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The geometry of evolved community matrix spectra.
Silja Borring Låstad1, Jan O Haerter2,3,4
1Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, Copenhagen, 2100, Denmark.
Random matrix theory predicts unstable food webs, but this study shows evolving food webs develop bi-modal spectra, challenging prior stability assumptions. This finding impacts ecological network analysis and stability predictions.
Area of Science:
- Ecology
- Theoretical Ecology
- Network Theory
Background:
- Random matrix theory (RMT) has been a dominant framework for analyzing food web stability.
- RMT predicts elliptical eigenvalue spectra for community matrices, suggesting large food webs are inherently unstable.
Purpose of the Study:
- To investigate food web stability beyond RMT predictions.
- To explore how complex food webs self-assemble and evolve.
- To determine the spectral properties of community matrices in evolving food webs.
Main Methods:
- Utilized simple Lotka-Volterra equations to model interactions within food webs.
- Simulated an evolutionary process where feasible food webs self-assemble.
- Introduced invasion attempts to drive evolutionary dynamics.
- Analyzed the eigenvalue spectra of the resulting community matrices.
Main Results:
- Evolving complex food webs exhibited bi-modal community matrix spectra.
- The observed spectra deviated significantly from the elliptical geometries predicted by RMT.
- Food web complexity and stability were shown to emerge through an evolutionary assembly process.
Conclusions:
- The bi-modal spectra suggest RMT may not accurately capture the stability dynamics of realistically evolving food webs.
- Findings challenge the direct applicability of RMT to food web steady-state analysis.
- This study highlights the importance of evolutionary processes in shaping ecological network structure and stability.
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