Complex systems in Ecology: a guided tour with large Lotka-Volterra models and random matrices

Akjouj, Imane; Barbier, Matthieu; Clenet, Maxime; Hachem, Walid; Maïda, Mylène; Massol, François; Najim, Jamal; Tran, Viet

doi:10.48550/arxiv.2212.06136

Cited by 2 publications

(3 citation statements)

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“…), different variations in interaction strength (e.g., Var A (11) ij = 0.01,0.02, …), and variations in trophic efficiency (i.e., A (12) ik = e A (21) lj with e < 1). These assumptions are standard practice in parameterizing the Lotka-Volterra model (Akjouj et al, 2022;Bunin, 2017;Gibbs et al, 2022;Serván et al, 2018;. Detailed descriptions of our parameterization methods are provided in Appendix S2.…”

Section: Robustness Of Assembly Patternsmentioning

confidence: 99%

Trophic tug‐of‐war: Coexistence mechanisms within and across trophic levels

Song,

Spaak

2024

Ecology Letters

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Ecological communities encompass rich diversity across multiple trophic levels. While modern coexistence theory has been widely applied to understand community assembly, its traditional formalism only allows assembly within a single trophic level. Here, using an expanded definition of niche and fitness differences applicable to multitrophic communities, we study how diversity within and across trophic levels affects species coexistence. If each trophic level is analysed separately, both lower‐ and higher trophic levels are governed by the same coexistence mechanisms. In contrast, if the multitrophic community is analysed as a whole, different trophic levels are governed by different coexistence mechanisms: coexistence at lower trophic levels is predominantly limited by fitness differences, whereas coexistence at higher trophic levels is predominantly limited by niche differences. This dichotomy in coexistence mechanisms is supported by theoretical derivations, simulations of phenomenological and trait‐based models, and a case study of a primeval forest ecosystem. Our work provides a general and testable prediction of coexistence mechanism operating in multitrophic communities.

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Section: Robustness Of Assembly Patternsmentioning

confidence: 99%

Trophic tug‐of‐war: Coexistence mechanisms within and across trophic levels

Song,

Spaak

2024

Ecology Letters

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“…In this work we wish to shine some light on the stability matrices of general disordered systems whose linearized dynamics gives rise to a non-trivial correlation structure contained within blocks. Let us motivate our work by starting at a typical Lotka-Volterra equation [11,13,14,37] written for a system of N species as…”

Section: Stability Analysis Of Complex Systems With Internal Degrees ...mentioning

confidence: 99%

“…Ever since Sir Robert May proposed his theory of ecological stability based on the properties of random matrices [1], there has been an large body of work extending his seminal insight to various ecological situations (see e.g. [2][3][4][5][6][7][8][9][10], and [11] for a review) as well as the more recent statistical mechanics approaches to the full non-linear analysis and marginal stability properties of such systems [12][13][14][15][16]. Interestingly, similar ideas have also appeared in the context of economic networks, see [17][18][19], and of random good-exchange networks [20] or of more general complex interacting systems [21].…”

Section: Introductionmentioning

confidence: 99%

The spectral boundary of block structured random matrices

Patil,

Aguirre-López,

Bouchaud

2024

J. Phys. Complex.

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Economic and ecological models can be extremely complex, with a large number of agents/species each featuring multiple interacting dynamical quantities. In an attempt to understand the generic stability properties of such systems, we define and study an interesting new matrix ensemble with extensive correlations, generalising the elliptic ensemble. We determine analytically the boundary of its eigenvalue spectrum in the complex plane, as a function of the correlations determined by the model at hand. We solve numerically our equations in several cases of interest, and show that the resulting spectra can take a surprisingly wide variety of shapes.

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Complex systems in Ecology: a guided tour with large Lotka-Volterra models and random matrices

Cited by 2 publications

References 0 publications

Trophic tug‐of‐war: Coexistence mechanisms within and across trophic levels

Trophic tug‐of‐war: Coexistence mechanisms within and across trophic levels

The spectral boundary of block structured random matrices

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