Stability-instability transition in tripartite merged ecological networks.

Area of Science:

• Ecology
• Theoretical Ecology
• Network Theory

Background:

• Ecological networks often focus on single interaction types (e.g., food webs).
• Integrating multiple interaction types (mutualistic, antagonistic) provides a more comprehensive ecosystem view.
• Understanding the stability of merged ecological networks is crucial for ecosystem functioning.

Purpose of the Study:

• To investigate the stability of tripartite ecological networks formed by merging mutualistic and antagonistic bipartite networks.
• To analyze the impact of the ratio of mutualistic to antagonistic interactions on network stability.
• To explore how network size and interaction disorder affect stability dynamics.

Main Methods:

• Construction of tripartite networks by merging random mutualistic and antagonistic bipartite networks.
• Analysis of network stability using the spectrum of the community matrix.
• Application of random-matrix theory to study eigenvalue phase transitions in large networks.
• Derivation of results for finite-sized networks and networks with interaction disorder.

Main Results:

• An eigenvalue phase transition occurs in the asymptotic limit of large species numbers.
• Increased ratio of mutualists to antagonists leads to abrupt network destabilization.
• The destabilization transition is observable in finite-sized networks and with interaction disorder.

Conclusions:

• Merged ecological networks exhibit complex stability dynamics influenced by the balance of interaction types.
• Random-matrix theory provides a valuable baseline for understanding stability in complex ecological networks.
• The findings highlight the critical role of interaction ratios in maintaining ecosystem stability.