ecology

Background:

• Semi-arid and arid landscapes are prone to vegetation pattern formation.
• Understanding vegetation dynamics is crucial for ecosystem stability and management.
• Interaction-redistribution models offer insights into spatial patterning.

Purpose of the Study:

• To investigate the formation of patchy vegetation using a generic interaction-redistribution model.
• To analyze the transition from super- to subcritical symmetry-breaking instability.
• To numerically simulate vegetation patch distribution.

Main Methods:

• Weakly nonlinear analysis of vegetation dynamics.
• Construction of biomass density bifurcation diagrams.
• Numerical simulation of random vegetation patch distribution.

Main Results:

• Established conditions for the transition between super- and subcritical instabilities.
• Demonstrated vegetation patch formation in regimes with coexisting bare and uniform states.
• Quantified biomass density and interaction ranges from field observations.

Conclusions:

• The interaction-redistribution model effectively explains patchy vegetation formation.
• Instability transitions play a key role in vegetation pattern development.
• Model parameters align with field observations of arid ecosystems.