Heterogeneous mean-field analysis of the generalized Lotka–Volterra model on a network

Journal of Physics A Mathematical and Theoretical, Journal Year: 2024, Volume and Issue: 57(34), P. 345002 - 345002

Published: Aug. 2, 2024

Abstract We study the dynamics of generalized Lotka–Volterra model with a network structure. Performing high connectivity expansion for graphs, we write down mean-field dynamical theory that incorporates degree heterogeneity. This allows us to describe fixed points in terms few simple order parameters. extend analysis even diverging abundances, using mapping replicator model. With this present unified approach both cooperative and competitive systems display complementary behaviors. In particular show central role an parameter called critical degree, g c . regime serves distinguish nodes are more likely go extinct, while it has reverse role, will determine low tend relatively extinct.

Language: Английский

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Interplay between an Absorbing Phase Transition and Synchronization in a Driven Granular System

Physical Review Letters, Journal Year: 2024, Volume and Issue: 132(23)

Published: June 4, 2024

Absorbing phase transitions (APTs) are widespread in nonequilibrium systems, spanning condensed matter, epidemics, earthquakes, ecology, and chemical reactions. APTs feature an absorbing state which the system becomes entrapped, along with a transition, either continuous or discontinuous, to active state. Understanding physical mechanisms determine order of these represents challenging open problem statistical mechanics. Here, by numerical simulations mean-field analysis, we show that quasi-2D vibrofluidized granular exhibits novel form APT. The is observed horizontal dynamics below critical packing fraction, can be discontinuous based on emergent degree synchronization vertical motion. Our results provide direct representation feasible experimental scenario, showcasing surprising interplay between dynamic transition synchronization.

Language: Английский

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Modeling tumors as complex ecosystems

iScience, Journal Year: 2024, Volume and Issue: 27(9), P. 110699 - 110699

Published: Aug. 10, 2024

Many cancers resist therapeutic intervention. This is fundamentally related to intratumor heterogeneity: multiple cell populations, each with different phenotypic signatures, coexist within a tumor and its metastases. Like species in an ecosystem, cancer populations are intertwined complex network of ecological interactions. Most mathematical models ecology, however, cannot account for such diversity or predict consequences. Here, we propose that the generalized Lotka-Volterra model (GLV), standard tool describe species-rich communities, provides suitable framework ecology heterogeneous tumors. We develop GLV growth discuss how emerging properties provide new understanding disease. potential extensions their application plasticity, cancer-immune interactions, metastatic growth. Our work outlines set questions road map further research ecology.

Language: Английский

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Stochastic spatiotemporal growth model reproducing the universal statistical laws of the gut microbiome

Physical Review Research, Journal Year: 2025, Volume and Issue: 7(1)

Published: March 13, 2025

Although gut microbiomes exhibit host-specific complexity, it is becoming clear that their dynamics are governed by common rules. In this paper, we empirically show three key statistical laws—the fat-tailed species abundance distribution, the scaling law of fluctuations, and tent-shaped log growth rate distribution—are quantitatively universal across humans mice. We further propose a simple stochastic model comprehensively reproduces these laws. The based on microscopic representing each at local sites wall, modeled as random multiplicative process. By introducing coarse-grained time spatial scales reflect real-world sampling processes, provides physical interpretation dynamic properties empirical data, including timescales temporal stochasticity. Furthermore, incorporation diffusion effects predicts heterogeneous distribution wall. This serves fundamental framework for unified analysis spatiotemporal patterns microbiome. Published American Physical Society 2025

Language: Английский

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Generalized correlations in disordered dynamical systems: Insights from the many-species Lotka-Volterra model

Physical review. E, Journal Year: 2025, Volume and Issue: 111(4)

Published: April 3, 2025

In the study of disordered systems, one often chooses a matrix independent identically distributed interaction coefficients to represent quenched random couplings between components, perhaps with some symmetry constraint or correlations diagonally opposite pairs elements. However, more general set couplings, which still preserves statistical interchangeability could involve sharing only single row column index. These have been shown arise naturally in systems such as generalized Lotka-Volterra equations (gLVEs). this work, we perform dynamic mean-field analysis understand how single-index affect dynamics and stability taking gLVEs our example. We show that in-row raise level noise process, even when overall variance is held constant. also see transpose rows columns can either enhance suppress feedback effects, depending on sign correlation coefficient. context gLVEs, row/column thus both species survival rate ecological equilibria. Published by American Physical Society 2025

Language: Английский

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Hierarchy of Chaotic Dynamics in Random Modular Networks

Physical Review Letters, Journal Year: 2025, Volume and Issue: 134(14)

Published: April 9, 2025

We introduce a model of randomly connected neural populations and study its dynamics by means the dynamical mean-field theory simulations. Our analysis uncovers rich phase diagram, featuring high- low-dimensional chaotic phases, separated crossover region characterized low values maximal Lyapunov exponent participation ratio dimension, but with high dimension that change significantly across region. Counterintuitively, chaos can be attenuated either adding noise to strongly modular connectivity or introducing modularity into random connectivity. Extending include multilevel, hierarchical reveals loose balance between activities levels drives system towards edge chaos. Published American Physical Society 2025

Language: Английский

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The persistence of bipartite ecological communities with Lotka–Volterra dynamics

Journal of Mathematical Biology, Journal Year: 2024, Volume and Issue: 89(2)

Published: July 2, 2024

Abstract The assembly and persistence of ecological communities can be understood as the result interaction migration species. Here we study a single community subject to from species pool in which inter-specific interactions are organised according bipartite network. Considering dynamics abundances governed by generalised Lotka–Volterra equations, extend work on unipartite networks derive exact results for phase diagram this model. Focusing antagonistic interactions, describe factors that influence two guilds, locate transitions multiple-attractor unbounded phases, well identifying region parameter space consumers essentially absent local community.

Language: Английский

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Landscape and environmental heterogeneity support coexistence in competitive metacommunities

Proceedings of the National Academy of Sciences, Journal Year: 2024, Volume and Issue: 121(44)

Published: Oct. 22, 2024

Metapopulation models have been instrumental in quantifying the ecological impact of landscape structure on survival a focal species. However, extensions to multiple species with arbitrary dispersal networks often rely phenomenological assumptions that inevitably limit their scope. Here, we propose multilayer network model competitive dispersing metacommunities investigate how spatially structured environments coexistence and ecosystem stability. We introduce concept landscape-mediated fitness, fit is given environment terms colonization extinction. show that, when all are equivalent, one excludes others—except marginal case where fitnesses exact trade-off. prove stable becomes possible sufficiently heterogeneous by introducing spatial disorder solving it exactly mean-field limit. Crucially, supported spontaneous localization through emergence niches. our results remain qualitatively valid networks, topological features can improve buffering competition. Finally, employ study correlated heterogeneity promotes patterns realistic terrestrial riverine landscapes. Our work provides framework understand enables acting as substrate for interactions.

Language: Английский

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Nonequilibrium microbial dynamics unveil a new macroecological pattern beyond Taylor's law

Physical review. E, Journal Year: 2024, Volume and Issue: 110(4)

Published: Oct. 15, 2024

We introduce a comprehensive analytical benchmark, relying on Fokker-Planck formalism, to study microbial dynamics in the presence of both biotic and abiotic forces. In equilibrium, we observe balance between two kinds forces, leading no correlations species abundances. This implies that real microbiomes, where have been observed, operate out equilibrium. Therefore, analyze nonequilibrium dynamics, presenting an ansatz for approximate solution embodies complex interplay forces system. is consistent with Taylor's law as coarse-grained approximation relation abundance variance, but subtler effects, predicting unobserved structure beyond law. Motivated by this theoretical prediction, refine analysis existing metagenomic data, unveiling novel universal macroecological pattern. Finally, speculate physical origin law: building upon analogy Brownian motion theory, propose emerges fluctuation-growth resulting from equipartition environmental resources among species.

Language: Английский

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Topological conditions drive stability in meta-ecosystems

Physical Review Research, Journal Year: 2024, Volume and Issue: 6(4)

Published: Oct. 23, 2024

On a global level, ecological communities are being perturbed at an unprecedented rate by human activities and environmental instabilities. Yet, we understand little about what factors facilitate or impede long-term persistence of these communities. While observational studies indicate that increased biodiversity must, somehow, be driving stability, theoretical have argued the exact opposite viewpoint instead. This encouraged many researchers to participate in ongoing debate. Within this context, however, there has been severe lack consider spatial features explicitly, even though nearly all habitats spatially embedded. To end, study here linear stability meta-ecosystems on networks describe how discrete patches connected dispersal between them. By combining results from random-matrix theory network theory, able show three distinct underlie stability: edge density, tendency triadic closure, isolation fragmentation. Our appear further sparsity does not necessarily reduce connections just as important, if more so, when studying large systems. Published American Physical Society 2024

Language: Английский

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