Feasibility and stability in large Lotka Volterra systems with interaction structure

Xiaoyuan Liu; George William Albert Constable; Jon Pitchford

doi:10.1103/PhysRevE.107.054301

Feasibility and stability in large Lotka Volterra systems with interaction structure

Xiaoyuan Liu^*, George William Albert Constable, Jon Pitchford

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

Complex system stability can be studied via linear stability analysis using Random Matrix Theory (RMT) or via feasibility (requiring positive equilibrium abundances). Both approaches highlight the importance of interaction structure. Here we show, analytically and numerically, how RMT and feasibility approaches can be complementary. In generalised Lotka-Volterra (GLV) models with random interaction matrices, feasibility increases when predator-prey interactions increase; increasing competition/mutualism has the opposite effect. These changes have crucial impact on the stability of the GLV model.

Original language	English
Article number	054301
Number of pages	7
Journal	Physical Review E
Volume	107
DOIs	https://doi.org/10.1103/PhysRevE.107.054301 https://doi.org/10.48550/arXiv.2211.12949
Publication status	Published - 5 May 2023

Keywords

ecological stability
ecological feasibility
random matrix theory
ecological modelling
Generalised Lotka-Volterra

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10.1103/PhysRevE.107.054301Licence: CC BY
10.48550/arXiv.2211.12949Licence: Unspecified

PhysRevE.107.054301Final published version, 855 KBLicence: CC BY

Cite this

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title = "Feasibility and stability in large Lotka Volterra systems with interaction structure",

abstract = "Complex system stability can be studied via linear stability analysis using Random Matrix Theory (RMT) or via feasibility (requiring positive equilibrium abundances). Both approaches highlight the importance of interaction structure. Here we show, analytically and numerically, how RMT and feasibility approaches can be complementary. In generalised Lotka-Volterra (GLV) models with random interaction matrices, feasibility increases when predator-prey interactions increase; increasing competition/mutualism has the opposite effect. These changes have crucial impact on the stability of the GLV model.",

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author = "Xiaoyuan Liu and Constable, {George William Albert} and Jon Pitchford",

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AU - Pitchford, Jon

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AB - Complex system stability can be studied via linear stability analysis using Random Matrix Theory (RMT) or via feasibility (requiring positive equilibrium abundances). Both approaches highlight the importance of interaction structure. Here we show, analytically and numerically, how RMT and feasibility approaches can be complementary. In generalised Lotka-Volterra (GLV) models with random interaction matrices, feasibility increases when predator-prey interactions increase; increasing competition/mutualism has the opposite effect. These changes have crucial impact on the stability of the GLV model.

KW - ecological stability

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KW - random matrix theory

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KW - Generalised Lotka-Volterra

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