Large scale patterns in mussel beds: stripes or spots?

Area of Science:

• Ecology
• Mathematical Biology
• Marine Biology

Background:

• Intertidal mussel beds exhibit large-scale striped patterns perpendicular to tidal flow.
• Previous models used one-dimensional traveling waves (wavetrains) to explain mussel density patterns.
• Stability analysis of these wavetrain solutions was limited.

Purpose of the Study:

• Extend analysis to two spatial dimensions to study stripe pattern stability.
• Investigate the impact of transverse two-dimensional perturbations on mussel bed patterns.
• Understand the role of tidal flow and algal dispersal in pattern formation and stability.

Main Methods:

• Numerical continuation techniques to analyze two-dimensional patterns.
• Simulation of a coupled partial differential equation model for mussel-algae interaction.
• Incorporation of a dispersal term to model random algal movement.

Main Results:

• Some previously stable wavetrain solutions are unstable to 2D transverse perturbations.
• Striped patterns break up into spotted patterns, particularly at low tidal flow rates.
• Increased algal dispersal can promote stripe formation but also their breakup into spots, revealing hysteresis.

Conclusions:

• Two-dimensional analysis reveals instabilities not apparent in 1D models.
• Tidal flow rate and algal dispersal are critical factors in mussel bed pattern dynamics.
• Transverse perturbations can lead to pattern transitions and novel hysteresis effects in intertidal ecosystems.