Fluctuation-driven Turing patterns.

Models of diffusion-driven pattern formation that rely on the Turing mechanism are utilized in many areas of science. However, many such models suffer from the defect of requiring fine tuning of parameters or an unrealistic separation of scales in the diffusivities of the constituents of the system in order to predict the formation of spatial patterns. In the context of a very generic model of ecological pattern formation, we show that the inclusion of intrinsic noise in Turing models leads to the formation of "quasipatterns" that form in generic regions of parameter space and are experimentally distinguishable from standard Turing patterns. The existence of quasipatterns removes the need for unphysical fine tuning or separation of scales in the application of Turing models to real systems.

• Publication year

  2010

• Venue

  Physical review. E, Statistical, nonlinear, and soft matter physics

• Publication date

  2010-11-01

• Fields of study

  Biology, Physics, Mathematics, Environmental Science, Medicine

• Identifiers
  DOI 10.1103/PhysRevE.84.011112arXiv 1011.0466PMID 21867118
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

• Stability and Complexity in Model Ecosystems

  2019cited by this paper
• A discrete geometric approach for simulating the dynamics of thin viscous threads

  2012cited by this paper
• Evolutionary dynamics, intrinsic noise, and cycles of cooperation.

  2010cited by this paper
• Stochastic Turing patterns in the Brusselator model.

  2009cited by this paper
• Robust ecological pattern formation induced by demographic noise.

  2009cited by this paper
• Optimality properties of a proposed precursor to the genetic code.

  2009cited by this paper
• The abundance threshold for plague as a critical percolation phenomenon

  2008cited by this paper
• Experimental Evidence for Spatial Self-Organization and Its Emergent Effects in Mussel Bed Ecosystems

  2008cited by this paper
• Predator-prey quasicycles from a path-integral formalism.

  2008cited by this paper
• Quasicycles in a spatial predator-prey model.

  2008cited by this paper
• Aspects of Mathematical Modelling

  2008cited by this paper
• Instabilities in spatially extended predator-prey systems: spatio-temporal patterns in the neighborhood of Turing-Hopf bifurcations.

  2007cited by this paper
• Plankton motility patterns and encounter rates

  2006cited by this paper
• Fluctuations and correlations in lattice models for predator-prey interaction.

  2005cited by this paper
• Stochastic Processes in Physics and Chemistry

  2005influential reference
• Predator-prey cycles from resonant amplification of demographic stochasticity.

  2005cited by this paper
• Stochastic models in population biology and their deterministic analogs.

  2004cited by this paper
• Travelling waves in the occurrence of dengue haemorrhagic fever in Thailand

  2004cited by this paper
• Pattern formation inside bacteria: fluctuations due to the low copy number of proteins.

  2003cited by this paper
• What Geometric Visual Hallucinations Tell Us about the Visual Cortex

  2002cited by this paper
• Macroecological patterns of phytoplankton in the northwestern North Atlantic Ocean

  2002cited by this paper
• Travelling waves and spatial hierarchies in measles epidemics

  2001cited by this paper
• Noisy Clockwork: Time Series Analysis of Population Fluctuations in Animals

  2001cited by this paper
• Population dynamical consequences of climate change for a small temperate songbird.

  2000cited by this paper
• Inverse density dependence and the Allee effect.

  1999cited by this paper
• Spatial pattern formation in an insect host-parasitoid system

  1997cited by this paper
• Thermally Induced Fluctuations below the Onset of Rayleigh-Bénard Convection.

  1995cited by this paper
• Stochastic Processes in Physics and Chemistry

  1995cited by this paper
• Effects of external noise on the Swift-Hohenberg equation.

  1993cited by this paper
• Microaggregations of Oceanic Plankton Observed by Towed Video Microscopy

  1992cited by this paper
• Experimental evidence of a sustained standing Turing-type nonequilibrium chemical pattern.

  1990cited by this paper
• Neural Computation

  1989cited by this paper
• Stochastic processes in physics and chemistry

  1981cited by this paper
• On a diffusive prey--predator model which exhibits patchiness.

  1978cited by this paper
• Lectures On Phase Transitions And The Renormalization Group

  1972cited by this paper
• Ecology

  1964cited by this paper
• Annals of Physics

  1957cited by this paper
• Ecological Complexity

  year unknowncited by this paper

• A diffusion approximation for systems with frequent weak resetting

  2026cites this paper
• Beyond Diagonal Noise: A Better Predator-Prey Modeling Framework with Cross-Covariance

  2026cites this paper
• An exact moment-based approach for high-order chemical reaction-diffusion networks: From mass action to Hill functions.

  2026cites this paper
• Stochastically bistable growth and decay in the Togashi-Kaneko model.

  2025cites this paper
• An Exact Moment-Based Approach for Chemical Reaction-Diffusion Networks: From Mass Action to Hill Functions

  2025cites this paper
• Trait-space patterning is dictated by the tempo and mode of mutation

  2025cites this paper
• Pattern Formation in Agent-Based and PDE Models for Evolutionary Games with Payoff-Driven Motion

  2025cites this paper
• Solution landscape of reaction-diffusion systems reveals a nonlinear mechanism and spatial robustness of pattern formation.

  2024cites this paper
• Turing patterns on discrete topologies: from networks to higher-order structures

  2024cites this paper
• Fluctuation-Driven Morphological Patterning: A Novel Approach to Morphogenesis

  2024cites this paper
• Turing instability and pattern formation induced by noise in the modified SIR model

  2024cites this paper
• Patterns governed by chemotaxis and time delay.

  2024cites this paper
• Computing macroscopic reaction rates in reaction-diffusion systems using Monte Carlo simulations.

  2024cites this paper
• A three-node Turing gene circuit forms periodic spatial patterns in bacteria.

  2024cites this paper
• Noise-driven odd elastic waves in living chiral active matter

  2024cites this paper
• Self-organization in spatial ecology.

  2024cites this paper
• Field theories and quantum methods for stochastic reaction-diffusion systems

  2024cites this paper
• Free energy dissipation enhances spatial accuracy and robustness of self-positioned Turing pattern in small biochemical systems

  2023cites this paper
• A three-node Turing gene circuit forms periodic spatial patterns in bacteria

  2023cites this paper
• Noise driven phase transitions in eco-evolutionary systems

  2023cites this paper
• Stochastic Turing patterns of trichomes in Arabidopsis leaves

  2023cites this paper
• Effects of noise on the critical points of Turing instability in complex ecosystems.

  2023cites this paper
• Computation of random time-shift distributions for stochastic population models

  2023cites this paper
• Symmetry–simplicity, broken symmetry–complexity

  2023cites this paper
• Numerical and renormalization group analysis of the phase diagram of a stochastic cubic autocatalytic reaction-diffusion system.

  2023cites this paper
• Perturbative field-theoretical analysis of three-species cyclic predator-prey models

  2023cites this paper
• Self-Organization in Randomly Forced Diffusion Systems: A Stochastic Sensitivity Technique

  2023cites this paper
• Stochastic Model for Quasi-One-Dimensional Transitional Turbulence with Streamwise Shear Interactions.

  2022cites this paper
• Free energy dissipation enhances spatial accuracy and robustness of Turing pattern in small reaction-diffusion systems

  2022cites this paper
• Spatial structure supports diversity in prebiotic autocatalytic chemical ecosystems

  2022cites this paper
• Constrained Langevin approximation for the Togashi-Kaneko model of autocatalytic reactions.

  2022cites this paper
• The Role of Noise-Induced Excitable Dynamics of Rho Family GTPases in the Regulation of Actin Cytoskeleton

  2021cites this paper
• Synthetic spatial patterning in bacteria: advances based on novel diffusible signals

  2021cites this paper
• Turing pattern design principles and their robustness

  2021cites this paper
• Stochastic sensitivity of Turing patterns: methods and applications to the analysis of noise-induced transitions

  2021cites this paper
• Stochastic self-assembly of reaction-diffusion patterns in synaptic membranes.

  2021cites this paper
• Stabilizing spiral structures and population diversity in the asymmetric May–Leonard model through immigration

  2021cites this paper
• Turing instability in quantum activator–inhibitor systems

  2021cites this paper
• Turing’s diffusive threshold in random reaction-diffusion systems

  2020cites this paper
• Precision and dissipation of a stochastic Turing pattern.

  2020cites this paper
• Stochastic Turing Pattern Formation in a Model with Active and Passive Transport

  2020cites this paper
• The Design Principles of Discrete Turing Patterning Systems

  2020cites this paper
• Plastic systemic inhibition controls amplitude while allowing phase pattern in a stochastic neural field model.

  2020cites this paper
• Systems Biology Approach to the Origin of the Tetrapod Limb

  2019cites this paper
• Using Synthetic Biology to Engineer Spatial Patterns

  2019cites this paper
• Pattern formation mechanisms of self-organizing reaction-diffusion systems

  2019cites this paper
• Spatial Interactions and Oscillatory Tragedies of the Commons.

  2019cites this paper
• Fluctuations and Correlations in Chemical Reaction Kinetics and Population Dynamics

  2019cites this paper
• A Spatial Filtering Approach to Biological Patterning

  2019influential citation
• Interface fingering instability triggered by density-coupled oscillatory chemical reaction via precipitation.

  2019cites this paper
• Stochastic Turing patterns in a synthetic bacterial population

  2018cites this paper
• Quasi-patterns produced by a Mexican Hat coupling of quasi-cycles

  2018cites this paper
• Robust stochastic Turing patterns in the development of a one-dimensional cyanobacterial organism

  2018cites this paper
• Noise sharing and Mexican-hat coupling in a stochastic neural field.

  2018cites this paper
• Analysing diffusion and flow-driven instability using semidefinite programming

  2018cites this paper
• Coloured Noise from Stochastic Inflows in Reaction–Diffusion Systems

  2018cites this paper
• Noise–Seeded Developmental Pattern Formation in Filamentous Cyanobacteria

  2018cites this paper
• Stochastic fluctuations and quasipattern formation in reaction-diffusion systems with anomalous transport.

  2018cites this paper
• Fluctuations and response in complex biological systems: Watching stochastic evolutionary and ecological pattern dynamics

  2018influential citation
• Rapidly forming, slowly evolving, spatial patterns from quasi-cycle Mexican Hat coupling.

  2018cites this paper
• An integrated computational & mammalian synthetic biology framework for engineering Turing patterns

  2018cites this paper
• Imperfect Diffusion-Controlled Reactions

  2018cites this paper
• Stochastic lattice model of synaptic membrane protein domains.

  2017cites this paper
• Turing Bifurcation and Pattern Formation of Stochastic Reaction-Diffusion System

  2017cites this paper
• Distribution of randomly diffusing particles in inhomogeneous media.

  2017cites this paper
• A stochastic analysis of the spatially extended May–Leonard model

  2017cites this paper
• Key Features of Turing Systems are Determined Purely by Network Topology

  2017cites this paper
• Coevolution Maintains Diversity in the Stochastic "Kill the Winner" Model.

  2017cites this paper
• Stochastic population dynamics in spatially extended predator–prey systems

  2017cites this paper
• Multimode Atomic Pattern Formation via Enhanced Light-atom Interactions

  2016influential citation
• Spatially Structured Neural Systems

  2016cites this paper
• The multicellular nature of filamentous heterocyst-forming cyanobacteria.

  2016cites this paper
• Turing Patterning Using Gene Circuits with Gas-Induced Degradation of Quorum Sensing Molecules

  2016cites this paper
• Stochastic facilitation in the brain?

  2016cites this paper
• Giant Amplification of Noise in Fluctuation-Induced Pattern Formation.

  2016cites this paper
• Correction: Turing Patterning Using Gene Circuits with Gas-Induced Degradation of Quorum Sensing Molecules

  2016cites this paper
• Multiscale Structure in Eco-Evolutionary Dynamics

  2015cites this paper
• Exploiting Structure and Input-Output Properties in Networked Dynamical Systems

  2015cites this paper
• Path-Integral Methods for Analyzing the Effects of Fluctuations in Stochastic Hybrid Neural Networks

  2015cites this paper
• Small-scale properties of a stochastic cubic-autocatalytic reaction-diffusion model.

  2015cites this paper
• Motif analysis for small-number effects in chemical reaction dynamics.

  2015cites this paper
• Self-assembly and plasticity of synaptic domains through a reaction-diffusion mechanism.

  2015cites this paper
• Intrinsic noise in systems with switching environments.

  2015cites this paper
• Dimension reduction for stochastic dynamical systems forced onto a manifold by large drift: a constructive approach with examples from theoretical biology

  2015cites this paper
• Feedback, receptor clustering, and receptor restriction to single cells yield large Turing spaces for ligand-receptor-based Turing models.

  2014cites this paper
• Self-Organization in Cells II: Reaction-Diffusion Models

  2014cites this paper
• Fluctuation-induced patterns and rapid evolution in predator-prey ecosystems

  2014cites this paper
• Coexistence of productive and non-productive populations by fluctuation-driven spatio-temporal patterns.

  2014cites this paper
• Path-integral calculation for the emergence of rapid evolution from demographic stochasticity.

  2014cites this paper
• Theoretical analysis of discreteness-induced transition in autocatalytic reaction dynamics.

  2014cites this paper
• Positive feedback can lead to dynamic nanometer-scale clustering on cell membranes.

  2014cites this paper
• Characterization of spiraling patterns in spatial rock-paper-scissors games.

  2014cites this paper
• Spatial patterns of competing random walkers

  2014cites this paper
• Stochastic patterns in a 1D Rock-Paper-Scissor model with mutation

  2014cites this paper
• Stochastic Waves on Regular Lattices

  2014cites this paper
• Stochastic processes with distributed delays: chemical Langevin equation and linear-noise approximation.

  2013cites this paper
• Pattern formation in individual-based systems with time-varying parameters.

  2013cites this paper
• A Graph Partitioning Approach to Predicting Patterns in Lateral Inhibition Systems

  2013cites this paper
• Linear noise approximation for stochastic oscillations of intracellular calcium.

  2013cites this paper
• Fluctuations and the role of collision duration in reaction-diffusion systems

  2013cites this paper