Local and extensive fluctuations in sparsely interacting ecological communities.

Area of Science:

• Ecology
• Theoretical Ecology
• Mathematical Biology

Background:

• Ecological communities can exist in distinct dynamical phases.
• Dense systems (all-to-all interactions) show fixed-point or fluctuating abundance phases.
• Sparse interaction dynamics remain largely unexplored.

Purpose of the Study:

• Investigate dynamical phases in ecological systems with sparse interactions.
• Explore the impact of unidirectional and bidirectional interactions on community dynamics.
• Identify and characterize novel dynamical phases unique to sparse networks.

Main Methods:

• Studied a model of sparse ecological interactions.
• Introduced constant and variable interaction strengths.
• Incorporated unidirectional and bidirectional interactions.
• Analyzed the phase diagram and species abundance fluctuations.

Main Results:

• Discovered a new dynamical phase unique to sparse interactions.
• This phase allows for mixed outcomes: some communities stabilize, others exhibit finite fluctuating species.
• Fluctuating species are linked to short cycles in the interaction graph and show nonlinear dynamics.
• Characterized the transition to extensive fluctuations, distinct from dense systems.

Conclusions:

• Sparse ecological interactions lead to novel community dynamics and phase behaviors.
• The emergent binary dynamics in sparse systems differ fundamentally from dense systems.
• Understanding these sparse dynamics is crucial for predicting ecological community stability and behavior.